xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision b961780643a09dddcde1fa5de76862b9b9b6ff18)
1 /*$Id: mpiaij.c,v 1.333 2001/03/23 23:21:56 balay Exp bsmith $*/
2 
3 #include "src/mat/impls/aij/mpi/mpiaij.h"
4 #include "src/vec/vecimpl.h"
5 #include "src/inline/spops.h"
6 
7 EXTERN int MatSetUpMultiply_MPIAIJ(Mat);
8 EXTERN int DisAssemble_MPIAIJ(Mat);
9 EXTERN int MatSetValues_SeqAIJ(Mat,int,int*,int,int*,Scalar*,InsertMode);
10 EXTERN int MatGetRow_SeqAIJ(Mat,int,int*,int**,Scalar**);
11 EXTERN int MatRestoreRow_SeqAIJ(Mat,int,int*,int**,Scalar**);
12 EXTERN int MatPrintHelp_SeqAIJ(Mat);
13 
14 /*
15   Local utility routine that creates a mapping from the global column
16 number to the local number in the off-diagonal part of the local
17 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
18 a slightly higher hash table cost; without it it is not scalable (each processor
19 has an order N integer array but is fast to acess.
20 */
21 #undef __FUNCT__
22 #define __FUNCT__ "CreateColmap_MPIAIJ_Private"
23 int CreateColmap_MPIAIJ_Private(Mat mat)
24 {
25   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
26   int        n = aij->B->n,i,ierr;
27 
28   PetscFunctionBegin;
29 #if defined (PETSC_USE_CTABLE)
30   ierr = PetscTableCreate(n,&aij->colmap);CHKERRQ(ierr);
31   for (i=0; i<n; i++){
32     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1);CHKERRQ(ierr);
33   }
34 #else
35   ierr = PetscMalloc((mat->N+1)*sizeof(int),&aij->colmap);CHKERRQ(ierr);
36   PetscLogObjectMemory(mat,mat->N*sizeof(int));
37   ierr = PetscMemzero(aij->colmap,mat->N*sizeof(int));CHKERRQ(ierr);
38   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
39 #endif
40   PetscFunctionReturn(0);
41 }
42 
43 #define CHUNKSIZE   15
44 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv) \
45 { \
46  \
47     rp   = aj + ai[row] + shift; ap = aa + ai[row] + shift; \
48     rmax = aimax[row]; nrow = ailen[row];  \
49     col1 = col - shift; \
50      \
51     low = 0; high = nrow; \
52     while (high-low > 5) { \
53       t = (low+high)/2; \
54       if (rp[t] > col) high = t; \
55       else             low  = t; \
56     } \
57       for (_i=low; _i<high; _i++) { \
58         if (rp[_i] > col1) break; \
59         if (rp[_i] == col1) { \
60           if (addv == ADD_VALUES) ap[_i] += value;   \
61           else                  ap[_i] = value; \
62           goto a_noinsert; \
63         } \
64       }  \
65       if (nonew == 1) goto a_noinsert; \
66       else if (nonew == -1) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero into matrix"); \
67       if (nrow >= rmax) { \
68         /* there is no extra room in row, therefore enlarge */ \
69         int    new_nz = ai[am] + CHUNKSIZE,len,*new_i,*new_j; \
70         Scalar *new_a; \
71  \
72         if (nonew == -2) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix"); \
73  \
74         /* malloc new storage space */ \
75         len     = new_nz*(sizeof(int)+sizeof(Scalar))+(am+1)*sizeof(int); \
76         ierr    = PetscMalloc(len,&new_a);CHKERRQ(ierr); \
77         new_j   = (int*)(new_a + new_nz); \
78         new_i   = new_j + new_nz; \
79  \
80         /* copy over old data into new slots */ \
81         for (ii=0; ii<row+1; ii++) {new_i[ii] = ai[ii];} \
82         for (ii=row+1; ii<am+1; ii++) {new_i[ii] = ai[ii]+CHUNKSIZE;} \
83         ierr = PetscMemcpy(new_j,aj,(ai[row]+nrow+shift)*sizeof(int));CHKERRQ(ierr); \
84         len = (new_nz - CHUNKSIZE - ai[row] - nrow - shift); \
85         ierr = PetscMemcpy(new_j+ai[row]+shift+nrow+CHUNKSIZE,aj+ai[row]+shift+nrow, \
86                                                            len*sizeof(int));CHKERRQ(ierr); \
87         ierr = PetscMemcpy(new_a,aa,(ai[row]+nrow+shift)*sizeof(Scalar));CHKERRQ(ierr); \
88         ierr = PetscMemcpy(new_a+ai[row]+shift+nrow+CHUNKSIZE,aa+ai[row]+shift+nrow, \
89                                                            len*sizeof(Scalar));CHKERRQ(ierr);  \
90         /* free up old matrix storage */ \
91  \
92         ierr = PetscFree(a->a);CHKERRQ(ierr);  \
93         if (!a->singlemalloc) { \
94            ierr = PetscFree(a->i);CHKERRQ(ierr); \
95            ierr = PetscFree(a->j);CHKERRQ(ierr); \
96         } \
97         aa = a->a = new_a; ai = a->i = new_i; aj = a->j = new_j;  \
98         a->singlemalloc = PETSC_TRUE; \
99  \
100         rp   = aj + ai[row] + shift; ap = aa + ai[row] + shift; \
101         rmax = aimax[row] = aimax[row] + CHUNKSIZE; \
102         PetscLogObjectMemory(A,CHUNKSIZE*(sizeof(int) + sizeof(Scalar))); \
103         a->maxnz += CHUNKSIZE; \
104         a->reallocs++; \
105       } \
106       N = nrow++ - 1; a->nz++; \
107       /* shift up all the later entries in this row */ \
108       for (ii=N; ii>=_i; ii--) { \
109         rp[ii+1] = rp[ii]; \
110         ap[ii+1] = ap[ii]; \
111       } \
112       rp[_i] = col1;  \
113       ap[_i] = value;  \
114       a_noinsert: ; \
115       ailen[row] = nrow; \
116 }
117 
118 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv) \
119 { \
120  \
121     rp   = bj + bi[row] + shift; ap = ba + bi[row] + shift; \
122     rmax = bimax[row]; nrow = bilen[row];  \
123     col1 = col - shift; \
124      \
125     low = 0; high = nrow; \
126     while (high-low > 5) { \
127       t = (low+high)/2; \
128       if (rp[t] > col) high = t; \
129       else             low  = t; \
130     } \
131        for (_i=low; _i<high; _i++) { \
132         if (rp[_i] > col1) break; \
133         if (rp[_i] == col1) { \
134           if (addv == ADD_VALUES) ap[_i] += value;   \
135           else                  ap[_i] = value; \
136           goto b_noinsert; \
137         } \
138       }  \
139       if (nonew == 1) goto b_noinsert; \
140       else if (nonew == -1) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero into matrix"); \
141       if (nrow >= rmax) { \
142         /* there is no extra room in row, therefore enlarge */ \
143         int    new_nz = bi[bm] + CHUNKSIZE,len,*new_i,*new_j; \
144         Scalar *new_a; \
145  \
146         if (nonew == -2) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix"); \
147  \
148         /* malloc new storage space */ \
149         len     = new_nz*(sizeof(int)+sizeof(Scalar))+(bm+1)*sizeof(int); \
150         ierr    = PetscMalloc(len,&new_a);CHKERRQ(ierr); \
151         new_j   = (int*)(new_a + new_nz); \
152         new_i   = new_j + new_nz; \
153  \
154         /* copy over old data into new slots */ \
155         for (ii=0; ii<row+1; ii++) {new_i[ii] = bi[ii];} \
156         for (ii=row+1; ii<bm+1; ii++) {new_i[ii] = bi[ii]+CHUNKSIZE;} \
157         ierr = PetscMemcpy(new_j,bj,(bi[row]+nrow+shift)*sizeof(int));CHKERRQ(ierr); \
158         len = (new_nz - CHUNKSIZE - bi[row] - nrow - shift); \
159         ierr = PetscMemcpy(new_j+bi[row]+shift+nrow+CHUNKSIZE,bj+bi[row]+shift+nrow, \
160                                                            len*sizeof(int));CHKERRQ(ierr); \
161         ierr = PetscMemcpy(new_a,ba,(bi[row]+nrow+shift)*sizeof(Scalar));CHKERRQ(ierr); \
162         ierr = PetscMemcpy(new_a+bi[row]+shift+nrow+CHUNKSIZE,ba+bi[row]+shift+nrow, \
163                                                            len*sizeof(Scalar));CHKERRQ(ierr);  \
164         /* free up old matrix storage */ \
165  \
166         ierr = PetscFree(b->a);CHKERRQ(ierr);  \
167         if (!b->singlemalloc) { \
168           ierr = PetscFree(b->i);CHKERRQ(ierr); \
169           ierr = PetscFree(b->j);CHKERRQ(ierr); \
170         } \
171         ba = b->a = new_a; bi = b->i = new_i; bj = b->j = new_j;  \
172         b->singlemalloc = PETSC_TRUE; \
173  \
174         rp   = bj + bi[row] + shift; ap = ba + bi[row] + shift; \
175         rmax = bimax[row] = bimax[row] + CHUNKSIZE; \
176         PetscLogObjectMemory(B,CHUNKSIZE*(sizeof(int) + sizeof(Scalar))); \
177         b->maxnz += CHUNKSIZE; \
178         b->reallocs++; \
179       } \
180       N = nrow++ - 1; b->nz++; \
181       /* shift up all the later entries in this row */ \
182       for (ii=N; ii>=_i; ii--) { \
183         rp[ii+1] = rp[ii]; \
184         ap[ii+1] = ap[ii]; \
185       } \
186       rp[_i] = col1;  \
187       ap[_i] = value;  \
188       b_noinsert: ; \
189       bilen[row] = nrow; \
190 }
191 
192 #undef __FUNCT__
193 #define __FUNCT__ "MatSetValues_MPIAIJ"
194 int MatSetValues_MPIAIJ(Mat mat,int m,int *im,int n,int *in,Scalar *v,InsertMode addv)
195 {
196   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
197   Scalar     value;
198   int        ierr,i,j,rstart = aij->rstart,rend = aij->rend;
199   int        cstart = aij->cstart,cend = aij->cend,row,col;
200   PetscTruth roworiented = aij->roworiented;
201 
202   /* Some Variables required in the macro */
203   Mat        A = aij->A;
204   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
205   int        *aimax = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
206   Scalar     *aa = a->a;
207   PetscTruth ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES))?PETSC_TRUE:PETSC_FALSE);
208   Mat        B = aij->B;
209   Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
210   int        *bimax = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->m,am = aij->A->m;
211   Scalar     *ba = b->a;
212 
213   int        *rp,ii,nrow,_i,rmax,N,col1,low,high,t;
214   int        nonew = a->nonew,shift = a->indexshift;
215   Scalar     *ap;
216 
217   PetscFunctionBegin;
218   for (i=0; i<m; i++) {
219     if (im[i] < 0) continue;
220 #if defined(PETSC_USE_BOPT_g)
221     if (im[i] >= mat->M) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
222 #endif
223     if (im[i] >= rstart && im[i] < rend) {
224       row = im[i] - rstart;
225       for (j=0; j<n; j++) {
226         if (in[j] >= cstart && in[j] < cend){
227           col = in[j] - cstart;
228           if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
229           if (ignorezeroentries && value == 0.0) continue;
230           MatSetValues_SeqAIJ_A_Private(row,col,value,addv);
231           /* ierr = MatSetValues_SeqAIJ(aij->A,1,&row,1,&col,&value,addv);CHKERRQ(ierr); */
232         } else if (in[j] < 0) continue;
233 #if defined(PETSC_USE_BOPT_g)
234         else if (in[j] >= mat->N) {SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Column too large");}
235 #endif
236         else {
237           if (mat->was_assembled) {
238             if (!aij->colmap) {
239               ierr = CreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
240             }
241 #if defined (PETSC_USE_CTABLE)
242             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
243 	    col--;
244 #else
245             col = aij->colmap[in[j]] - 1;
246 #endif
247             if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
248               ierr = DisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
249               col =  in[j];
250               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
251               B = aij->B;
252               b = (Mat_SeqAIJ*)B->data;
253               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
254               ba = b->a;
255             }
256           } else col = in[j];
257           if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
258           if (ignorezeroentries && value == 0.0) continue;
259           MatSetValues_SeqAIJ_B_Private(row,col,value,addv);
260           /* ierr = MatSetValues_SeqAIJ(aij->B,1,&row,1,&col,&value,addv);CHKERRQ(ierr); */
261         }
262       }
263     } else {
264       if (!aij->donotstash) {
265         if (roworiented) {
266           if (ignorezeroentries && v[i*n] == 0.0) continue;
267           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n);CHKERRQ(ierr);
268         } else {
269           if (ignorezeroentries && v[i] == 0.0) continue;
270           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m);CHKERRQ(ierr);
271         }
272       }
273     }
274   }
275   PetscFunctionReturn(0);
276 }
277 
278 #undef __FUNCT__
279 #define __FUNCT__ "MatGetValues_MPIAIJ"
280 int MatGetValues_MPIAIJ(Mat mat,int m,int *idxm,int n,int *idxn,Scalar *v)
281 {
282   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
283   int        ierr,i,j,rstart = aij->rstart,rend = aij->rend;
284   int        cstart = aij->cstart,cend = aij->cend,row,col;
285 
286   PetscFunctionBegin;
287   for (i=0; i<m; i++) {
288     if (idxm[i] < 0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative row");
289     if (idxm[i] >= mat->M) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
290     if (idxm[i] >= rstart && idxm[i] < rend) {
291       row = idxm[i] - rstart;
292       for (j=0; j<n; j++) {
293         if (idxn[j] < 0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative column");
294         if (idxn[j] >= mat->N) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
295         if (idxn[j] >= cstart && idxn[j] < cend){
296           col = idxn[j] - cstart;
297           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
298         } else {
299           if (!aij->colmap) {
300             ierr = CreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
301           }
302 #if defined (PETSC_USE_CTABLE)
303           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
304           col --;
305 #else
306           col = aij->colmap[idxn[j]] - 1;
307 #endif
308           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
309           else {
310             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
311           }
312         }
313       }
314     } else {
315       SETERRQ(PETSC_ERR_SUP,"Only local values currently supported");
316     }
317   }
318   PetscFunctionReturn(0);
319 }
320 
321 #undef __FUNCT__
322 #define __FUNCT__ "MatAssemblyBegin_MPIAIJ"
323 int MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
324 {
325   Mat_MPIAIJ  *aij = (Mat_MPIAIJ*)mat->data;
326   int         ierr,nstash,reallocs;
327   InsertMode  addv;
328 
329   PetscFunctionBegin;
330   if (aij->donotstash) {
331     PetscFunctionReturn(0);
332   }
333 
334   /* make sure all processors are either in INSERTMODE or ADDMODE */
335   ierr = MPI_Allreduce(&mat->insertmode,&addv,1,MPI_INT,MPI_BOR,mat->comm);CHKERRQ(ierr);
336   if (addv == (ADD_VALUES|INSERT_VALUES)) {
337     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
338   }
339   mat->insertmode = addv; /* in case this processor had no cache */
340 
341   ierr = MatStashScatterBegin_Private(&mat->stash,aij->rowners);CHKERRQ(ierr);
342   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
343   PetscLogInfo(aij->A,"MatAssemblyBegin_MPIAIJ:Stash has %d entries, uses %d mallocs.\n",nstash,reallocs);
344   PetscFunctionReturn(0);
345 }
346 
347 
348 #undef __FUNCT__
349 #define __FUNCT__ "MatAssemblyEnd_MPIAIJ"
350 int MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
351 {
352   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
353   int         i,j,rstart,ncols,n,ierr,flg;
354   int         *row,*col,other_disassembled;
355   Scalar      *val;
356   InsertMode  addv = mat->insertmode;
357 
358   PetscFunctionBegin;
359   if (!aij->donotstash) {
360     while (1) {
361       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
362       if (!flg) break;
363 
364       for (i=0; i<n;) {
365         /* Now identify the consecutive vals belonging to the same row */
366         for (j=i,rstart=row[j]; j<n; j++) { if (row[j] != rstart) break; }
367         if (j < n) ncols = j-i;
368         else       ncols = n-i;
369         /* Now assemble all these values with a single function call */
370         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,addv);CHKERRQ(ierr);
371         i = j;
372       }
373     }
374     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
375   }
376 
377   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
378   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
379 
380   /* determine if any processor has disassembled, if so we must
381      also disassemble ourselfs, in order that we may reassemble. */
382   /*
383      if nonzero structure of submatrix B cannot change then we know that
384      no processor disassembled thus we can skip this stuff
385   */
386   if (!((Mat_SeqAIJ*)aij->B->data)->nonew)  {
387     ierr = MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPI_INT,MPI_PROD,mat->comm);CHKERRQ(ierr);
388     if (mat->was_assembled && !other_disassembled) {
389       ierr = DisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
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   PetscFunctionReturn(0);
404 }
405 
406 #undef __FUNCT__
407 #define __FUNCT__ "MatZeroEntries_MPIAIJ"
408 int MatZeroEntries_MPIAIJ(Mat A)
409 {
410   Mat_MPIAIJ *l = (Mat_MPIAIJ*)A->data;
411   int        ierr;
412 
413   PetscFunctionBegin;
414   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
415   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
416   PetscFunctionReturn(0);
417 }
418 
419 #undef __FUNCT__
420 #define __FUNCT__ "MatZeroRows_MPIAIJ"
421 int MatZeroRows_MPIAIJ(Mat A,IS is,Scalar *diag)
422 {
423   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
424   int            i,ierr,N,*rows,*owners = l->rowners,size = l->size;
425   int            *procs,*nprocs,j,idx,nsends,*work,row;
426   int            nmax,*svalues,*starts,*owner,nrecvs,rank = l->rank;
427   int            *rvalues,tag = A->tag,count,base,slen,n,*source;
428   int            *lens,imdex,*lrows,*values,rstart=l->rstart;
429   MPI_Comm       comm = A->comm;
430   MPI_Request    *send_waits,*recv_waits;
431   MPI_Status     recv_status,*send_status;
432   IS             istmp;
433   PetscTruth     found;
434 
435   PetscFunctionBegin;
436   ierr = ISGetLocalSize(is,&N);CHKERRQ(ierr);
437   ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);
438 
439   /*  first count number of contributors to each processor */
440   ierr = PetscMalloc(2*size*sizeof(int),&nprocs);CHKERRQ(ierr);
441   ierr   = PetscMemzero(nprocs,2*size*sizeof(int));CHKERRQ(ierr);
442   procs  = nprocs + size;
443   ierr = PetscMalloc((N+1)*sizeof(int),&owner);CHKERRQ(ierr); /* see note*/
444   for (i=0; i<N; i++) {
445     idx = rows[i];
446     found = PETSC_FALSE;
447     for (j=0; j<size; j++) {
448       if (idx >= owners[j] && idx < owners[j+1]) {
449         nprocs[j]++; procs[j] = 1; owner[i] = j; found = PETSC_TRUE; break;
450       }
451     }
452     if (!found) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Index out of range");
453   }
454   nsends = 0;  for (i=0; i<size; i++) { nsends += procs[i];}
455 
456   /* inform other processors of number of messages and max length*/
457   ierr = PetscMalloc(2*size*sizeof(int),&work);CHKERRQ(ierr);
458   ierr   = MPI_Allreduce(nprocs,work,2*size,MPI_INT,PetscMaxSum_Op,comm);CHKERRQ(ierr);
459   nrecvs = work[size+rank];
460   nmax   = work[rank];
461   ierr   = PetscFree(work);CHKERRQ(ierr);
462 
463   /* post receives:   */
464   ierr = PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(int),&rvalues);CHKERRQ(ierr);
465   ierr = PetscMalloc((nrecvs+1)*sizeof(MPI_Request),&recv_waits);CHKERRQ(ierr);
466   for (i=0; i<nrecvs; i++) {
467     ierr = MPI_Irecv(rvalues+nmax*i,nmax,MPI_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);CHKERRQ(ierr);
468   }
469 
470   /* do sends:
471       1) starts[i] gives the starting index in svalues for stuff going to
472          the ith processor
473   */
474   ierr = PetscMalloc((N+1)*sizeof(int),&svalues);CHKERRQ(ierr);
475   ierr = PetscMalloc((nsends+1)*sizeof(MPI_Request),&send_waits);CHKERRQ(ierr);
476   ierr = PetscMalloc((size+1)*sizeof(int),&starts);CHKERRQ(ierr);
477   starts[0] = 0;
478   for (i=1; i<size; i++) { starts[i] = starts[i-1] + nprocs[i-1];}
479   for (i=0; i<N; i++) {
480     svalues[starts[owner[i]]++] = rows[i];
481   }
482   ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);
483 
484   starts[0] = 0;
485   for (i=1; i<size+1; i++) { starts[i] = starts[i-1] + nprocs[i-1];}
486   count = 0;
487   for (i=0; i<size; i++) {
488     if (procs[i]) {
489       ierr = MPI_Isend(svalues+starts[i],nprocs[i],MPI_INT,i,tag,comm,send_waits+count++);CHKERRQ(ierr);
490     }
491   }
492   ierr = PetscFree(starts);CHKERRQ(ierr);
493 
494   base = owners[rank];
495 
496   /*  wait on receives */
497   ierr   = PetscMalloc(2*(nrecvs+1)*sizeof(int),&lens);CHKERRQ(ierr);
498   source = lens + nrecvs;
499   count  = nrecvs; slen = 0;
500   while (count) {
501     ierr = MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);CHKERRQ(ierr);
502     /* unpack receives into our local space */
503     ierr = MPI_Get_count(&recv_status,MPI_INT,&n);CHKERRQ(ierr);
504     source[imdex]  = recv_status.MPI_SOURCE;
505     lens[imdex]    = n;
506     slen          += n;
507     count--;
508   }
509   ierr = PetscFree(recv_waits);CHKERRQ(ierr);
510 
511   /* move the data into the send scatter */
512   ierr = PetscMalloc((slen+1)*sizeof(int),&lrows);CHKERRQ(ierr);
513   count = 0;
514   for (i=0; i<nrecvs; i++) {
515     values = rvalues + i*nmax;
516     for (j=0; j<lens[i]; j++) {
517       lrows[count++] = values[j] - base;
518     }
519   }
520   ierr = PetscFree(rvalues);CHKERRQ(ierr);
521   ierr = PetscFree(lens);CHKERRQ(ierr);
522   ierr = PetscFree(owner);CHKERRQ(ierr);
523   ierr = PetscFree(nprocs);CHKERRQ(ierr);
524 
525   /* actually zap the local rows */
526   ierr = ISCreateGeneral(PETSC_COMM_SELF,slen,lrows,&istmp);CHKERRQ(ierr);
527   PetscLogObjectParent(A,istmp);
528 
529   /*
530         Zero the required rows. If the "diagonal block" of the matrix
531      is square and the user wishes to set the diagonal we use seperate
532      code so that MatSetValues() is not called for each diagonal allocating
533      new memory, thus calling lots of mallocs and slowing things down.
534 
535        Contributed by: Mathew Knepley
536   */
537   /* must zero l->B before l->A because the (diag) case below may put values into l->B*/
538   ierr = MatZeroRows(l->B,istmp,0);CHKERRQ(ierr);
539   if (diag && (l->A->M == l->A->N)) {
540     ierr      = MatZeroRows(l->A,istmp,diag);CHKERRQ(ierr);
541   } else if (diag) {
542     ierr = MatZeroRows(l->A,istmp,0);CHKERRQ(ierr);
543     if (((Mat_SeqAIJ*)l->A->data)->nonew) {
544       SETERRQ(PETSC_ERR_SUP,"MatZeroRows() on rectangular matrices cannot be used with the Mat options\n\
545 MAT_NO_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
546     }
547     for (i = 0; i < slen; i++) {
548       row  = lrows[i] + rstart;
549       ierr = MatSetValues(A,1,&row,1,&row,diag,INSERT_VALUES);CHKERRQ(ierr);
550     }
551     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
552     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
553   } else {
554     ierr = MatZeroRows(l->A,istmp,0);CHKERRQ(ierr);
555   }
556   ierr = ISDestroy(istmp);CHKERRQ(ierr);
557   ierr = PetscFree(lrows);CHKERRQ(ierr);
558 
559   /* wait on sends */
560   if (nsends) {
561     ierr = PetscMalloc(nsends*sizeof(MPI_Status),&send_status);CHKERRQ(ierr);
562     ierr = MPI_Waitall(nsends,send_waits,send_status);CHKERRQ(ierr);
563     ierr = PetscFree(send_status);CHKERRQ(ierr);
564   }
565   ierr = PetscFree(send_waits);CHKERRQ(ierr);
566   ierr = PetscFree(svalues);CHKERRQ(ierr);
567 
568   PetscFunctionReturn(0);
569 }
570 
571 #undef __FUNCT__
572 #define __FUNCT__ "MatMult_MPIAIJ"
573 int MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
574 {
575   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
576   int        ierr,nt;
577 
578   PetscFunctionBegin;
579   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
580   if (nt != A->n) {
581     SETERRQ2(PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%d) and xx (%d)",A->n,nt);
582   }
583   ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
584   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
585   ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
586   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
587   PetscFunctionReturn(0);
588 }
589 
590 #undef __FUNCT__
591 #define __FUNCT__ "MatMultAdd_MPIAIJ"
592 int MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
593 {
594   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
595   int        ierr;
596 
597   PetscFunctionBegin;
598   ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
599   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
600   ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD,a->Mvctx);CHKERRQ(ierr);
601   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
602   PetscFunctionReturn(0);
603 }
604 
605 #undef __FUNCT__
606 #define __FUNCT__ "MatMultTranspose_MPIAIJ"
607 int MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
608 {
609   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
610   int        ierr;
611 
612   PetscFunctionBegin;
613   /* do nondiagonal part */
614   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
615   /* send it on its way */
616   ierr = VecScatterBegin(a->lvec,yy,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
617   /* do local part */
618   ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
619   /* receive remote parts: note this assumes the values are not actually */
620   /* inserted in yy until the next line, which is true for my implementation*/
621   /* but is not perhaps always true. */
622   ierr = VecScatterEnd(a->lvec,yy,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
623   PetscFunctionReturn(0);
624 }
625 
626 #undef __FUNCT__
627 #define __FUNCT__ "MatMultTransposeAdd_MPIAIJ"
628 int MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
629 {
630   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
631   int        ierr;
632 
633   PetscFunctionBegin;
634   /* do nondiagonal part */
635   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
636   /* send it on its way */
637   ierr = VecScatterBegin(a->lvec,zz,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
638   /* do local part */
639   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
640   /* receive remote parts: note this assumes the values are not actually */
641   /* inserted in yy until the next line, which is true for my implementation*/
642   /* but is not perhaps always true. */
643   ierr = VecScatterEnd(a->lvec,zz,ADD_VALUES,SCATTER_REVERSE,a->Mvctx);CHKERRQ(ierr);
644   PetscFunctionReturn(0);
645 }
646 
647 /*
648   This only works correctly for square matrices where the subblock A->A is the
649    diagonal block
650 */
651 #undef __FUNCT__
652 #define __FUNCT__ "MatGetDiagonal_MPIAIJ"
653 int MatGetDiagonal_MPIAIJ(Mat A,Vec v)
654 {
655   int        ierr;
656   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
657 
658   PetscFunctionBegin;
659   if (A->M != A->N) SETERRQ(PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
660   if (a->rstart != a->cstart || a->rend != a->cend) {
661     SETERRQ(PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
662   }
663   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
664   PetscFunctionReturn(0);
665 }
666 
667 #undef __FUNCT__
668 #define __FUNCT__ "MatScale_MPIAIJ"
669 int MatScale_MPIAIJ(Scalar *aa,Mat A)
670 {
671   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
672   int        ierr;
673 
674   PetscFunctionBegin;
675   ierr = MatScale(aa,a->A);CHKERRQ(ierr);
676   ierr = MatScale(aa,a->B);CHKERRQ(ierr);
677   PetscFunctionReturn(0);
678 }
679 
680 #undef __FUNCT__
681 #define __FUNCT__ "MatDestroy_MPIAIJ"
682 int MatDestroy_MPIAIJ(Mat mat)
683 {
684   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
685   int        ierr;
686 
687   PetscFunctionBegin;
688 #if defined(PETSC_USE_LOG)
689   PetscLogObjectState((PetscObject)mat,"Rows=%d, Cols=%d",mat->M,mat->N);
690 #endif
691   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
692   ierr = PetscFree(aij->rowners);CHKERRQ(ierr);
693   ierr = MatDestroy(aij->A);CHKERRQ(ierr);
694   ierr = MatDestroy(aij->B);CHKERRQ(ierr);
695 #if defined (PETSC_USE_CTABLE)
696   if (aij->colmap) {ierr = PetscTableDelete(aij->colmap);CHKERRQ(ierr);}
697 #else
698   if (aij->colmap) {ierr = PetscFree(aij->colmap);CHKERRQ(ierr);}
699 #endif
700   if (aij->garray) {ierr = PetscFree(aij->garray);CHKERRQ(ierr);}
701   if (aij->lvec)   {ierr = VecDestroy(aij->lvec);CHKERRQ(ierr);}
702   if (aij->Mvctx)  {ierr = VecScatterDestroy(aij->Mvctx);CHKERRQ(ierr);}
703   if (aij->rowvalues) {ierr = PetscFree(aij->rowvalues);CHKERRQ(ierr);}
704   ierr = PetscFree(aij);CHKERRQ(ierr);
705   PetscFunctionReturn(0);
706 }
707 
708 #undef __FUNCT__
709 #define __FUNCT__ "MatView_MPIAIJ_ASCIIorDraworSocket"
710 int MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
711 {
712   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
713   Mat_SeqAIJ*       C = (Mat_SeqAIJ*)aij->A->data;
714   int               ierr,shift = C->indexshift,rank = aij->rank,size = aij->size;
715   PetscTruth        isdraw,isascii,flg;
716   PetscViewer       sviewer;
717   PetscViewerFormat format;
718 
719   PetscFunctionBegin;
720   ierr  = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
721   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&isascii);CHKERRQ(ierr);
722   if (isascii) {
723     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
724     if (format == PETSC_VIEWER_ASCII_INFO_LONG) {
725       MatInfo info;
726       ierr = MPI_Comm_rank(mat->comm,&rank);CHKERRQ(ierr);
727       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
728       ierr = PetscOptionsHasName(PETSC_NULL,"-mat_aij_no_inode",&flg);CHKERRQ(ierr);
729       if (flg) {
730         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %d nz %d nz alloced %d mem %d, not using I-node routines\n",
731 					      rank,mat->m,(int)info.nz_used,(int)info.nz_allocated,(int)info.memory);CHKERRQ(ierr);
732       } else {
733         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %d nz %d nz alloced %d mem %d, using I-node routines\n",
734 		    rank,mat->m,(int)info.nz_used,(int)info.nz_allocated,(int)info.memory);CHKERRQ(ierr);
735       }
736       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
737       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %d \n",rank,(int)info.nz_used);CHKERRQ(ierr);
738       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
739       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %d \n",rank,(int)info.nz_used);CHKERRQ(ierr);
740       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
741       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
742       PetscFunctionReturn(0);
743     } else if (format == PETSC_VIEWER_ASCII_INFO) {
744       PetscFunctionReturn(0);
745     }
746   } else if (isdraw) {
747     PetscDraw       draw;
748     PetscTruth isnull;
749     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
750     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
751   }
752 
753   if (size == 1) {
754     ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
755   } else {
756     /* assemble the entire matrix onto first processor. */
757     Mat         A;
758     Mat_SeqAIJ *Aloc;
759     int         M = mat->M,N = mat->N,m,*ai,*aj,row,*cols,i,*ct;
760     Scalar      *a;
761 
762     if (!rank) {
763       ierr = MatCreateMPIAIJ(mat->comm,M,N,M,N,0,PETSC_NULL,0,PETSC_NULL,&A);CHKERRQ(ierr);
764     } else {
765       ierr = MatCreateMPIAIJ(mat->comm,0,0,M,N,0,PETSC_NULL,0,PETSC_NULL,&A);CHKERRQ(ierr);
766     }
767     PetscLogObjectParent(mat,A);
768 
769     /* copy over the A part */
770     Aloc = (Mat_SeqAIJ*)aij->A->data;
771     m = aij->A->m; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
772     row = aij->rstart;
773     for (i=0; i<ai[m]+shift; i++) {aj[i] += aij->cstart + shift;}
774     for (i=0; i<m; i++) {
775       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
776       row++; a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
777     }
778     aj = Aloc->j;
779     for (i=0; i<ai[m]+shift; i++) {aj[i] -= aij->cstart + shift;}
780 
781     /* copy over the B part */
782     Aloc = (Mat_SeqAIJ*)aij->B->data;
783     m    = aij->B->m;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
784     row  = aij->rstart;
785     ierr = PetscMalloc((ai[m]+1)*sizeof(int),&cols);CHKERRQ(ierr);
786     ct   = cols;
787     for (i=0; i<ai[m]+shift; i++) {cols[i] = aij->garray[aj[i]+shift];}
788     for (i=0; i<m; i++) {
789       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
790       row++; a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
791     }
792     ierr = PetscFree(ct);CHKERRQ(ierr);
793     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
794     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
795     /*
796        Everyone has to call to draw the matrix since the graphics waits are
797        synchronized across all processors that share the PetscDraw object
798     */
799     ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
800     if (!rank) {
801       ierr = MatView(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
802     }
803     ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
804     ierr = MatDestroy(A);CHKERRQ(ierr);
805   }
806   PetscFunctionReturn(0);
807 }
808 
809 #undef __FUNCT__
810 #define __FUNCT__ "MatView_MPIAIJ"
811 int MatView_MPIAIJ(Mat mat,PetscViewer viewer)
812 {
813   int        ierr;
814   PetscTruth isascii,isdraw,issocket,isbinary;
815 
816   PetscFunctionBegin;
817   ierr  = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&isascii);CHKERRQ(ierr);
818   ierr  = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
819   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
820   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_SOCKET,&issocket);CHKERRQ(ierr);
821   if (isascii || isdraw || isbinary || issocket) {
822     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
823   } else {
824     SETERRQ1(1,"Viewer type %s not supported by MPIAIJ matrices",((PetscObject)viewer)->type_name);
825   }
826   PetscFunctionReturn(0);
827 }
828 
829 /*
830     This has to provide several versions.
831 
832      2) a) use only local smoothing updating outer values only once.
833         b) local smoothing updating outer values each inner iteration
834      3) color updating out values betwen colors.
835 */
836 #undef __FUNCT__
837 #define __FUNCT__ "MatRelax_MPIAIJ"
838 int MatRelax_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,int its,Vec xx)
839 {
840   Mat_MPIAIJ *mat = (Mat_MPIAIJ*)matin->data;
841   Mat        AA = mat->A,BB = mat->B;
842   Mat_SeqAIJ *A = (Mat_SeqAIJ*)AA->data,*B = (Mat_SeqAIJ *)BB->data;
843   Scalar     *b,*x,*xs,*ls,d,*v,sum;
844   int        ierr,*idx,*diag;
845   int        n = matin->n,m = matin->m,i,shift = A->indexshift;
846 
847   PetscFunctionBegin;
848   if (!A->diag) {ierr = MatMarkDiagonal_SeqAIJ(AA);CHKERRQ(ierr);}
849   diag = A->diag;
850   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP){
851     if (flag & SOR_ZERO_INITIAL_GUESS) {
852       ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,its,xx);CHKERRQ(ierr);
853       PetscFunctionReturn(0);
854     }
855     ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
856     ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
857     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
858     if (xx != bb) {
859       ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
860     } else {
861       b = x;
862     }
863     ierr = VecGetArray(mat->lvec,&ls);CHKERRQ(ierr);
864     xs = x + shift; /* shift by one for index start of 1 */
865     ls = ls + shift;
866     while (its--) {
867       /* go down through the rows */
868       for (i=0; i<m; i++) {
869         n    = A->i[i+1] - A->i[i];
870 	PetscLogFlops(4*n+3);
871         idx  = A->j + A->i[i] + shift;
872         v    = A->a + A->i[i] + shift;
873         sum  = b[i];
874         SPARSEDENSEMDOT(sum,xs,v,idx,n);
875         d    = fshift + A->a[diag[i]+shift];
876         n    = B->i[i+1] - B->i[i];
877         idx  = B->j + B->i[i] + shift;
878         v    = B->a + B->i[i] + shift;
879         SPARSEDENSEMDOT(sum,ls,v,idx,n);
880         x[i] = (1. - omega)*x[i] + omega*(sum + A->a[diag[i]+shift]*x[i])/d;
881       }
882       /* come up through the rows */
883       for (i=m-1; i>-1; i--) {
884         n    = A->i[i+1] - A->i[i];
885 	PetscLogFlops(4*n+3);
886         idx  = A->j + A->i[i] + shift;
887         v    = A->a + A->i[i] + shift;
888         sum  = b[i];
889         SPARSEDENSEMDOT(sum,xs,v,idx,n);
890         d    = fshift + A->a[diag[i]+shift];
891         n    = B->i[i+1] - B->i[i];
892         idx  = B->j + B->i[i] + shift;
893         v    = B->a + B->i[i] + shift;
894         SPARSEDENSEMDOT(sum,ls,v,idx,n);
895         x[i] = (1. - omega)*x[i] + omega*(sum + A->a[diag[i]+shift]*x[i])/d;
896       }
897     }
898     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
899     if (bb != xx) {ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); }
900     ierr = VecRestoreArray(mat->lvec,&ls);CHKERRQ(ierr);
901   } else if (flag & SOR_LOCAL_FORWARD_SWEEP){
902     if (flag & SOR_ZERO_INITIAL_GUESS) {
903       ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,its,xx);CHKERRQ(ierr);
904       PetscFunctionReturn(0);
905     }
906     ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
907     ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
908     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
909     if (xx != bb) {
910       ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
911     } else {
912       b = x;
913     }
914     ierr = VecGetArray(mat->lvec,&ls);CHKERRQ(ierr);
915     xs = x + shift; /* shift by one for index start of 1 */
916     ls = ls + shift;
917     while (its--) {
918       for (i=0; i<m; i++) {
919         n    = A->i[i+1] - A->i[i];
920 	PetscLogFlops(4*n+3);
921         idx  = A->j + A->i[i] + shift;
922         v    = A->a + A->i[i] + shift;
923         sum  = b[i];
924         SPARSEDENSEMDOT(sum,xs,v,idx,n);
925         d    = fshift + A->a[diag[i]+shift];
926         n    = B->i[i+1] - B->i[i];
927         idx  = B->j + B->i[i] + shift;
928         v    = B->a + B->i[i] + shift;
929         SPARSEDENSEMDOT(sum,ls,v,idx,n);
930         x[i] = (1. - omega)*x[i] + omega*(sum + A->a[diag[i]+shift]*x[i])/d;
931       }
932     }
933     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
934     if (bb != xx) {ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); }
935     ierr = VecRestoreArray(mat->lvec,&ls);CHKERRQ(ierr);
936   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP){
937     if (flag & SOR_ZERO_INITIAL_GUESS) {
938       ierr = (*mat->A->ops->relax)(mat->A,bb,omega,flag,fshift,its,xx);CHKERRQ(ierr);
939       PetscFunctionReturn(0);
940     }
941     ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
942     ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD,mat->Mvctx);CHKERRQ(ierr);
943     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
944     if (xx != bb) {
945       ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
946     } else {
947       b = x;
948     }
949     ierr = VecGetArray(mat->lvec,&ls);CHKERRQ(ierr);
950     xs = x + shift; /* shift by one for index start of 1 */
951     ls = ls + shift;
952     while (its--) {
953       for (i=m-1; i>-1; i--) {
954         n    = A->i[i+1] - A->i[i];
955 	PetscLogFlops(4*n+3);
956         idx  = A->j + A->i[i] + shift;
957         v    = A->a + A->i[i] + shift;
958         sum  = b[i];
959         SPARSEDENSEMDOT(sum,xs,v,idx,n);
960         d    = fshift + A->a[diag[i]+shift];
961         n    = B->i[i+1] - B->i[i];
962         idx  = B->j + B->i[i] + shift;
963         v    = B->a + B->i[i] + shift;
964         SPARSEDENSEMDOT(sum,ls,v,idx,n);
965         x[i] = (1. - omega)*x[i] + omega*(sum + A->a[diag[i]+shift]*x[i])/d;
966       }
967     }
968     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
969     if (bb != xx) {ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); }
970     ierr = VecRestoreArray(mat->lvec,&ls);CHKERRQ(ierr);
971   } else {
972     SETERRQ(PETSC_ERR_SUP,"Parallel SOR not supported");
973   }
974   PetscFunctionReturn(0);
975 }
976 
977 #undef __FUNCT__
978 #define __FUNCT__ "MatGetInfo_MPIAIJ"
979 int MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
980 {
981   Mat_MPIAIJ *mat = (Mat_MPIAIJ*)matin->data;
982   Mat        A = mat->A,B = mat->B;
983   int        ierr;
984   PetscReal  isend[5],irecv[5];
985 
986   PetscFunctionBegin;
987   info->block_size     = 1.0;
988   ierr = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
989   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
990   isend[3] = info->memory;  isend[4] = info->mallocs;
991   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
992   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
993   isend[3] += info->memory;  isend[4] += info->mallocs;
994   if (flag == MAT_LOCAL) {
995     info->nz_used      = isend[0];
996     info->nz_allocated = isend[1];
997     info->nz_unneeded  = isend[2];
998     info->memory       = isend[3];
999     info->mallocs      = isend[4];
1000   } else if (flag == MAT_GLOBAL_MAX) {
1001     ierr = MPI_Allreduce(isend,irecv,5,MPI_DOUBLE,MPI_MAX,matin->comm);CHKERRQ(ierr);
1002     info->nz_used      = irecv[0];
1003     info->nz_allocated = irecv[1];
1004     info->nz_unneeded  = irecv[2];
1005     info->memory       = irecv[3];
1006     info->mallocs      = irecv[4];
1007   } else if (flag == MAT_GLOBAL_SUM) {
1008     ierr = MPI_Allreduce(isend,irecv,5,MPI_DOUBLE,MPI_SUM,matin->comm);CHKERRQ(ierr);
1009     info->nz_used      = irecv[0];
1010     info->nz_allocated = irecv[1];
1011     info->nz_unneeded  = irecv[2];
1012     info->memory       = irecv[3];
1013     info->mallocs      = irecv[4];
1014   }
1015   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1016   info->fill_ratio_needed = 0;
1017   info->factor_mallocs    = 0;
1018   info->rows_global       = (double)matin->M;
1019   info->columns_global    = (double)matin->N;
1020   info->rows_local        = (double)matin->m;
1021   info->columns_local     = (double)matin->N;
1022 
1023   PetscFunctionReturn(0);
1024 }
1025 
1026 #undef __FUNCT__
1027 #define __FUNCT__ "MatSetOption_MPIAIJ"
1028 int MatSetOption_MPIAIJ(Mat A,MatOption op)
1029 {
1030   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
1031   int        ierr;
1032 
1033   PetscFunctionBegin;
1034   if (op == MAT_NO_NEW_NONZERO_LOCATIONS ||
1035       op == MAT_YES_NEW_NONZERO_LOCATIONS ||
1036       op == MAT_COLUMNS_UNSORTED ||
1037       op == MAT_COLUMNS_SORTED ||
1038       op == MAT_NEW_NONZERO_ALLOCATION_ERR ||
1039       op == MAT_KEEP_ZEROED_ROWS ||
1040       op == MAT_NEW_NONZERO_LOCATION_ERR ||
1041       op == MAT_USE_INODES ||
1042       op == MAT_DO_NOT_USE_INODES ||
1043       op == MAT_IGNORE_ZERO_ENTRIES) {
1044         ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
1045         ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
1046   } else if (op == MAT_ROW_ORIENTED) {
1047     a->roworiented = PETSC_TRUE;
1048     ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
1049     ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
1050   } else if (op == MAT_ROWS_SORTED ||
1051              op == MAT_ROWS_UNSORTED ||
1052              op == MAT_YES_NEW_DIAGONALS) {
1053     PetscLogInfo(A,"MatSetOption_MPIAIJ:Option ignored\n");
1054   } else if (op == MAT_COLUMN_ORIENTED) {
1055     a->roworiented = PETSC_FALSE;
1056     ierr = MatSetOption(a->A,op);CHKERRQ(ierr);
1057     ierr = MatSetOption(a->B,op);CHKERRQ(ierr);
1058   } else if (op == MAT_IGNORE_OFF_PROC_ENTRIES) {
1059     a->donotstash = PETSC_TRUE;
1060   } else if (op == MAT_NO_NEW_DIAGONALS){
1061     SETERRQ(PETSC_ERR_SUP,"MAT_NO_NEW_DIAGONALS");
1062   } else {
1063     SETERRQ(PETSC_ERR_SUP,"unknown option");
1064   }
1065   PetscFunctionReturn(0);
1066 }
1067 
1068 #undef __FUNCT__
1069 #define __FUNCT__ "MatGetOwnershipRange_MPIAIJ"
1070 int MatGetOwnershipRange_MPIAIJ(Mat matin,int *m,int *n)
1071 {
1072   Mat_MPIAIJ *mat = (Mat_MPIAIJ*)matin->data;
1073 
1074   PetscFunctionBegin;
1075   if (m) *m = mat->rstart;
1076   if (n) *n = mat->rend;
1077   PetscFunctionReturn(0);
1078 }
1079 
1080 #undef __FUNCT__
1081 #define __FUNCT__ "MatGetRow_MPIAIJ"
1082 int MatGetRow_MPIAIJ(Mat matin,int row,int *nz,int **idx,Scalar **v)
1083 {
1084   Mat_MPIAIJ *mat = (Mat_MPIAIJ*)matin->data;
1085   Scalar     *vworkA,*vworkB,**pvA,**pvB,*v_p;
1086   int        i,ierr,*cworkA,*cworkB,**pcA,**pcB,cstart = mat->cstart;
1087   int        nztot,nzA,nzB,lrow,rstart = mat->rstart,rend = mat->rend;
1088   int        *cmap,*idx_p;
1089 
1090   PetscFunctionBegin;
1091   if (mat->getrowactive == PETSC_TRUE) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Already active");
1092   mat->getrowactive = PETSC_TRUE;
1093 
1094   if (!mat->rowvalues && (idx || v)) {
1095     /*
1096         allocate enough space to hold information from the longest row.
1097     */
1098     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1099     int     max = 1,tmp;
1100     for (i=0; i<matin->m; i++) {
1101       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1102       if (max < tmp) { max = tmp; }
1103     }
1104     ierr = PetscMalloc(max*(sizeof(int)+sizeof(Scalar)),&mat->rowvalues);CHKERRQ(ierr);
1105     mat->rowindices = (int*)(mat->rowvalues + max);
1106   }
1107 
1108   if (row < rstart || row >= rend) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Only local rows")
1109   lrow = row - rstart;
1110 
1111   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1112   if (!v)   {pvA = 0; pvB = 0;}
1113   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1114   ierr = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1115   ierr = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1116   nztot = nzA + nzB;
1117 
1118   cmap  = mat->garray;
1119   if (v  || idx) {
1120     if (nztot) {
1121       /* Sort by increasing column numbers, assuming A and B already sorted */
1122       int imark = -1;
1123       if (v) {
1124         *v = v_p = mat->rowvalues;
1125         for (i=0; i<nzB; i++) {
1126           if (cmap[cworkB[i]] < cstart)   v_p[i] = vworkB[i];
1127           else break;
1128         }
1129         imark = i;
1130         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1131         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1132       }
1133       if (idx) {
1134         *idx = idx_p = mat->rowindices;
1135         if (imark > -1) {
1136           for (i=0; i<imark; i++) {
1137             idx_p[i] = cmap[cworkB[i]];
1138           }
1139         } else {
1140           for (i=0; i<nzB; i++) {
1141             if (cmap[cworkB[i]] < cstart)   idx_p[i] = cmap[cworkB[i]];
1142             else break;
1143           }
1144           imark = i;
1145         }
1146         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1147         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1148       }
1149     } else {
1150       if (idx) *idx = 0;
1151       if (v)   *v   = 0;
1152     }
1153   }
1154   *nz = nztot;
1155   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1156   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1157   PetscFunctionReturn(0);
1158 }
1159 
1160 #undef __FUNCT__
1161 #define __FUNCT__ "MatRestoreRow_MPIAIJ"
1162 int MatRestoreRow_MPIAIJ(Mat mat,int row,int *nz,int **idx,Scalar **v)
1163 {
1164   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1165 
1166   PetscFunctionBegin;
1167   if (aij->getrowactive == PETSC_FALSE) {
1168     SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"MatGetRow not called");
1169   }
1170   aij->getrowactive = PETSC_FALSE;
1171   PetscFunctionReturn(0);
1172 }
1173 
1174 #undef __FUNCT__
1175 #define __FUNCT__ "MatNorm_MPIAIJ"
1176 int MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1177 {
1178   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1179   Mat_SeqAIJ *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1180   int        ierr,i,j,cstart = aij->cstart,shift = amat->indexshift;
1181   PetscReal  sum = 0.0;
1182   Scalar     *v;
1183 
1184   PetscFunctionBegin;
1185   if (aij->size == 1) {
1186     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1187   } else {
1188     if (type == NORM_FROBENIUS) {
1189       v = amat->a;
1190       for (i=0; i<amat->nz; i++) {
1191 #if defined(PETSC_USE_COMPLEX)
1192         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1193 #else
1194         sum += (*v)*(*v); v++;
1195 #endif
1196       }
1197       v = bmat->a;
1198       for (i=0; i<bmat->nz; i++) {
1199 #if defined(PETSC_USE_COMPLEX)
1200         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1201 #else
1202         sum += (*v)*(*v); v++;
1203 #endif
1204       }
1205       ierr = MPI_Allreduce(&sum,norm,1,MPI_DOUBLE,MPI_SUM,mat->comm);CHKERRQ(ierr);
1206       *norm = sqrt(*norm);
1207     } else if (type == NORM_1) { /* max column norm */
1208       PetscReal *tmp,*tmp2;
1209       int    *jj,*garray = aij->garray;
1210       ierr = PetscMalloc((mat->N+1)*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
1211       ierr = PetscMalloc((mat->N+1)*sizeof(PetscReal),&tmp2);CHKERRQ(ierr);
1212       ierr = PetscMemzero(tmp,mat->N*sizeof(PetscReal));CHKERRQ(ierr);
1213       *norm = 0.0;
1214       v = amat->a; jj = amat->j;
1215       for (j=0; j<amat->nz; j++) {
1216         tmp[cstart + *jj++ + shift] += PetscAbsScalar(*v);  v++;
1217       }
1218       v = bmat->a; jj = bmat->j;
1219       for (j=0; j<bmat->nz; j++) {
1220         tmp[garray[*jj++ + shift]] += PetscAbsScalar(*v); v++;
1221       }
1222       ierr = MPI_Allreduce(tmp,tmp2,mat->N,MPI_DOUBLE,MPI_SUM,mat->comm);CHKERRQ(ierr);
1223       for (j=0; j<mat->N; j++) {
1224         if (tmp2[j] > *norm) *norm = tmp2[j];
1225       }
1226       ierr = PetscFree(tmp);CHKERRQ(ierr);
1227       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1228     } else if (type == NORM_INFINITY) { /* max row norm */
1229       PetscReal ntemp = 0.0;
1230       for (j=0; j<aij->A->m; j++) {
1231         v = amat->a + amat->i[j] + shift;
1232         sum = 0.0;
1233         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1234           sum += PetscAbsScalar(*v); v++;
1235         }
1236         v = bmat->a + bmat->i[j] + shift;
1237         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1238           sum += PetscAbsScalar(*v); v++;
1239         }
1240         if (sum > ntemp) ntemp = sum;
1241       }
1242       ierr = MPI_Allreduce(&ntemp,norm,1,MPI_DOUBLE,MPI_MAX,mat->comm);CHKERRQ(ierr);
1243     } else {
1244       SETERRQ(PETSC_ERR_SUP,"No support for two norm");
1245     }
1246   }
1247   PetscFunctionReturn(0);
1248 }
1249 
1250 #undef __FUNCT__
1251 #define __FUNCT__ "MatTranspose_MPIAIJ"
1252 int MatTranspose_MPIAIJ(Mat A,Mat *matout)
1253 {
1254   Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data;
1255   Mat_SeqAIJ *Aloc = (Mat_SeqAIJ*)a->A->data;
1256   int        ierr,shift = Aloc->indexshift;
1257   int        M = A->M,N = A->N,m,*ai,*aj,row,*cols,i,*ct;
1258   Mat        B;
1259   Scalar     *array;
1260 
1261   PetscFunctionBegin;
1262   if (!matout && M != N) {
1263     SETERRQ(PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1264   }
1265 
1266   ierr = MatCreateMPIAIJ(A->comm,A->n,A->m,N,M,0,PETSC_NULL,0,PETSC_NULL,&B);CHKERRQ(ierr);
1267 
1268   /* copy over the A part */
1269   Aloc = (Mat_SeqAIJ*)a->A->data;
1270   m = a->A->m; ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
1271   row = a->rstart;
1272   for (i=0; i<ai[m]+shift; i++) {aj[i] += a->cstart + shift;}
1273   for (i=0; i<m; i++) {
1274     ierr = MatSetValues(B,ai[i+1]-ai[i],aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1275     row++; array += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1276   }
1277   aj = Aloc->j;
1278   for (i=0; i<ai[m]+shift; i++) {aj[i] -= a->cstart + shift;}
1279 
1280   /* copy over the B part */
1281   Aloc = (Mat_SeqAIJ*)a->B->data;
1282   m = a->B->m;  ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
1283   row  = a->rstart;
1284   ierr = PetscMalloc((1+ai[m]-shift)*sizeof(int),&cols);CHKERRQ(ierr);
1285   ct   = cols;
1286   for (i=0; i<ai[m]+shift; i++) {cols[i] = a->garray[aj[i]+shift];}
1287   for (i=0; i<m; i++) {
1288     ierr = MatSetValues(B,ai[i+1]-ai[i],cols,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1289     row++; array += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1290   }
1291   ierr = PetscFree(ct);CHKERRQ(ierr);
1292   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1293   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1294   if (matout) {
1295     *matout = B;
1296   } else {
1297     ierr = MatHeaderCopy(A,B);CHKERRQ(ierr);
1298   }
1299   PetscFunctionReturn(0);
1300 }
1301 
1302 #undef __FUNCT__
1303 #define __FUNCT__ "MatDiagonalScale_MPIAIJ"
1304 int MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1305 {
1306   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1307   Mat        a = aij->A,b = aij->B;
1308   int        ierr,s1,s2,s3;
1309 
1310   PetscFunctionBegin;
1311   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1312   if (rr) {
1313     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1314     if (s1!=s3) SETERRQ(PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1315     /* Overlap communication with computation. */
1316     ierr = VecScatterBegin(rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD,aij->Mvctx);CHKERRQ(ierr);
1317   }
1318   if (ll) {
1319     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1320     if (s1!=s2) SETERRQ(PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1321     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
1322   }
1323   /* scale  the diagonal block */
1324   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
1325 
1326   if (rr) {
1327     /* Do a scatter end and then right scale the off-diagonal block */
1328     ierr = VecScatterEnd(rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD,aij->Mvctx);CHKERRQ(ierr);
1329     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
1330   }
1331 
1332   PetscFunctionReturn(0);
1333 }
1334 
1335 
1336 #undef __FUNCT__
1337 #define __FUNCT__ "MatPrintHelp_MPIAIJ"
1338 int MatPrintHelp_MPIAIJ(Mat A)
1339 {
1340   Mat_MPIAIJ *a   = (Mat_MPIAIJ*)A->data;
1341   int        ierr;
1342 
1343   PetscFunctionBegin;
1344   if (!a->rank) {
1345     ierr = MatPrintHelp_SeqAIJ(a->A);CHKERRQ(ierr);
1346   }
1347   PetscFunctionReturn(0);
1348 }
1349 
1350 #undef __FUNCT__
1351 #define __FUNCT__ "MatGetBlockSize_MPIAIJ"
1352 int MatGetBlockSize_MPIAIJ(Mat A,int *bs)
1353 {
1354   PetscFunctionBegin;
1355   *bs = 1;
1356   PetscFunctionReturn(0);
1357 }
1358 #undef __FUNCT__
1359 #define __FUNCT__ "MatSetUnfactored_MPIAIJ"
1360 int MatSetUnfactored_MPIAIJ(Mat A)
1361 {
1362   Mat_MPIAIJ *a   = (Mat_MPIAIJ*)A->data;
1363   int        ierr;
1364 
1365   PetscFunctionBegin;
1366   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
1367   PetscFunctionReturn(0);
1368 }
1369 
1370 #undef __FUNCT__
1371 #define __FUNCT__ "MatEqual_MPIAIJ"
1372 int MatEqual_MPIAIJ(Mat A,Mat B,PetscTruth *flag)
1373 {
1374   Mat_MPIAIJ *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
1375   Mat        a,b,c,d;
1376   PetscTruth flg;
1377   int        ierr;
1378 
1379   PetscFunctionBegin;
1380   ierr = PetscTypeCompare((PetscObject)B,MATMPIAIJ,&flg);CHKERRQ(ierr);
1381   if (!flg) SETERRQ(PETSC_ERR_ARG_INCOMP,"Matrices must be same type");
1382   a = matA->A; b = matA->B;
1383   c = matB->A; d = matB->B;
1384 
1385   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
1386   if (flg == PETSC_TRUE) {
1387     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
1388   }
1389   ierr = MPI_Allreduce(&flg,flag,1,MPI_INT,MPI_LAND,A->comm);CHKERRQ(ierr);
1390   PetscFunctionReturn(0);
1391 }
1392 
1393 #undef __FUNCT__
1394 #define __FUNCT__ "MatCopy_MPIAIJ"
1395 int MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
1396 {
1397   int        ierr;
1398   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1399   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
1400   PetscTruth flg;
1401 
1402   PetscFunctionBegin;
1403   ierr = PetscTypeCompare((PetscObject)B,MATMPIAIJ,&flg);CHKERRQ(ierr);
1404   if (str != SAME_NONZERO_PATTERN || !flg) {
1405     /* because of the column compression in the off-processor part of the matrix a->B,
1406        the number of columns in a->B and b->B may be different, hence we cannot call
1407        the MatCopy() directly on the two parts. If need be, we can provide a more
1408        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
1409        then copying the submatrices */
1410     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
1411   } else {
1412     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
1413     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
1414   }
1415   PetscFunctionReturn(0);
1416 }
1417 
1418 #undef __FUNCT__
1419 #define __FUNCT__ "MatSetUpPreallocation_MPIAIJ"
1420 int MatSetUpPreallocation_MPIAIJ(Mat A)
1421 {
1422   int        ierr;
1423 
1424   PetscFunctionBegin;
1425   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
1426   PetscFunctionReturn(0);
1427 }
1428 
1429 EXTERN int MatDuplicate_MPIAIJ(Mat,MatDuplicateOption,Mat *);
1430 EXTERN int MatIncreaseOverlap_MPIAIJ(Mat,int,IS *,int);
1431 EXTERN int MatFDColoringCreate_MPIAIJ(Mat,ISColoring,MatFDColoring);
1432 EXTERN int MatGetSubMatrices_MPIAIJ (Mat,int,IS *,IS *,MatReuse,Mat **);
1433 EXTERN int MatGetSubMatrix_MPIAIJ (Mat,IS,IS,int,MatReuse,Mat *);
1434 #if !defined(PETSC_USE_COMPLEX)
1435 EXTERN int MatLUFactorSymbolic_MPIAIJ_TFS(Mat,IS,IS,MatLUInfo*,Mat*);
1436 #endif
1437 
1438 /* -------------------------------------------------------------------*/
1439 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
1440        MatGetRow_MPIAIJ,
1441        MatRestoreRow_MPIAIJ,
1442        MatMult_MPIAIJ,
1443        MatMultAdd_MPIAIJ,
1444        MatMultTranspose_MPIAIJ,
1445        MatMultTransposeAdd_MPIAIJ,
1446        0,
1447        0,
1448        0,
1449        0,
1450        0,
1451        0,
1452        MatRelax_MPIAIJ,
1453        MatTranspose_MPIAIJ,
1454        MatGetInfo_MPIAIJ,
1455        MatEqual_MPIAIJ,
1456        MatGetDiagonal_MPIAIJ,
1457        MatDiagonalScale_MPIAIJ,
1458        MatNorm_MPIAIJ,
1459        MatAssemblyBegin_MPIAIJ,
1460        MatAssemblyEnd_MPIAIJ,
1461        0,
1462        MatSetOption_MPIAIJ,
1463        MatZeroEntries_MPIAIJ,
1464        MatZeroRows_MPIAIJ,
1465 #if !defined(PETSC_USE_COMPLEX)
1466 				       MatLUFactorSymbolic_MPIAIJ_TFS,
1467 #else
1468        0,
1469 #endif
1470        0,
1471        0,
1472        0,
1473        MatSetUpPreallocation_MPIAIJ,
1474        0,
1475        MatGetOwnershipRange_MPIAIJ,
1476        0,
1477        0,
1478        0,
1479        0,
1480        MatDuplicate_MPIAIJ,
1481        0,
1482        0,
1483        0,
1484        0,
1485        0,
1486        MatGetSubMatrices_MPIAIJ,
1487        MatIncreaseOverlap_MPIAIJ,
1488        MatGetValues_MPIAIJ,
1489        MatCopy_MPIAIJ,
1490        MatPrintHelp_MPIAIJ,
1491        MatScale_MPIAIJ,
1492        0,
1493        0,
1494        0,
1495        MatGetBlockSize_MPIAIJ,
1496        0,
1497        0,
1498        0,
1499        0,
1500        MatFDColoringCreate_MPIAIJ,
1501        0,
1502        MatSetUnfactored_MPIAIJ,
1503        0,
1504        0,
1505        MatGetSubMatrix_MPIAIJ,
1506        MatDestroy_MPIAIJ,
1507        MatView_MPIAIJ,
1508        MatGetMaps_Petsc};
1509 
1510 /* ----------------------------------------------------------------------------------------*/
1511 
1512 EXTERN_C_BEGIN
1513 #undef __FUNCT__
1514 #define __FUNCT__ "MatStoreValues_MPIAIJ"
1515 int MatStoreValues_MPIAIJ(Mat mat)
1516 {
1517   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
1518   int        ierr;
1519 
1520   PetscFunctionBegin;
1521   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
1522   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
1523   PetscFunctionReturn(0);
1524 }
1525 EXTERN_C_END
1526 
1527 EXTERN_C_BEGIN
1528 #undef __FUNCT__
1529 #define __FUNCT__ "MatRetrieveValues_MPIAIJ"
1530 int MatRetrieveValues_MPIAIJ(Mat mat)
1531 {
1532   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
1533   int        ierr;
1534 
1535   PetscFunctionBegin;
1536   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
1537   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
1538   PetscFunctionReturn(0);
1539 }
1540 EXTERN_C_END
1541 
1542 #include "petscpc.h"
1543 EXTERN_C_BEGIN
1544 EXTERN int MatGetDiagonalBlock_MPIAIJ(Mat,PetscTruth *,MatReuse,Mat *);
1545 EXTERN_C_END
1546 
1547 EXTERN_C_BEGIN
1548 #undef __FUNCT__
1549 #define __FUNCT__ "MatCreate_MPIAIJ"
1550 int MatCreate_MPIAIJ(Mat B)
1551 {
1552   Mat_MPIAIJ   *b;
1553   int          ierr,i,size;
1554 
1555   PetscFunctionBegin;
1556   ierr = MPI_Comm_size(B->comm,&size);CHKERRQ(ierr);
1557 
1558   ierr            = PetscNew(Mat_MPIAIJ,&b);CHKERRQ(ierr);
1559   B->data         = (void*)b;
1560   ierr            = PetscMemzero(b,sizeof(Mat_MPIAIJ));CHKERRQ(ierr);
1561   ierr            = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
1562   B->factor       = 0;
1563   B->assembled    = PETSC_FALSE;
1564   B->mapping      = 0;
1565 
1566   B->insertmode      = NOT_SET_VALUES;
1567   b->size            = size;
1568   ierr = MPI_Comm_rank(B->comm,&b->rank);CHKERRQ(ierr);
1569 
1570   ierr = PetscSplitOwnership(B->comm,&B->m,&B->M);CHKERRQ(ierr);
1571   ierr = PetscSplitOwnership(B->comm,&B->n,&B->N);CHKERRQ(ierr);
1572 
1573   /* the information in the maps duplicates the information computed below, eventually
1574      we should remove the duplicate information that is not contained in the maps */
1575   ierr = MapCreateMPI(B->comm,B->m,B->M,&B->rmap);CHKERRQ(ierr);
1576   ierr = MapCreateMPI(B->comm,B->n,B->N,&B->cmap);CHKERRQ(ierr);
1577 
1578   /* build local table of row and column ownerships */
1579   ierr = PetscMalloc(2*(b->size+2)*sizeof(int),&b->rowners);CHKERRQ(ierr);
1580   PetscLogObjectMemory(B,2*(b->size+2)*sizeof(int)+sizeof(struct _p_Mat)+sizeof(Mat_MPIAIJ));
1581   b->cowners = b->rowners + b->size + 2;
1582   ierr = MPI_Allgather(&B->m,1,MPI_INT,b->rowners+1,1,MPI_INT,B->comm);CHKERRQ(ierr);
1583   b->rowners[0] = 0;
1584   for (i=2; i<=b->size; i++) {
1585     b->rowners[i] += b->rowners[i-1];
1586   }
1587   b->rstart = b->rowners[b->rank];
1588   b->rend   = b->rowners[b->rank+1];
1589   ierr = MPI_Allgather(&B->n,1,MPI_INT,b->cowners+1,1,MPI_INT,B->comm);CHKERRQ(ierr);
1590   b->cowners[0] = 0;
1591   for (i=2; i<=b->size; i++) {
1592     b->cowners[i] += b->cowners[i-1];
1593   }
1594   b->cstart = b->cowners[b->rank];
1595   b->cend   = b->cowners[b->rank+1];
1596 
1597   /* build cache for off array entries formed */
1598   ierr = MatStashCreate_Private(B->comm,1,&B->stash);CHKERRQ(ierr);
1599   b->donotstash  = PETSC_FALSE;
1600   b->colmap      = 0;
1601   b->garray      = 0;
1602   b->roworiented = PETSC_TRUE;
1603 
1604   /* stuff used for matrix vector multiply */
1605   b->lvec      = PETSC_NULL;
1606   b->Mvctx     = PETSC_NULL;
1607 
1608   /* stuff for MatGetRow() */
1609   b->rowindices   = 0;
1610   b->rowvalues    = 0;
1611   b->getrowactive = PETSC_FALSE;
1612 
1613   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatStoreValues_C",
1614                                      "MatStoreValues_MPIAIJ",
1615                                      MatStoreValues_MPIAIJ);CHKERRQ(ierr);
1616   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatRetrieveValues_C",
1617                                      "MatRetrieveValues_MPIAIJ",
1618                                      MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
1619   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatGetDiagonalBlock_C",
1620                                      "MatGetDiagonalBlock_MPIAIJ",
1621                                      MatGetDiagonalBlock_MPIAIJ);CHKERRQ(ierr);
1622   PetscFunctionReturn(0);
1623 }
1624 EXTERN_C_END
1625 
1626 #undef __FUNCT__
1627 #define __FUNCT__ "MatDuplicate_MPIAIJ"
1628 int MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
1629 {
1630   Mat        mat;
1631   Mat_MPIAIJ *a,*oldmat = (Mat_MPIAIJ*)matin->data;
1632   int        ierr;
1633 
1634   PetscFunctionBegin;
1635   *newmat       = 0;
1636   ierr = MatCreate(matin->comm,matin->m,matin->n,matin->M,matin->N,&mat);CHKERRQ(ierr);
1637   ierr = MatSetType(mat,MATMPIAIJ);CHKERRQ(ierr);
1638   a    = (Mat_MPIAIJ*)mat->data;
1639   ierr              = PetscMemcpy(mat->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
1640   mat->factor       = matin->factor;
1641   mat->assembled    = PETSC_TRUE;
1642   mat->insertmode   = NOT_SET_VALUES;
1643   mat->preallocated = PETSC_TRUE;
1644 
1645   a->rstart       = oldmat->rstart;
1646   a->rend         = oldmat->rend;
1647   a->cstart       = oldmat->cstart;
1648   a->cend         = oldmat->cend;
1649   a->size         = oldmat->size;
1650   a->rank         = oldmat->rank;
1651   a->donotstash   = oldmat->donotstash;
1652   a->roworiented  = oldmat->roworiented;
1653   a->rowindices   = 0;
1654   a->rowvalues    = 0;
1655   a->getrowactive = PETSC_FALSE;
1656 
1657   ierr       = PetscMemcpy(a->rowners,oldmat->rowners,2*(a->size+2)*sizeof(int));CHKERRQ(ierr);
1658   ierr       = MatStashCreate_Private(matin->comm,1,&mat->stash);CHKERRQ(ierr);
1659   if (oldmat->colmap) {
1660 #if defined (PETSC_USE_CTABLE)
1661     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
1662 #else
1663     ierr = PetscMalloc((mat->N)*sizeof(int),&a->colmap);CHKERRQ(ierr);
1664     PetscLogObjectMemory(mat,(mat->N)*sizeof(int));
1665     ierr      = PetscMemcpy(a->colmap,oldmat->colmap,(mat->N)*sizeof(int));CHKERRQ(ierr);
1666 #endif
1667   } else a->colmap = 0;
1668   if (oldmat->garray) {
1669     int len;
1670     len  = oldmat->B->n;
1671     ierr = PetscMalloc((len+1)*sizeof(int),&a->garray);CHKERRQ(ierr);
1672     PetscLogObjectMemory(mat,len*sizeof(int));
1673     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(int));CHKERRQ(ierr); }
1674   } else a->garray = 0;
1675 
1676   ierr =  VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
1677   PetscLogObjectParent(mat,a->lvec);
1678   ierr =  VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
1679   PetscLogObjectParent(mat,a->Mvctx);
1680   ierr =  MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
1681   PetscLogObjectParent(mat,a->A);
1682   ierr =  MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
1683   PetscLogObjectParent(mat,a->B);
1684   ierr = PetscFListDuplicate(matin->qlist,&mat->qlist);CHKERRQ(ierr);
1685   *newmat = mat;
1686   PetscFunctionReturn(0);
1687 }
1688 
1689 #include "petscsys.h"
1690 
1691 EXTERN_C_BEGIN
1692 #undef __FUNCT__
1693 #define __FUNCT__ "MatLoad_MPIAIJ"
1694 int MatLoad_MPIAIJ(PetscViewer viewer,MatType type,Mat *newmat)
1695 {
1696   Mat          A;
1697   Scalar       *vals,*svals;
1698   MPI_Comm     comm = ((PetscObject)viewer)->comm;
1699   MPI_Status   status;
1700   int          i,nz,ierr,j,rstart,rend,fd;
1701   int          header[4],rank,size,*rowlengths = 0,M,N,m,*rowners,maxnz,*cols;
1702   int          *ourlens,*sndcounts = 0,*procsnz = 0,*offlens,jj,*mycols,*smycols;
1703   int          tag = ((PetscObject)viewer)->tag,cend,cstart,n;
1704 
1705   PetscFunctionBegin;
1706   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1707   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1708   if (!rank) {
1709     ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1710     ierr = PetscBinaryRead(fd,(char *)header,4,PETSC_INT);CHKERRQ(ierr);
1711     if (header[0] != MAT_COOKIE) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
1712     if (header[3] < 0) {
1713       SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"Matrix in special format on disk, cannot load as MPIAIJ");
1714     }
1715   }
1716 
1717   ierr = MPI_Bcast(header+1,3,MPI_INT,0,comm);CHKERRQ(ierr);
1718   M = header[1]; N = header[2];
1719   /* determine ownership of all rows */
1720   m = M/size + ((M % size) > rank);
1721   ierr = PetscMalloc((size+2)*sizeof(int),&rowners);CHKERRQ(ierr);
1722   ierr = MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPI_INT,comm);CHKERRQ(ierr);
1723   rowners[0] = 0;
1724   for (i=2; i<=size; i++) {
1725     rowners[i] += rowners[i-1];
1726   }
1727   rstart = rowners[rank];
1728   rend   = rowners[rank+1];
1729 
1730   /* distribute row lengths to all processors */
1731   ierr    = PetscMalloc(2*(rend-rstart+1)*sizeof(int),&ourlens);CHKERRQ(ierr);
1732   offlens = ourlens + (rend-rstart);
1733   if (!rank) {
1734     ierr = PetscMalloc(M*sizeof(int),&rowlengths);CHKERRQ(ierr);
1735     ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
1736     ierr = PetscMalloc(size*sizeof(int),&sndcounts);CHKERRQ(ierr);
1737     for (i=0; i<size; i++) sndcounts[i] = rowners[i+1] - rowners[i];
1738     ierr = MPI_Scatterv(rowlengths,sndcounts,rowners,MPI_INT,ourlens,rend-rstart,MPI_INT,0,comm);CHKERRQ(ierr);
1739     ierr = PetscFree(sndcounts);CHKERRQ(ierr);
1740   } else {
1741     ierr = MPI_Scatterv(0,0,0,MPI_INT,ourlens,rend-rstart,MPI_INT,0,comm);CHKERRQ(ierr);
1742   }
1743 
1744   if (!rank) {
1745     /* calculate the number of nonzeros on each processor */
1746     ierr = PetscMalloc(size*sizeof(int),&procsnz);CHKERRQ(ierr);
1747     ierr = PetscMemzero(procsnz,size*sizeof(int));CHKERRQ(ierr);
1748     for (i=0; i<size; i++) {
1749       for (j=rowners[i]; j< rowners[i+1]; j++) {
1750         procsnz[i] += rowlengths[j];
1751       }
1752     }
1753     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
1754 
1755     /* determine max buffer needed and allocate it */
1756     maxnz = 0;
1757     for (i=0; i<size; i++) {
1758       maxnz = PetscMax(maxnz,procsnz[i]);
1759     }
1760     ierr = PetscMalloc(maxnz*sizeof(int),&cols);CHKERRQ(ierr);
1761 
1762     /* read in my part of the matrix column indices  */
1763     nz   = procsnz[0];
1764     ierr = PetscMalloc(nz*sizeof(int),&mycols);CHKERRQ(ierr);
1765     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
1766 
1767     /* read in every one elses and ship off */
1768     for (i=1; i<size; i++) {
1769       nz   = procsnz[i];
1770       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
1771       ierr = MPI_Send(cols,nz,MPI_INT,i,tag,comm);CHKERRQ(ierr);
1772     }
1773     ierr = PetscFree(cols);CHKERRQ(ierr);
1774   } else {
1775     /* determine buffer space needed for message */
1776     nz = 0;
1777     for (i=0; i<m; i++) {
1778       nz += ourlens[i];
1779     }
1780     ierr = PetscMalloc((nz+1)*sizeof(int),&mycols);CHKERRQ(ierr);
1781 
1782     /* receive message of column indices*/
1783     ierr = MPI_Recv(mycols,nz,MPI_INT,0,tag,comm,&status);CHKERRQ(ierr);
1784     ierr = MPI_Get_count(&status,MPI_INT,&maxnz);CHKERRQ(ierr);
1785     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1786   }
1787 
1788   /* determine column ownership if matrix is not square */
1789   if (N != M) {
1790     n      = N/size + ((N % size) > rank);
1791     ierr   = MPI_Scan(&n,&cend,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
1792     cstart = cend - n;
1793   } else {
1794     cstart = rstart;
1795     cend   = rend;
1796     n      = cend - cstart;
1797   }
1798 
1799   /* loop over local rows, determining number of off diagonal entries */
1800   ierr = PetscMemzero(offlens,m*sizeof(int));CHKERRQ(ierr);
1801   jj = 0;
1802   for (i=0; i<m; i++) {
1803     for (j=0; j<ourlens[i]; j++) {
1804       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
1805       jj++;
1806     }
1807   }
1808 
1809   /* create our matrix */
1810   for (i=0; i<m; i++) {
1811     ourlens[i] -= offlens[i];
1812   }
1813   ierr = MatCreateMPIAIJ(comm,m,n,M,N,0,ourlens,0,offlens,newmat);CHKERRQ(ierr);
1814   A = *newmat;
1815   ierr = MatSetOption(A,MAT_COLUMNS_SORTED);CHKERRQ(ierr);
1816   for (i=0; i<m; i++) {
1817     ourlens[i] += offlens[i];
1818   }
1819 
1820   if (!rank) {
1821     ierr = PetscMalloc(maxnz*sizeof(Scalar),&vals);CHKERRQ(ierr);
1822 
1823     /* read in my part of the matrix numerical values  */
1824     nz   = procsnz[0];
1825     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1826 
1827     /* insert into matrix */
1828     jj      = rstart;
1829     smycols = mycols;
1830     svals   = vals;
1831     for (i=0; i<m; i++) {
1832       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1833       smycols += ourlens[i];
1834       svals   += ourlens[i];
1835       jj++;
1836     }
1837 
1838     /* read in other processors and ship out */
1839     for (i=1; i<size; i++) {
1840       nz   = procsnz[i];
1841       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
1842       ierr = MPI_Send(vals,nz,MPIU_SCALAR,i,A->tag,comm);CHKERRQ(ierr);
1843     }
1844     ierr = PetscFree(procsnz);CHKERRQ(ierr);
1845   } else {
1846     /* receive numeric values */
1847     ierr = PetscMalloc((nz+1)*sizeof(Scalar),&vals);CHKERRQ(ierr);
1848 
1849     /* receive message of values*/
1850     ierr = MPI_Recv(vals,nz,MPIU_SCALAR,0,A->tag,comm,&status);CHKERRQ(ierr);
1851     ierr = MPI_Get_count(&status,MPIU_SCALAR,&maxnz);CHKERRQ(ierr);
1852     if (maxnz != nz) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"something is wrong with file");
1853 
1854     /* insert into matrix */
1855     jj      = rstart;
1856     smycols = mycols;
1857     svals   = vals;
1858     for (i=0; i<m; i++) {
1859       ierr     = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1860       smycols += ourlens[i];
1861       svals   += ourlens[i];
1862       jj++;
1863     }
1864   }
1865   ierr = PetscFree(ourlens);CHKERRQ(ierr);
1866   ierr = PetscFree(vals);CHKERRQ(ierr);
1867   ierr = PetscFree(mycols);CHKERRQ(ierr);
1868   ierr = PetscFree(rowners);CHKERRQ(ierr);
1869 
1870   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1871   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1872   PetscFunctionReturn(0);
1873 }
1874 EXTERN_C_END
1875 
1876 #undef __FUNCT__
1877 #define __FUNCT__ "MatGetSubMatrix_MPIAIJ"
1878 /*
1879     Not great since it makes two copies of the submatrix, first an SeqAIJ
1880   in local and then by concatenating the local matrices the end result.
1881   Writing it directly would be much like MatGetSubMatrices_MPIAIJ()
1882 */
1883 int MatGetSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,int csize,MatReuse call,Mat *newmat)
1884 {
1885   int        ierr,i,m,n,rstart,row,rend,nz,*cwork,size,rank,j;
1886   int        *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend;
1887   Mat        *local,M,Mreuse;
1888   Scalar     *vwork,*aa;
1889   MPI_Comm   comm = mat->comm;
1890   Mat_SeqAIJ *aij;
1891 
1892 
1893   PetscFunctionBegin;
1894   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1895   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1896 
1897   if (call ==  MAT_REUSE_MATRIX) {
1898     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject *)&Mreuse);CHKERRQ(ierr);
1899     if (!Mreuse) SETERRQ(1,"Submatrix passed in was not used before, cannot reuse");
1900     local = &Mreuse;
1901     ierr  = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&local);CHKERRQ(ierr);
1902   } else {
1903     ierr = MatGetSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&local);CHKERRQ(ierr);
1904     Mreuse = *local;
1905     ierr = PetscFree(local);CHKERRQ(ierr);
1906   }
1907 
1908   /*
1909       m - number of local rows
1910       n - number of columns (same on all processors)
1911       rstart - first row in new global matrix generated
1912   */
1913   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
1914   if (call == MAT_INITIAL_MATRIX) {
1915     aij = (Mat_SeqAIJ*)(Mreuse)->data;
1916     if (aij->indexshift) SETERRQ(PETSC_ERR_SUP,"No support for index shifted matrix");
1917     ii  = aij->i;
1918     jj  = aij->j;
1919 
1920     /*
1921         Determine the number of non-zeros in the diagonal and off-diagonal
1922         portions of the matrix in order to do correct preallocation
1923     */
1924 
1925     /* first get start and end of "diagonal" columns */
1926     if (csize == PETSC_DECIDE) {
1927       nlocal = n/size + ((n % size) > rank);
1928     } else {
1929       nlocal = csize;
1930     }
1931     ierr   = MPI_Scan(&nlocal,&rend,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
1932     rstart = rend - nlocal;
1933     if (rank == size - 1 && rend != n) {
1934       SETERRQ(1,"Local column sizes do not add up to total number of columns");
1935     }
1936 
1937     /* next, compute all the lengths */
1938     ierr  = PetscMalloc((2*m+1)*sizeof(int),&dlens);CHKERRQ(ierr);
1939     olens = dlens + m;
1940     for (i=0; i<m; i++) {
1941       jend = ii[i+1] - ii[i];
1942       olen = 0;
1943       dlen = 0;
1944       for (j=0; j<jend; j++) {
1945         if (*jj < rstart || *jj >= rend) olen++;
1946         else dlen++;
1947         jj++;
1948       }
1949       olens[i] = olen;
1950       dlens[i] = dlen;
1951     }
1952     ierr = MatCreateMPIAIJ(comm,m,nlocal,PETSC_DECIDE,n,0,dlens,0,olens,&M);CHKERRQ(ierr);
1953     ierr = PetscFree(dlens);CHKERRQ(ierr);
1954   } else {
1955     int ml,nl;
1956 
1957     M = *newmat;
1958     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
1959     if (ml != m) SETERRQ(PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
1960     ierr = MatZeroEntries(M);CHKERRQ(ierr);
1961     /*
1962          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
1963        rather than the slower MatSetValues().
1964     */
1965     M->was_assembled = PETSC_TRUE;
1966     M->assembled     = PETSC_FALSE;
1967   }
1968   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
1969   aij = (Mat_SeqAIJ*)(Mreuse)->data;
1970   if (aij->indexshift) SETERRQ(PETSC_ERR_SUP,"No support for index shifted matrix");
1971   ii  = aij->i;
1972   jj  = aij->j;
1973   aa  = aij->a;
1974   for (i=0; i<m; i++) {
1975     row   = rstart + i;
1976     nz    = ii[i+1] - ii[i];
1977     cwork = jj;     jj += nz;
1978     vwork = aa;     aa += nz;
1979     ierr = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
1980   }
1981 
1982   ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1983   ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1984   *newmat = M;
1985 
1986   /* save submatrix used in processor for next request */
1987   if (call ==  MAT_INITIAL_MATRIX) {
1988     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
1989     ierr = PetscObjectDereference((PetscObject)Mreuse);CHKERRQ(ierr);
1990   }
1991 
1992   PetscFunctionReturn(0);
1993 }
1994 
1995 #undef __FUNCT__
1996 #define __FUNCT__ "MatMPIAIJSetPreallocation"
1997 /*@C
1998    MatMPIAIJSetPreallocation - Creates a sparse parallel matrix in AIJ format
1999    (the default parallel PETSc format).  For good matrix assembly performance
2000    the user should preallocate the matrix storage by setting the parameters
2001    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
2002    performance can be increased by more than a factor of 50.
2003 
2004    Collective on MPI_Comm
2005 
2006    Input Parameters:
2007 +  A - the matrix
2008 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
2009            (same value is used for all local rows)
2010 .  d_nnz - array containing the number of nonzeros in the various rows of the
2011            DIAGONAL portion of the local submatrix (possibly different for each row)
2012            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
2013            The size of this array is equal to the number of local rows, i.e 'm'.
2014            You must leave room for the diagonal entry even if it is zero.
2015 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
2016            submatrix (same value is used for all local rows).
2017 -  o_nnz - array containing the number of nonzeros in the various rows of the
2018            OFF-DIAGONAL portion of the local submatrix (possibly different for
2019            each row) or PETSC_NULL, if o_nz is used to specify the nonzero
2020            structure. The size of this array is equal to the number
2021            of local rows, i.e 'm'.
2022 
2023    The AIJ format (also called the Yale sparse matrix format or
2024    compressed row storage), is fully compatible with standard Fortran 77
2025    storage.  That is, the stored row and column indices can begin at
2026    either one (as in Fortran) or zero.  See the users manual for details.
2027 
2028    The user MUST specify either the local or global matrix dimensions
2029    (possibly both).
2030 
2031    The parallel matrix is partitioned such that the first m0 rows belong to
2032    process 0, the next m1 rows belong to process 1, the next m2 rows belong
2033    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
2034 
2035    The DIAGONAL portion of the local submatrix of a processor can be defined
2036    as the submatrix which is obtained by extraction the part corresponding
2037    to the rows r1-r2 and columns r1-r2 of the global matrix, where r1 is the
2038    first row that belongs to the processor, and r2 is the last row belonging
2039    to the this processor. This is a square mxm matrix. The remaining portion
2040    of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.
2041 
2042    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
2043 
2044    By default, this format uses inodes (identical nodes) when possible.
2045    We search for consecutive rows with the same nonzero structure, thereby
2046    reusing matrix information to achieve increased efficiency.
2047 
2048    Options Database Keys:
2049 +  -mat_aij_no_inode  - Do not use inodes
2050 .  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
2051 -  -mat_aij_oneindex - Internally use indexing starting at 1
2052         rather than 0.  Note that when calling MatSetValues(),
2053         the user still MUST index entries starting at 0!
2054 
2055    Example usage:
2056 
2057    Consider the following 8x8 matrix with 34 non-zero values, that is
2058    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
2059    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
2060    as follows:
2061 
2062 .vb
2063             1  2  0  |  0  3  0  |  0  4
2064     Proc0   0  5  6  |  7  0  0  |  8  0
2065             9  0 10  | 11  0  0  | 12  0
2066     -------------------------------------
2067            13  0 14  | 15 16 17  |  0  0
2068     Proc1   0 18  0  | 19 20 21  |  0  0
2069             0  0  0  | 22 23  0  | 24  0
2070     -------------------------------------
2071     Proc2  25 26 27  |  0  0 28  | 29  0
2072            30  0  0  | 31 32 33  |  0 34
2073 .ve
2074 
2075    This can be represented as a collection of submatrices as:
2076 
2077 .vb
2078       A B C
2079       D E F
2080       G H I
2081 .ve
2082 
2083    Where the submatrices A,B,C are owned by proc0, D,E,F are
2084    owned by proc1, G,H,I are owned by proc2.
2085 
2086    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2087    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2088    The 'M','N' parameters are 8,8, and have the same values on all procs.
2089 
2090    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
2091    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
2092    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
2093    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
2094    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
2095    matrix, ans [DF] as another SeqAIJ matrix.
2096 
2097    When d_nz, o_nz parameters are specified, d_nz storage elements are
2098    allocated for every row of the local diagonal submatrix, and o_nz
2099    storage locations are allocated for every row of the OFF-DIAGONAL submat.
2100    One way to choose d_nz and o_nz is to use the max nonzerors per local
2101    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
2102    In this case, the values of d_nz,o_nz are:
2103 .vb
2104      proc0 : dnz = 2, o_nz = 2
2105      proc1 : dnz = 3, o_nz = 2
2106      proc2 : dnz = 1, o_nz = 4
2107 .ve
2108    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
2109    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
2110    for proc3. i.e we are using 12+15+10=37 storage locations to store
2111    34 values.
2112 
2113    When d_nnz, o_nnz parameters are specified, the storage is specified
2114    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
2115    In the above case the values for d_nnz,o_nnz are:
2116 .vb
2117      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
2118      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
2119      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
2120 .ve
2121    Here the space allocated is sum of all the above values i.e 34, and
2122    hence pre-allocation is perfect.
2123 
2124    Level: intermediate
2125 
2126 .keywords: matrix, aij, compressed row, sparse, parallel
2127 
2128 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues()
2129 @*/
2130 int MatMPIAIJSetPreallocation(Mat B,int d_nz,int *d_nnz,int o_nz,int *o_nnz)
2131 {
2132   Mat_MPIAIJ   *b;
2133   int          ierr,i;
2134   PetscTruth   flg2;
2135 
2136   PetscFunctionBegin;
2137   ierr = PetscTypeCompare((PetscObject)B,MATMPIAIJ,&flg2);CHKERRQ(ierr);
2138   if (!flg2) PetscFunctionReturn(0);
2139   B->preallocated = PETSC_TRUE;
2140   if (d_nz == PETSC_DEFAULT || d_nz == PETSC_DECIDE) d_nz = 5;
2141   if (o_nz == PETSC_DEFAULT || o_nz == PETSC_DECIDE) o_nz = 2;
2142   if (d_nz < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"d_nz cannot be less than 0: value %d",d_nz);
2143   if (o_nz < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"o_nz cannot be less than 0: value %d",o_nz);
2144   if (d_nnz) {
2145     for (i=0; i<B->m; i++) {
2146       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]);
2147     }
2148   }
2149   if (o_nnz) {
2150     for (i=0; i<B->m; i++) {
2151       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]);
2152     }
2153   }
2154   b = (Mat_MPIAIJ*)B->data;
2155 
2156   ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,B->m,B->n,d_nz,d_nnz,&b->A);CHKERRQ(ierr);
2157   PetscLogObjectParent(B,b->A);
2158   ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,B->m,B->N,o_nz,o_nnz,&b->B);CHKERRQ(ierr);
2159   PetscLogObjectParent(B,b->B);
2160 
2161   PetscFunctionReturn(0);
2162 }
2163 
2164 #undef __FUNCT__
2165 #define __FUNCT__ "MatCreateMPIAIJ"
2166 /*@C
2167    MatCreateMPIAIJ - Creates a sparse parallel matrix in AIJ format
2168    (the default parallel PETSc format).  For good matrix assembly performance
2169    the user should preallocate the matrix storage by setting the parameters
2170    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
2171    performance can be increased by more than a factor of 50.
2172 
2173    Collective on MPI_Comm
2174 
2175    Input Parameters:
2176 +  comm - MPI communicator
2177 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
2178            This value should be the same as the local size used in creating the
2179            y vector for the matrix-vector product y = Ax.
2180 .  n - This value should be the same as the local size used in creating the
2181        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
2182        calculated if N is given) For square matrices n is almost always m.
2183 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
2184 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
2185 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
2186            (same value is used for all local rows)
2187 .  d_nnz - array containing the number of nonzeros in the various rows of the
2188            DIAGONAL portion of the local submatrix (possibly different for each row)
2189            or PETSC_NULL, if d_nz is used to specify the nonzero structure.
2190            The size of this array is equal to the number of local rows, i.e 'm'.
2191            You must leave room for the diagonal entry even if it is zero.
2192 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
2193            submatrix (same value is used for all local rows).
2194 -  o_nnz - array containing the number of nonzeros in the various rows of the
2195            OFF-DIAGONAL portion of the local submatrix (possibly different for
2196            each row) or PETSC_NULL, if o_nz is used to specify the nonzero
2197            structure. The size of this array is equal to the number
2198            of local rows, i.e 'm'.
2199 
2200    Output Parameter:
2201 .  A - the matrix
2202 
2203    Notes:
2204    m,n,M,N parameters specify the size of the matrix, and its partitioning across
2205    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
2206    storage requirements for this matrix.
2207 
2208    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
2209    processor than it must be used on all processors that share the object for
2210    that argument.
2211 
2212    The AIJ format (also called the Yale sparse matrix format or
2213    compressed row storage), is fully compatible with standard Fortran 77
2214    storage.  That is, the stored row and column indices can begin at
2215    either one (as in Fortran) or zero.  See the users manual for details.
2216 
2217    The user MUST specify either the local or global matrix dimensions
2218    (possibly both).
2219 
2220    The parallel matrix is partitioned such that the first m0 rows belong to
2221    process 0, the next m1 rows belong to process 1, the next m2 rows belong
2222    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
2223 
2224    The DIAGONAL portion of the local submatrix of a processor can be defined
2225    as the submatrix which is obtained by extraction the part corresponding
2226    to the rows r1-r2 and columns r1-r2 of the global matrix, where r1 is the
2227    first row that belongs to the processor, and r2 is the last row belonging
2228    to the this processor. This is a square mxm matrix. The remaining portion
2229    of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.
2230 
2231    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
2232 
2233    By default, this format uses inodes (identical nodes) when possible.
2234    We search for consecutive rows with the same nonzero structure, thereby
2235    reusing matrix information to achieve increased efficiency.
2236 
2237    Options Database Keys:
2238 +  -mat_aij_no_inode  - Do not use inodes
2239 .  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
2240 -  -mat_aij_oneindex - Internally use indexing starting at 1
2241         rather than 0.  Note that when calling MatSetValues(),
2242         the user still MUST index entries starting at 0!
2243 
2244 
2245    Example usage:
2246 
2247    Consider the following 8x8 matrix with 34 non-zero values, that is
2248    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
2249    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
2250    as follows:
2251 
2252 .vb
2253             1  2  0  |  0  3  0  |  0  4
2254     Proc0   0  5  6  |  7  0  0  |  8  0
2255             9  0 10  | 11  0  0  | 12  0
2256     -------------------------------------
2257            13  0 14  | 15 16 17  |  0  0
2258     Proc1   0 18  0  | 19 20 21  |  0  0
2259             0  0  0  | 22 23  0  | 24  0
2260     -------------------------------------
2261     Proc2  25 26 27  |  0  0 28  | 29  0
2262            30  0  0  | 31 32 33  |  0 34
2263 .ve
2264 
2265    This can be represented as a collection of submatrices as:
2266 
2267 .vb
2268       A B C
2269       D E F
2270       G H I
2271 .ve
2272 
2273    Where the submatrices A,B,C are owned by proc0, D,E,F are
2274    owned by proc1, G,H,I are owned by proc2.
2275 
2276    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2277    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
2278    The 'M','N' parameters are 8,8, and have the same values on all procs.
2279 
2280    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
2281    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
2282    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
2283    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
2284    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
2285    matrix, ans [DF] as another SeqAIJ matrix.
2286 
2287    When d_nz, o_nz parameters are specified, d_nz storage elements are
2288    allocated for every row of the local diagonal submatrix, and o_nz
2289    storage locations are allocated for every row of the OFF-DIAGONAL submat.
2290    One way to choose d_nz and o_nz is to use the max nonzerors per local
2291    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
2292    In this case, the values of d_nz,o_nz are:
2293 .vb
2294      proc0 : dnz = 2, o_nz = 2
2295      proc1 : dnz = 3, o_nz = 2
2296      proc2 : dnz = 1, o_nz = 4
2297 .ve
2298    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
2299    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
2300    for proc3. i.e we are using 12+15+10=37 storage locations to store
2301    34 values.
2302 
2303    When d_nnz, o_nnz parameters are specified, the storage is specified
2304    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
2305    In the above case the values for d_nnz,o_nnz are:
2306 .vb
2307      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
2308      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
2309      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
2310 .ve
2311    Here the space allocated is sum of all the above values i.e 34, and
2312    hence pre-allocation is perfect.
2313 
2314    Level: intermediate
2315 
2316 .keywords: matrix, aij, compressed row, sparse, parallel
2317 
2318 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues()
2319 @*/
2320 int MatCreateMPIAIJ(MPI_Comm comm,int m,int n,int M,int N,int d_nz,int *d_nnz,int o_nz,int *o_nnz,Mat *A)
2321 {
2322   int ierr,size;
2323 
2324   PetscFunctionBegin;
2325   ierr = MatCreate(comm,m,n,M,N,A);CHKERRQ(ierr);
2326   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2327   if (size > 1) {
2328     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
2329     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
2330   } else {
2331     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
2332     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
2333   }
2334   PetscFunctionReturn(0);
2335 }
2336 
2337 #undef __FUNCT__
2338 #define __FUNCT__ "MatMPIAIJGetSeqAIJ"
2339 int MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,int **colmap)
2340 {
2341   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2342   PetscFunctionBegin;
2343   *Ad     = a->A;
2344   *Ao     = a->B;
2345   *colmap = a->garray;
2346   PetscFunctionReturn(0);
2347 }
2348