xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 83e1b59cb1046d00ed4e5740a19a4a527e6508b2)
1 #ifndef lint
2 static char vcid[] = "$Id: mpiaij.c,v 1.143 1996/05/07 20:43:35 balay Exp curfman $";
3 #endif
4 
5 #include "mpiaij.h"
6 #include "src/vec/vecimpl.h"
7 #include "src/inline/spops.h"
8 
9 /* local utility routine that creates a mapping from the global column
10 number to the local number in the off-diagonal part of the local
11 storage of the matrix.  This is done in a non scable way since the
12 length of colmap equals the global matrix length.
13 */
14 static int CreateColmap_Private(Mat mat)
15 {
16   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
17   Mat_SeqAIJ *B = (Mat_SeqAIJ*) aij->B->data;
18   int        n = B->n,i,shift = B->indexshift;
19 
20   aij->colmap = (int *) PetscMalloc(aij->N*sizeof(int));CHKPTRQ(aij->colmap);
21   PLogObjectMemory(mat,aij->N*sizeof(int));
22   PetscMemzero(aij->colmap,aij->N*sizeof(int));
23   for ( i=0; i<n; i++ ) aij->colmap[aij->garray[i]] = i-shift;
24   return 0;
25 }
26 
27 extern int DisAssemble_MPIAIJ(Mat);
28 
29 static int MatGetReordering_MPIAIJ(Mat mat,MatOrdering type,IS *rperm,IS *cperm)
30 {
31   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
32   int        ierr;
33   if (aij->size == 1) {
34     ierr = MatGetReordering(aij->A,type,rperm,cperm); CHKERRQ(ierr);
35   } else SETERRQ(1,"MatGetReordering_MPIAIJ:not supported in parallel");
36   return 0;
37 }
38 
39 static int MatSetValues_MPIAIJ(Mat mat,int m,int *im,int n,int *in,Scalar *v,InsertMode addv)
40 {
41   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
42   Mat_SeqAIJ *C = (Mat_SeqAIJ*) aij->A->data;
43   Scalar     value;
44   int        ierr,i,j, rstart = aij->rstart, rend = aij->rend;
45   int        cstart = aij->cstart, cend = aij->cend,row,col;
46   int        shift = C->indexshift,roworiented = aij->roworiented;
47 
48   if (aij->insertmode != NOT_SET_VALUES && aij->insertmode != addv) {
49     SETERRQ(1,"MatSetValues_MPIAIJ:Cannot mix inserts and adds");
50   }
51   aij->insertmode = addv;
52   for ( i=0; i<m; i++ ) {
53     if (im[i] < 0) SETERRQ(1,"MatSetValues_MPIAIJ:Negative row");
54     if (im[i] >= aij->M) SETERRQ(1,"MatSetValues_MPIAIJ:Row too large");
55     if (im[i] >= rstart && im[i] < rend) {
56       row = im[i] - rstart;
57       for ( j=0; j<n; j++ ) {
58         if (in[j] < 0) SETERRQ(1,"MatSetValues_MPIAIJ:Negative column");
59         if (in[j] >= aij->N) SETERRQ(1,"MatSetValues_MPIAIJ:Col too large");
60         if (in[j] >= cstart && in[j] < cend){
61           col = in[j] - cstart;
62           if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
63           ierr = MatSetValues(aij->A,1,&row,1,&col,&value,addv);CHKERRQ(ierr);
64         }
65         else {
66           if (mat->was_assembled) {
67             if (!aij->colmap) {ierr = CreateColmap_Private(mat);CHKERRQ(ierr);}
68             col = aij->colmap[in[j]] + shift;
69             if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
70               ierr = DisAssemble_MPIAIJ(mat); CHKERRQ(ierr);
71               col =  in[j];
72             }
73           }
74           else col = in[j];
75           if (roworiented) value = v[i*n+j]; else value = v[i+j*m];
76           ierr = MatSetValues(aij->B,1,&row,1,&col,&value,addv);CHKERRQ(ierr);
77         }
78       }
79     }
80     else {
81       if (roworiented) {
82         ierr = StashValues_Private(&aij->stash,im[i],n,in,v+i*n,addv);CHKERRQ(ierr);
83       }
84       else {
85         row = im[i];
86         for ( j=0; j<n; j++ ) {
87           ierr = StashValues_Private(&aij->stash,row,1,in+j,v+i+j*m,addv);CHKERRQ(ierr);
88         }
89       }
90     }
91   }
92   return 0;
93 }
94 
95 static int MatGetValues_MPIAIJ(Mat mat,int m,int *idxm,int n,int *idxn,Scalar *v)
96 {
97   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
98   Mat_SeqAIJ *C = (Mat_SeqAIJ*) aij->A->data;
99   int        ierr,i,j, rstart = aij->rstart, rend = aij->rend;
100   int        cstart = aij->cstart, cend = aij->cend,row,col;
101   int        shift = C->indexshift;
102 
103   for ( i=0; i<m; i++ ) {
104     if (idxm[i] < 0) SETERRQ(1,"MatGetValues_MPIAIJ:Negative row");
105     if (idxm[i] >= aij->M) SETERRQ(1,"MatGetValues_MPIAIJ:Row too large");
106     if (idxm[i] >= rstart && idxm[i] < rend) {
107       row = idxm[i] - rstart;
108       for ( j=0; j<n; j++ ) {
109         if (idxn[j] < 0) SETERRQ(1,"MatGetValues_MPIAIJ:Negative column");
110         if (idxn[j] >= aij->N) SETERRQ(1,"MatGetValues_MPIAIJ:Col too large");
111         if (idxn[j] >= cstart && idxn[j] < cend){
112           col = idxn[j] - cstart;
113           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j); CHKERRQ(ierr);
114         }
115         else {
116           col = aij->colmap[idxn[j]] + shift;
117           ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j); CHKERRQ(ierr);
118         }
119       }
120     }
121     else {
122       SETERRQ(1,"MatGetValues_MPIAIJ:Only local values currently supported");
123     }
124   }
125   return 0;
126 }
127 
128 static int MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
129 {
130   Mat_MPIAIJ  *aij = (Mat_MPIAIJ *) mat->data;
131   MPI_Comm    comm = mat->comm;
132   int         size = aij->size, *owners = aij->rowners;
133   int         rank = aij->rank,tag = mat->tag, *owner,*starts,count,ierr;
134   MPI_Request *send_waits,*recv_waits;
135   int         *nprocs,i,j,idx,*procs,nsends,nreceives,nmax,*work;
136   InsertMode  addv;
137   Scalar      *rvalues,*svalues;
138 
139   /* make sure all processors are either in INSERTMODE or ADDMODE */
140   MPI_Allreduce(&aij->insertmode,&addv,1,MPI_INT,MPI_BOR,comm);
141   if (addv == (ADD_VALUES|INSERT_VALUES)) {
142     SETERRQ(1,"MatAssemblyBegin_MPIAIJ:Some processors inserted others added");
143   }
144   aij->insertmode = addv; /* in case this processor had no cache */
145 
146   /*  first count number of contributors to each processor */
147   nprocs = (int *) PetscMalloc( 2*size*sizeof(int) ); CHKPTRQ(nprocs);
148   PetscMemzero(nprocs,2*size*sizeof(int)); procs = nprocs + size;
149   owner = (int *) PetscMalloc( (aij->stash.n+1)*sizeof(int) ); CHKPTRQ(owner);
150   for ( i=0; i<aij->stash.n; i++ ) {
151     idx = aij->stash.idx[i];
152     for ( j=0; j<size; j++ ) {
153       if (idx >= owners[j] && idx < owners[j+1]) {
154         nprocs[j]++; procs[j] = 1; owner[i] = j; break;
155       }
156     }
157   }
158   nsends = 0;  for ( i=0; i<size; i++ ) { nsends += procs[i];}
159 
160   /* inform other processors of number of messages and max length*/
161   work = (int *) PetscMalloc( size*sizeof(int) ); CHKPTRQ(work);
162   MPI_Allreduce(procs, work,size,MPI_INT,MPI_SUM,comm);
163   nreceives = work[rank];
164   MPI_Allreduce( nprocs, work,size,MPI_INT,MPI_MAX,comm);
165   nmax = work[rank];
166   PetscFree(work);
167 
168   /* post receives:
169        1) each message will consist of ordered pairs
170      (global index,value) we store the global index as a double
171      to simplify the message passing.
172        2) since we don't know how long each individual message is we
173      allocate the largest needed buffer for each receive. Potentially
174      this is a lot of wasted space.
175 
176 
177        This could be done better.
178   */
179   rvalues = (Scalar *) PetscMalloc(3*(nreceives+1)*(nmax+1)*sizeof(Scalar));
180   CHKPTRQ(rvalues);
181   recv_waits = (MPI_Request *) PetscMalloc((nreceives+1)*sizeof(MPI_Request));
182   CHKPTRQ(recv_waits);
183   for ( i=0; i<nreceives; i++ ) {
184     MPI_Irecv(rvalues+3*nmax*i,3*nmax,MPIU_SCALAR,MPI_ANY_SOURCE,tag,
185               comm,recv_waits+i);
186   }
187 
188   /* do sends:
189       1) starts[i] gives the starting index in svalues for stuff going to
190          the ith processor
191   */
192   svalues = (Scalar *) PetscMalloc(3*(aij->stash.n+1)*sizeof(Scalar));CHKPTRQ(svalues);
193   send_waits = (MPI_Request *) PetscMalloc( (nsends+1)*sizeof(MPI_Request));
194   CHKPTRQ(send_waits);
195   starts = (int *) PetscMalloc( size*sizeof(int) ); CHKPTRQ(starts);
196   starts[0] = 0;
197   for ( i=1; i<size; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
198   for ( i=0; i<aij->stash.n; i++ ) {
199     svalues[3*starts[owner[i]]]       = (Scalar)  aij->stash.idx[i];
200     svalues[3*starts[owner[i]]+1]     = (Scalar)  aij->stash.idy[i];
201     svalues[3*(starts[owner[i]]++)+2] =  aij->stash.array[i];
202   }
203   PetscFree(owner);
204   starts[0] = 0;
205   for ( i=1; i<size; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
206   count = 0;
207   for ( i=0; i<size; i++ ) {
208     if (procs[i]) {
209       MPI_Isend(svalues+3*starts[i],3*nprocs[i],MPIU_SCALAR,i,tag,
210                 comm,send_waits+count++);
211     }
212   }
213   PetscFree(starts); PetscFree(nprocs);
214 
215   /* Free cache space */
216   PLogInfo(0,"[%d]MatAssemblyBegin_MPIAIJ:Number of off processor values %d\n",rank,aij->stash.n);
217   ierr = StashDestroy_Private(&aij->stash); CHKERRQ(ierr);
218 
219   aij->svalues    = svalues;    aij->rvalues    = rvalues;
220   aij->nsends     = nsends;     aij->nrecvs     = nreceives;
221   aij->send_waits = send_waits; aij->recv_waits = recv_waits;
222   aij->rmax       = nmax;
223 
224   return 0;
225 }
226 extern int MatSetUpMultiply_MPIAIJ(Mat);
227 
228 static int MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
229 {
230   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
231   Mat_SeqAIJ *C = (Mat_SeqAIJ *) aij->A->data;
232   MPI_Status  *send_status,recv_status;
233   int         imdex,nrecvs = aij->nrecvs, count = nrecvs, i, n, ierr;
234   int         row,col,other_disassembled,shift = C->indexshift;
235   Scalar      *values,val;
236   InsertMode  addv = aij->insertmode;
237 
238   /*  wait on receives */
239   while (count) {
240     MPI_Waitany(nrecvs,aij->recv_waits,&imdex,&recv_status);
241     /* unpack receives into our local space */
242     values = aij->rvalues + 3*imdex*aij->rmax;
243     MPI_Get_count(&recv_status,MPIU_SCALAR,&n);
244     n = n/3;
245     for ( i=0; i<n; i++ ) {
246       row = (int) PetscReal(values[3*i]) - aij->rstart;
247       col = (int) PetscReal(values[3*i+1]);
248       val = values[3*i+2];
249       if (col >= aij->cstart && col < aij->cend) {
250         col -= aij->cstart;
251         MatSetValues(aij->A,1,&row,1,&col,&val,addv);
252       }
253       else {
254         if (mat->was_assembled) {
255           if (!aij->colmap) {ierr = CreateColmap_Private(mat);CHKERRQ(ierr);}
256           col = aij->colmap[col] + shift;
257           if (col < 0  && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
258             ierr = DisAssemble_MPIAIJ(mat); CHKERRQ(ierr);
259             col = (int) PetscReal(values[3*i+1]);
260           }
261         }
262         MatSetValues(aij->B,1,&row,1,&col,&val,addv);
263       }
264     }
265     count--;
266   }
267   PetscFree(aij->recv_waits); PetscFree(aij->rvalues);
268 
269   /* wait on sends */
270   if (aij->nsends) {
271     send_status = (MPI_Status *) PetscMalloc(aij->nsends*sizeof(MPI_Status));
272     CHKPTRQ(send_status);
273     MPI_Waitall(aij->nsends,aij->send_waits,send_status);
274     PetscFree(send_status);
275   }
276   PetscFree(aij->send_waits); PetscFree(aij->svalues);
277 
278   aij->insertmode = NOT_SET_VALUES;
279   ierr = MatAssemblyBegin(aij->A,mode); CHKERRQ(ierr);
280   ierr = MatAssemblyEnd(aij->A,mode); CHKERRQ(ierr);
281 
282   /* determine if any processor has disassembled, if so we must
283      also disassemble ourselfs, in order that we may reassemble. */
284   MPI_Allreduce(&mat->was_assembled,&other_disassembled,1,MPI_INT,MPI_PROD,mat->comm);
285   if (mat->was_assembled && !other_disassembled) {
286     ierr = DisAssemble_MPIAIJ(mat); CHKERRQ(ierr);
287   }
288 
289   if (!mat->was_assembled && mode == FINAL_ASSEMBLY) {
290     ierr = MatSetUpMultiply_MPIAIJ(mat); CHKERRQ(ierr);
291   }
292   ierr = MatAssemblyBegin(aij->B,mode); CHKERRQ(ierr);
293   ierr = MatAssemblyEnd(aij->B,mode); CHKERRQ(ierr);
294 
295   if (aij->rowvalues) {PetscFree(aij->rowvalues); aij->rowvalues = 0;}
296   return 0;
297 }
298 
299 static int MatZeroEntries_MPIAIJ(Mat A)
300 {
301   Mat_MPIAIJ *l = (Mat_MPIAIJ *) A->data;
302   int        ierr;
303   ierr = MatZeroEntries(l->A); CHKERRQ(ierr);
304   ierr = MatZeroEntries(l->B); CHKERRQ(ierr);
305   return 0;
306 }
307 
308 /* the code does not do the diagonal entries correctly unless the
309    matrix is square and the column and row owerships are identical.
310    This is a BUG. The only way to fix it seems to be to access
311    aij->A and aij->B directly and not through the MatZeroRows()
312    routine.
313 */
314 static int MatZeroRows_MPIAIJ(Mat A,IS is,Scalar *diag)
315 {
316   Mat_MPIAIJ     *l = (Mat_MPIAIJ *) A->data;
317   int            i,ierr,N, *rows,*owners = l->rowners,size = l->size;
318   int            *procs,*nprocs,j,found,idx,nsends,*work;
319   int            nmax,*svalues,*starts,*owner,nrecvs,rank = l->rank;
320   int            *rvalues,tag = A->tag,count,base,slen,n,*source;
321   int            *lens,imdex,*lrows,*values;
322   MPI_Comm       comm = A->comm;
323   MPI_Request    *send_waits,*recv_waits;
324   MPI_Status     recv_status,*send_status;
325   IS             istmp;
326 
327   ierr = ISGetSize(is,&N); CHKERRQ(ierr);
328   ierr = ISGetIndices(is,&rows); CHKERRQ(ierr);
329 
330   /*  first count number of contributors to each processor */
331   nprocs = (int *) PetscMalloc( 2*size*sizeof(int) ); CHKPTRQ(nprocs);
332   PetscMemzero(nprocs,2*size*sizeof(int)); procs = nprocs + size;
333   owner = (int *) PetscMalloc((N+1)*sizeof(int)); CHKPTRQ(owner); /* see note*/
334   for ( i=0; i<N; i++ ) {
335     idx = rows[i];
336     found = 0;
337     for ( j=0; j<size; j++ ) {
338       if (idx >= owners[j] && idx < owners[j+1]) {
339         nprocs[j]++; procs[j] = 1; owner[i] = j; found = 1; break;
340       }
341     }
342     if (!found) SETERRQ(1,"MatZeroRows_MPIAIJ:Index out of range");
343   }
344   nsends = 0;  for ( i=0; i<size; i++ ) { nsends += procs[i];}
345 
346   /* inform other processors of number of messages and max length*/
347   work = (int *) PetscMalloc( size*sizeof(int) ); CHKPTRQ(work);
348   MPI_Allreduce( procs, work,size,MPI_INT,MPI_SUM,comm);
349   nrecvs = work[rank];
350   MPI_Allreduce( nprocs, work,size,MPI_INT,MPI_MAX,comm);
351   nmax = work[rank];
352   PetscFree(work);
353 
354   /* post receives:   */
355   rvalues = (int *) PetscMalloc((nrecvs+1)*(nmax+1)*sizeof(int)); /*see note */
356   CHKPTRQ(rvalues);
357   recv_waits = (MPI_Request *) PetscMalloc((nrecvs+1)*sizeof(MPI_Request));
358   CHKPTRQ(recv_waits);
359   for ( i=0; i<nrecvs; i++ ) {
360     MPI_Irecv(rvalues+nmax*i,nmax,MPI_INT,MPI_ANY_SOURCE,tag,comm,recv_waits+i);
361   }
362 
363   /* do sends:
364       1) starts[i] gives the starting index in svalues for stuff going to
365          the ith processor
366   */
367   svalues = (int *) PetscMalloc( (N+1)*sizeof(int) ); CHKPTRQ(svalues);
368   send_waits = (MPI_Request *) PetscMalloc( (nsends+1)*sizeof(MPI_Request));
369   CHKPTRQ(send_waits);
370   starts = (int *) PetscMalloc( (size+1)*sizeof(int) ); CHKPTRQ(starts);
371   starts[0] = 0;
372   for ( i=1; i<size; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
373   for ( i=0; i<N; i++ ) {
374     svalues[starts[owner[i]]++] = rows[i];
375   }
376   ISRestoreIndices(is,&rows);
377 
378   starts[0] = 0;
379   for ( i=1; i<size+1; i++ ) { starts[i] = starts[i-1] + nprocs[i-1];}
380   count = 0;
381   for ( i=0; i<size; i++ ) {
382     if (procs[i]) {
383       MPI_Isend(svalues+starts[i],nprocs[i],MPI_INT,i,tag,comm,send_waits+count++);
384     }
385   }
386   PetscFree(starts);
387 
388   base = owners[rank];
389 
390   /*  wait on receives */
391   lens   = (int *) PetscMalloc( 2*(nrecvs+1)*sizeof(int) ); CHKPTRQ(lens);
392   source = lens + nrecvs;
393   count  = nrecvs; slen = 0;
394   while (count) {
395     MPI_Waitany(nrecvs,recv_waits,&imdex,&recv_status);
396     /* unpack receives into our local space */
397     MPI_Get_count(&recv_status,MPI_INT,&n);
398     source[imdex]  = recv_status.MPI_SOURCE;
399     lens[imdex]  = n;
400     slen += n;
401     count--;
402   }
403   PetscFree(recv_waits);
404 
405   /* move the data into the send scatter */
406   lrows = (int *) PetscMalloc( (slen+1)*sizeof(int) ); CHKPTRQ(lrows);
407   count = 0;
408   for ( i=0; i<nrecvs; i++ ) {
409     values = rvalues + i*nmax;
410     for ( j=0; j<lens[i]; j++ ) {
411       lrows[count++] = values[j] - base;
412     }
413   }
414   PetscFree(rvalues); PetscFree(lens);
415   PetscFree(owner); PetscFree(nprocs);
416 
417   /* actually zap the local rows */
418   ierr = ISCreateSeq(MPI_COMM_SELF,slen,lrows,&istmp);CHKERRQ(ierr);
419   PLogObjectParent(A,istmp);
420   PetscFree(lrows);
421   ierr = MatZeroRows(l->A,istmp,diag); CHKERRQ(ierr);
422   ierr = MatZeroRows(l->B,istmp,0); CHKERRQ(ierr);
423   ierr = ISDestroy(istmp); CHKERRQ(ierr);
424 
425   /* wait on sends */
426   if (nsends) {
427     send_status = (MPI_Status *) PetscMalloc(nsends*sizeof(MPI_Status));
428     CHKPTRQ(send_status);
429     MPI_Waitall(nsends,send_waits,send_status);
430     PetscFree(send_status);
431   }
432   PetscFree(send_waits); PetscFree(svalues);
433 
434   return 0;
435 }
436 
437 static int MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
438 {
439   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
440   int        ierr;
441 
442   ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_ALL,a->Mvctx); CHKERRQ(ierr);
443   ierr = (*a->A->ops.mult)(a->A,xx,yy); CHKERRQ(ierr);
444   ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_ALL,a->Mvctx); CHKERRQ(ierr);
445   ierr = (*a->B->ops.multadd)(a->B,a->lvec,yy,yy); CHKERRQ(ierr);
446   return 0;
447 }
448 
449 static int MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
450 {
451   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
452   int        ierr;
453   ierr = VecScatterBegin(xx,a->lvec,INSERT_VALUES,SCATTER_ALL,a->Mvctx);CHKERRQ(ierr);
454   ierr = (*a->A->ops.multadd)(a->A,xx,yy,zz); CHKERRQ(ierr);
455   ierr = VecScatterEnd(xx,a->lvec,INSERT_VALUES,SCATTER_ALL,a->Mvctx);CHKERRQ(ierr);
456   ierr = (*a->B->ops.multadd)(a->B,a->lvec,zz,zz); CHKERRQ(ierr);
457   return 0;
458 }
459 
460 static int MatMultTrans_MPIAIJ(Mat A,Vec xx,Vec yy)
461 {
462   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
463   int        ierr;
464 
465   /* do nondiagonal part */
466   ierr = (*a->B->ops.multtrans)(a->B,xx,a->lvec); CHKERRQ(ierr);
467   /* send it on its way */
468   ierr = VecScatterBegin(a->lvec,yy,ADD_VALUES,
469                 (ScatterMode)(SCATTER_ALL|SCATTER_REVERSE),a->Mvctx); CHKERRQ(ierr);
470   /* do local part */
471   ierr = (*a->A->ops.multtrans)(a->A,xx,yy); CHKERRQ(ierr);
472   /* receive remote parts: note this assumes the values are not actually */
473   /* inserted in yy until the next line, which is true for my implementation*/
474   /* but is not perhaps always true. */
475   ierr = VecScatterEnd(a->lvec,yy,ADD_VALUES,
476                   (ScatterMode)(SCATTER_ALL|SCATTER_REVERSE),a->Mvctx); CHKERRQ(ierr);
477   return 0;
478 }
479 
480 static int MatMultTransAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
481 {
482   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
483   int        ierr;
484 
485   /* do nondiagonal part */
486   ierr = (*a->B->ops.multtrans)(a->B,xx,a->lvec); CHKERRQ(ierr);
487   /* send it on its way */
488   ierr = VecScatterBegin(a->lvec,zz,ADD_VALUES,
489                  (ScatterMode)(SCATTER_ALL|SCATTER_REVERSE),a->Mvctx); CHKERRQ(ierr);
490   /* do local part */
491   ierr = (*a->A->ops.multtransadd)(a->A,xx,yy,zz); CHKERRQ(ierr);
492   /* receive remote parts: note this assumes the values are not actually */
493   /* inserted in yy until the next line, which is true for my implementation*/
494   /* but is not perhaps always true. */
495   ierr = VecScatterEnd(a->lvec,zz,ADD_VALUES,
496                   (ScatterMode)(SCATTER_ALL|SCATTER_REVERSE),a->Mvctx); CHKERRQ(ierr);
497   return 0;
498 }
499 
500 /*
501   This only works correctly for square matrices where the subblock A->A is the
502    diagonal block
503 */
504 static int MatGetDiagonal_MPIAIJ(Mat A,Vec v)
505 {
506   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
507   if (a->M != a->N)
508     SETERRQ(1,"MatGetDiagonal_MPIAIJ:Supports only square matrix where A->A is diag block");
509   return MatGetDiagonal(a->A,v);
510 }
511 
512 static int MatScale_MPIAIJ(Scalar *aa,Mat A)
513 {
514   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
515   int        ierr;
516   ierr = MatScale(aa,a->A); CHKERRQ(ierr);
517   ierr = MatScale(aa,a->B); CHKERRQ(ierr);
518   return 0;
519 }
520 
521 static int MatDestroy_MPIAIJ(PetscObject obj)
522 {
523   Mat        mat = (Mat) obj;
524   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
525   int        ierr;
526 #if defined(PETSC_LOG)
527   PLogObjectState(obj,"Rows=%d, Cols=%d",aij->M,aij->N);
528 #endif
529   PetscFree(aij->rowners);
530   ierr = MatDestroy(aij->A); CHKERRQ(ierr);
531   ierr = MatDestroy(aij->B); CHKERRQ(ierr);
532   if (aij->colmap) PetscFree(aij->colmap);
533   if (aij->garray) PetscFree(aij->garray);
534   if (aij->lvec)   VecDestroy(aij->lvec);
535   if (aij->Mvctx)  VecScatterDestroy(aij->Mvctx);
536   if (aij->rowvalues) PetscFree(aij->rowvalues);
537   PetscFree(aij);
538   PLogObjectDestroy(mat);
539   PetscHeaderDestroy(mat);
540   return 0;
541 }
542 #include "draw.h"
543 #include "pinclude/pviewer.h"
544 
545 static int MatView_MPIAIJ_Binary(Mat mat,Viewer viewer)
546 {
547   Mat_MPIAIJ  *aij = (Mat_MPIAIJ *) mat->data;
548   int         ierr;
549 
550   if (aij->size == 1) {
551     ierr = MatView(aij->A,viewer); CHKERRQ(ierr);
552   }
553   else SETERRQ(1,"MatView_MPIAIJ_Binary:Only uniprocessor output supported");
554   return 0;
555 }
556 
557 static int MatView_MPIAIJ_ASCIIorDraworMatlab(Mat mat,Viewer viewer)
558 {
559   Mat_MPIAIJ  *aij = (Mat_MPIAIJ *) mat->data;
560   Mat_SeqAIJ* C = (Mat_SeqAIJ*)aij->A->data;
561   int         ierr, format,shift = C->indexshift,rank;
562   FILE        *fd;
563   ViewerType  vtype;
564 
565   ierr = ViewerGetType(viewer,&vtype); CHKERRQ(ierr);
566   if (vtype  == ASCII_FILES_VIEWER || vtype == ASCII_FILE_VIEWER) {
567     ierr = ViewerGetFormat(viewer,&format);
568     if (format == ASCII_FORMAT_INFO_DETAILED) {
569       int nz, nzalloc, mem, flg;
570       MPI_Comm_rank(mat->comm,&rank);
571       ierr = ViewerASCIIGetPointer(viewer,&fd); CHKERRQ(ierr);
572       ierr = MatGetInfo(mat,MAT_LOCAL,&nz,&nzalloc,&mem);
573       ierr = OptionsHasName(PETSC_NULL,"-mat_aij_no_inode",&flg); CHKERRQ(ierr);
574       PetscSequentialPhaseBegin(mat->comm,1);
575       if (flg) fprintf(fd,"[%d] Local rows %d nz %d nz alloced %d mem %d, not using I-node routines\n",
576          rank,aij->m,nz,nzalloc,mem);
577       else fprintf(fd,"[%d] Local rows %d nz %d nz alloced %d mem %d, using I-node routines\n",
578          rank,aij->m,nz,nzalloc,mem);
579       ierr = MatGetInfo(aij->A,MAT_LOCAL,&nz,&nzalloc,&mem);
580       fprintf(fd,"[%d] on-diagonal part: nz %d \n",rank,nz);
581       ierr = MatGetInfo(aij->B,MAT_LOCAL,&nz,&nzalloc,&mem);
582       fprintf(fd,"[%d] off-diagonal part: nz %d \n",rank,nz);
583       fflush(fd);
584       PetscSequentialPhaseEnd(mat->comm,1);
585       ierr = VecScatterView(aij->Mvctx,viewer); CHKERRQ(ierr);
586       return 0;
587     }
588     else if (format == ASCII_FORMAT_INFO) {
589       return 0;
590     }
591   }
592 
593   if (vtype == DRAW_VIEWER) {
594     Draw       draw;
595     PetscTruth isnull;
596     ierr = ViewerDrawGetDraw(viewer,&draw); CHKERRQ(ierr);
597     ierr = DrawIsNull(draw,&isnull); CHKERRQ(ierr); if (isnull) return 0;
598   }
599 
600   if (vtype == ASCII_FILE_VIEWER) {
601     ierr = ViewerASCIIGetPointer(viewer,&fd); CHKERRQ(ierr);
602     PetscSequentialPhaseBegin(mat->comm,1);
603     fprintf(fd,"[%d] rows %d starts %d ends %d cols %d starts %d ends %d\n",
604            aij->rank,aij->m,aij->rstart,aij->rend,aij->n,aij->cstart,
605            aij->cend);
606     ierr = MatView(aij->A,viewer); CHKERRQ(ierr);
607     ierr = MatView(aij->B,viewer); CHKERRQ(ierr);
608     fflush(fd);
609     PetscSequentialPhaseEnd(mat->comm,1);
610   }
611   else {
612     int size = aij->size;
613     rank = aij->rank;
614     if (size == 1) {
615       ierr = MatView(aij->A,viewer); CHKERRQ(ierr);
616     }
617     else {
618       /* assemble the entire matrix onto first processor. */
619       Mat         A;
620       Mat_SeqAIJ *Aloc;
621       int         M = aij->M, N = aij->N,m,*ai,*aj,row,*cols,i,*ct;
622       Scalar      *a;
623 
624       if (!rank) {
625         ierr = MatCreateMPIAIJ(mat->comm,M,N,M,N,0,PETSC_NULL,0,PETSC_NULL,&A);
626                CHKERRQ(ierr);
627       }
628       else {
629         ierr = MatCreateMPIAIJ(mat->comm,0,0,M,N,0,PETSC_NULL,0,PETSC_NULL,&A);
630                CHKERRQ(ierr);
631       }
632       PLogObjectParent(mat,A);
633 
634       /* copy over the A part */
635       Aloc = (Mat_SeqAIJ*) aij->A->data;
636       m = Aloc->m; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
637       row = aij->rstart;
638       for ( i=0; i<ai[m]+shift; i++ ) {aj[i] += aij->cstart + shift;}
639       for ( i=0; i<m; i++ ) {
640         ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
641         row++; a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
642       }
643       aj = Aloc->j;
644       for ( i=0; i<ai[m]+shift; i++ ) {aj[i] -= aij->cstart + shift;}
645 
646       /* copy over the B part */
647       Aloc = (Mat_SeqAIJ*) aij->B->data;
648       m = Aloc->m;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
649       row = aij->rstart;
650       ct = cols = (int *) PetscMalloc( (ai[m]+1)*sizeof(int) ); CHKPTRQ(cols);
651       for ( i=0; i<ai[m]+shift; i++ ) {cols[i] = aij->garray[aj[i]+shift];}
652       for ( i=0; i<m; i++ ) {
653         ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
654         row++; a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
655       }
656       PetscFree(ct);
657       ierr = MatAssemblyBegin(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
658       ierr = MatAssemblyEnd(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
659       if (!rank) {
660         ierr = MatView(((Mat_MPIAIJ*)(A->data))->A,viewer); CHKERRQ(ierr);
661       }
662       ierr = MatDestroy(A); CHKERRQ(ierr);
663     }
664   }
665   return 0;
666 }
667 
668 static int MatView_MPIAIJ(PetscObject obj,Viewer viewer)
669 {
670   Mat         mat = (Mat) obj;
671   int         ierr;
672   ViewerType  vtype;
673 
674   if (!viewer) {
675     viewer = STDOUT_VIEWER_SELF;
676   }
677   ierr = ViewerGetType(viewer,&vtype); CHKERRQ(ierr);
678   if (vtype == ASCII_FILE_VIEWER || vtype == ASCII_FILES_VIEWER ||
679       vtype == DRAW_VIEWER       || vtype == MATLAB_VIEWER) {
680     ierr = MatView_MPIAIJ_ASCIIorDraworMatlab(mat,viewer); CHKERRQ(ierr);
681   }
682   else if (vtype == BINARY_FILE_VIEWER) {
683     return MatView_MPIAIJ_Binary(mat,viewer);
684   }
685   return 0;
686 }
687 
688 /*
689     This has to provide several versions.
690 
691      1) per sequential
692      2) a) use only local smoothing updating outer values only once.
693         b) local smoothing updating outer values each inner iteration
694      3) color updating out values betwen colors.
695 */
696 static int MatRelax_MPIAIJ(Mat matin,Vec bb,double omega,MatSORType flag,
697                            double fshift,int its,Vec xx)
698 {
699   Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
700   Mat        AA = mat->A, BB = mat->B;
701   Mat_SeqAIJ *A = (Mat_SeqAIJ *) AA->data, *B = (Mat_SeqAIJ *)BB->data;
702   Scalar     zero = 0.0,*b,*x,*xs,*ls,d,*v,sum,scale,*t,*ts;
703   int        ierr,*idx, *diag;
704   int        n = mat->n, m = mat->m, i,shift = A->indexshift;
705   Vec        tt;
706 
707   VecGetArray(xx,&x); VecGetArray(bb,&b); VecGetArray(mat->lvec,&ls);
708   xs = x + shift; /* shift by one for index start of 1 */
709   ls = ls + shift;
710   if (!A->diag) {if ((ierr = MatMarkDiag_SeqAIJ(AA))) return ierr;}
711   diag = A->diag;
712   if (flag == SOR_APPLY_UPPER || flag == SOR_APPLY_LOWER) {
713     SETERRQ(1,"MatRelax_MPIAIJ:Option not supported");
714   }
715   if (flag & SOR_EISENSTAT) {
716     /* Let  A = L + U + D; where L is lower trianglar,
717     U is upper triangular, E is diagonal; This routine applies
718 
719             (L + E)^{-1} A (U + E)^{-1}
720 
721     to a vector efficiently using Eisenstat's trick. This is for
722     the case of SSOR preconditioner, so E is D/omega where omega
723     is the relaxation factor.
724     */
725     ierr = VecDuplicate(xx,&tt); CHKERRQ(ierr);
726     PLogObjectParent(matin,tt);
727     VecGetArray(tt,&t);
728     scale = (2.0/omega) - 1.0;
729     /*  x = (E + U)^{-1} b */
730     VecSet(&zero,mat->lvec);
731     ierr = VecPipelineBegin(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
732                               mat->Mvctx); CHKERRQ(ierr);
733     for ( i=m-1; i>-1; i-- ) {
734       n    = A->i[i+1] - diag[i] - 1;
735       idx  = A->j + diag[i] + !shift;
736       v    = A->a + diag[i] + !shift;
737       sum  = b[i];
738       SPARSEDENSEMDOT(sum,xs,v,idx,n);
739       d    = fshift + A->a[diag[i]+shift];
740       n    = B->i[i+1] - B->i[i];
741       idx  = B->j + B->i[i] + shift;
742       v    = B->a + B->i[i] + shift;
743       SPARSEDENSEMDOT(sum,ls,v,idx,n);
744       x[i] = omega*(sum/d);
745     }
746     ierr = VecPipelineEnd(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
747                             mat->Mvctx); CHKERRQ(ierr);
748 
749     /*  t = b - (2*E - D)x */
750     v = A->a;
751     for ( i=0; i<m; i++ ) { t[i] = b[i] - scale*(v[*diag++ + shift])*x[i]; }
752 
753     /*  t = (E + L)^{-1}t */
754     ts = t + shift; /* shifted by one for index start of a or mat->j*/
755     diag = A->diag;
756     VecSet(&zero,mat->lvec);
757     ierr = VecPipelineBegin(tt,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
758                                                  mat->Mvctx); CHKERRQ(ierr);
759     for ( i=0; i<m; i++ ) {
760       n    = diag[i] - A->i[i];
761       idx  = A->j + A->i[i] + shift;
762       v    = A->a + A->i[i] + shift;
763       sum  = t[i];
764       SPARSEDENSEMDOT(sum,ts,v,idx,n);
765       d    = fshift + A->a[diag[i]+shift];
766       n    = B->i[i+1] - B->i[i];
767       idx  = B->j + B->i[i] + shift;
768       v    = B->a + B->i[i] + shift;
769       SPARSEDENSEMDOT(sum,ls,v,idx,n);
770       t[i] = omega*(sum/d);
771     }
772     ierr = VecPipelineEnd(tt,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
773                                                     mat->Mvctx); CHKERRQ(ierr);
774     /*  x = x + t */
775     for ( i=0; i<m; i++ ) { x[i] += t[i]; }
776     VecDestroy(tt);
777     return 0;
778   }
779 
780 
781   if ((flag & SOR_SYMMETRIC_SWEEP) == SOR_SYMMETRIC_SWEEP){
782     if (flag & SOR_ZERO_INITIAL_GUESS) {
783       VecSet(&zero,mat->lvec); VecSet(&zero,xx);
784     }
785     else {
786       ierr=VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_UP,mat->Mvctx);
787       CHKERRQ(ierr);
788       ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_UP,mat->Mvctx);
789       CHKERRQ(ierr);
790     }
791     while (its--) {
792       /* go down through the rows */
793       ierr = VecPipelineBegin(xx,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
794                               mat->Mvctx); CHKERRQ(ierr);
795       for ( i=0; i<m; i++ ) {
796         n    = A->i[i+1] - A->i[i];
797         idx  = A->j + A->i[i] + shift;
798         v    = A->a + A->i[i] + shift;
799         sum  = b[i];
800         SPARSEDENSEMDOT(sum,xs,v,idx,n);
801         d    = fshift + A->a[diag[i]+shift];
802         n    = B->i[i+1] - B->i[i];
803         idx  = B->j + B->i[i] + shift;
804         v    = B->a + B->i[i] + shift;
805         SPARSEDENSEMDOT(sum,ls,v,idx,n);
806         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
807       }
808       ierr = VecPipelineEnd(xx,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
809                             mat->Mvctx); CHKERRQ(ierr);
810       /* come up through the rows */
811       ierr = VecPipelineBegin(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
812                               mat->Mvctx); CHKERRQ(ierr);
813       for ( i=m-1; i>-1; i-- ) {
814         n    = A->i[i+1] - A->i[i];
815         idx  = A->j + A->i[i] + shift;
816         v    = A->a + A->i[i] + shift;
817         sum  = b[i];
818         SPARSEDENSEMDOT(sum,xs,v,idx,n);
819         d    = fshift + A->a[diag[i]+shift];
820         n    = B->i[i+1] - B->i[i];
821         idx  = B->j + B->i[i] + shift;
822         v    = B->a + B->i[i] + shift;
823         SPARSEDENSEMDOT(sum,ls,v,idx,n);
824         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
825       }
826       ierr = VecPipelineEnd(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
827                             mat->Mvctx); CHKERRQ(ierr);
828     }
829   }
830   else if (flag & SOR_FORWARD_SWEEP){
831     if (flag & SOR_ZERO_INITIAL_GUESS) {
832       VecSet(&zero,mat->lvec);
833       ierr = VecPipelineBegin(xx,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
834                               mat->Mvctx); CHKERRQ(ierr);
835       for ( i=0; i<m; i++ ) {
836         n    = diag[i] - A->i[i];
837         idx  = A->j + A->i[i] + shift;
838         v    = A->a + A->i[i] + shift;
839         sum  = b[i];
840         SPARSEDENSEMDOT(sum,xs,v,idx,n);
841         d    = fshift + A->a[diag[i]+shift];
842         n    = B->i[i+1] - B->i[i];
843         idx  = B->j + B->i[i] + shift;
844         v    = B->a + B->i[i] + shift;
845         SPARSEDENSEMDOT(sum,ls,v,idx,n);
846         x[i] = omega*(sum/d);
847       }
848       ierr = VecPipelineEnd(xx,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
849                             mat->Mvctx); CHKERRQ(ierr);
850       its--;
851     }
852     while (its--) {
853       ierr=VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_UP,mat->Mvctx);
854       CHKERRQ(ierr);
855       ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_UP,mat->Mvctx);
856       CHKERRQ(ierr);
857       ierr = VecPipelineBegin(xx,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
858                               mat->Mvctx); CHKERRQ(ierr);
859       for ( i=0; i<m; i++ ) {
860         n    = A->i[i+1] - A->i[i];
861         idx  = A->j + A->i[i] + shift;
862         v    = A->a + A->i[i] + shift;
863         sum  = b[i];
864         SPARSEDENSEMDOT(sum,xs,v,idx,n);
865         d    = fshift + A->a[diag[i]+shift];
866         n    = B->i[i+1] - B->i[i];
867         idx  = B->j + B->i[i] + shift;
868         v    = B->a + B->i[i] + shift;
869         SPARSEDENSEMDOT(sum,ls,v,idx,n);
870         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
871       }
872       ierr = VecPipelineEnd(xx,mat->lvec,INSERT_VALUES,PIPELINE_DOWN,
873                             mat->Mvctx); CHKERRQ(ierr);
874     }
875   }
876   else if (flag & SOR_BACKWARD_SWEEP){
877     if (flag & SOR_ZERO_INITIAL_GUESS) {
878       VecSet(&zero,mat->lvec);
879       ierr = VecPipelineBegin(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
880                               mat->Mvctx); CHKERRQ(ierr);
881       for ( i=m-1; i>-1; i-- ) {
882         n    = A->i[i+1] - diag[i] - 1;
883         idx  = A->j + diag[i] + !shift;
884         v    = A->a + diag[i] + !shift;
885         sum  = b[i];
886         SPARSEDENSEMDOT(sum,xs,v,idx,n);
887         d    = fshift + A->a[diag[i]+shift];
888         n    = B->i[i+1] - B->i[i];
889         idx  = B->j + B->i[i] + shift;
890         v    = B->a + B->i[i] + shift;
891         SPARSEDENSEMDOT(sum,ls,v,idx,n);
892         x[i] = omega*(sum/d);
893       }
894       ierr = VecPipelineEnd(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
895                             mat->Mvctx); CHKERRQ(ierr);
896       its--;
897     }
898     while (its--) {
899       ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_DOWN,
900                             mat->Mvctx); CHKERRQ(ierr);
901       ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_DOWN,
902                             mat->Mvctx); CHKERRQ(ierr);
903       ierr = VecPipelineBegin(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
904                               mat->Mvctx); CHKERRQ(ierr);
905       for ( i=m-1; i>-1; i-- ) {
906         n    = A->i[i+1] - A->i[i];
907         idx  = A->j + A->i[i] + shift;
908         v    = A->a + A->i[i] + shift;
909         sum  = b[i];
910         SPARSEDENSEMDOT(sum,xs,v,idx,n);
911         d    = fshift + A->a[diag[i]+shift];
912         n    = B->i[i+1] - B->i[i];
913         idx  = B->j + B->i[i] + shift;
914         v    = B->a + B->i[i] + shift;
915         SPARSEDENSEMDOT(sum,ls,v,idx,n);
916         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
917       }
918       ierr = VecPipelineEnd(xx,mat->lvec,INSERT_VALUES,PIPELINE_UP,
919                             mat->Mvctx); CHKERRQ(ierr);
920     }
921   }
922   else if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP){
923     if (flag & SOR_ZERO_INITIAL_GUESS) {
924       return (*mat->A->ops.relax)(mat->A,bb,omega,flag,fshift,its,xx);
925     }
926     ierr=VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_ALL,mat->Mvctx);
927     CHKERRQ(ierr);
928     ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_ALL,mat->Mvctx);
929     CHKERRQ(ierr);
930     while (its--) {
931       /* go down through the rows */
932       for ( i=0; i<m; i++ ) {
933         n    = A->i[i+1] - A->i[i];
934         idx  = A->j + A->i[i] + shift;
935         v    = A->a + A->i[i] + shift;
936         sum  = b[i];
937         SPARSEDENSEMDOT(sum,xs,v,idx,n);
938         d    = fshift + A->a[diag[i]+shift];
939         n    = B->i[i+1] - B->i[i];
940         idx  = B->j + B->i[i] + shift;
941         v    = B->a + B->i[i] + shift;
942         SPARSEDENSEMDOT(sum,ls,v,idx,n);
943         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
944       }
945       /* come up through the rows */
946       for ( i=m-1; i>-1; i-- ) {
947         n    = A->i[i+1] - A->i[i];
948         idx  = A->j + A->i[i] + shift;
949         v    = A->a + A->i[i] + shift;
950         sum  = b[i];
951         SPARSEDENSEMDOT(sum,xs,v,idx,n);
952         d    = fshift + A->a[diag[i]+shift];
953         n    = B->i[i+1] - B->i[i];
954         idx  = B->j + B->i[i] + shift;
955         v    = B->a + B->i[i] + shift;
956         SPARSEDENSEMDOT(sum,ls,v,idx,n);
957         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
958       }
959     }
960   }
961   else if (flag & SOR_LOCAL_FORWARD_SWEEP){
962     if (flag & SOR_ZERO_INITIAL_GUESS) {
963       return (*mat->A->ops.relax)(mat->A,bb,omega,flag,fshift,its,xx);
964     }
965     ierr=VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_ALL,mat->Mvctx);
966     CHKERRQ(ierr);
967     ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_ALL,mat->Mvctx);
968     CHKERRQ(ierr);
969     while (its--) {
970       for ( i=0; i<m; i++ ) {
971         n    = A->i[i+1] - A->i[i];
972         idx  = A->j + A->i[i] + shift;
973         v    = A->a + A->i[i] + shift;
974         sum  = b[i];
975         SPARSEDENSEMDOT(sum,xs,v,idx,n);
976         d    = fshift + A->a[diag[i]+shift];
977         n    = B->i[i+1] - B->i[i];
978         idx  = B->j + B->i[i] + shift;
979         v    = B->a + B->i[i] + shift;
980         SPARSEDENSEMDOT(sum,ls,v,idx,n);
981         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
982       }
983     }
984   }
985   else if (flag & SOR_LOCAL_BACKWARD_SWEEP){
986     if (flag & SOR_ZERO_INITIAL_GUESS) {
987       return (*mat->A->ops.relax)(mat->A,bb,omega,flag,fshift,its,xx);
988     }
989     ierr = VecScatterBegin(xx,mat->lvec,INSERT_VALUES,SCATTER_ALL,
990                             mat->Mvctx); CHKERRQ(ierr);
991     ierr = VecScatterEnd(xx,mat->lvec,INSERT_VALUES,SCATTER_ALL,
992                             mat->Mvctx); CHKERRQ(ierr);
993     while (its--) {
994       for ( i=m-1; i>-1; i-- ) {
995         n    = A->i[i+1] - A->i[i];
996         idx  = A->j + A->i[i] + shift;
997         v    = A->a + A->i[i] + shift;
998         sum  = b[i];
999         SPARSEDENSEMDOT(sum,xs,v,idx,n);
1000         d    = fshift + A->a[diag[i]+shift];
1001         n    = B->i[i+1] - B->i[i];
1002         idx  = B->j + B->i[i] + shift;
1003         v    = B->a + B->i[i] + shift;
1004         SPARSEDENSEMDOT(sum,ls,v,idx,n);
1005         x[i] = (1. - omega)*x[i] + omega*(sum/d + x[i]);
1006       }
1007     }
1008   }
1009   return 0;
1010 }
1011 
1012 static int MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,int *nz,
1013                              int *nzalloc,int *mem)
1014 {
1015   Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
1016   Mat        A = mat->A, B = mat->B;
1017   int        ierr, isend[3], irecv[3], nzA, nzallocA, memA;
1018 
1019   ierr = MatGetInfo(A,MAT_LOCAL,&nzA,&nzallocA,&memA); CHKERRQ(ierr);
1020   ierr = MatGetInfo(B,MAT_LOCAL,&isend[0],&isend[1],&isend[2]); CHKERRQ(ierr);
1021   isend[0] += nzA; isend[1] += nzallocA; isend[2] += memA;
1022   if (flag == MAT_LOCAL) {
1023     if (nz)       *nz      = isend[0];
1024     if (nzalloc)  *nzalloc = isend[1];
1025     if (mem)      *mem     = isend[2];
1026   } else if (flag == MAT_GLOBAL_MAX) {
1027     MPI_Allreduce( isend, irecv,3,MPI_INT,MPI_MAX,matin->comm);
1028     if (nz)      *nz      = irecv[0];
1029     if (nzalloc) *nzalloc = irecv[1];
1030     if (mem)     *mem     = irecv[2];
1031   } else if (flag == MAT_GLOBAL_SUM) {
1032     MPI_Allreduce( isend, irecv,3,MPI_INT,MPI_SUM,matin->comm);
1033     if (nz)      *nz      = irecv[0];
1034     if (nzalloc) *nzalloc = irecv[1];
1035     if (mem)     *mem     = irecv[2];
1036   }
1037   return 0;
1038 }
1039 
1040 extern int MatLUFactorSymbolic_MPIAIJ(Mat,IS,IS,double,Mat*);
1041 extern int MatLUFactorNumeric_MPIAIJ(Mat,Mat*);
1042 extern int MatLUFactor_MPIAIJ(Mat,IS,IS,double);
1043 extern int MatILUFactorSymbolic_MPIAIJ(Mat,IS,IS,double,int,Mat *);
1044 extern int MatSolve_MPIAIJ(Mat,Vec,Vec);
1045 extern int MatSolveAdd_MPIAIJ(Mat,Vec,Vec,Vec);
1046 extern int MatSolveTrans_MPIAIJ(Mat,Vec,Vec);
1047 extern int MatSolveTransAdd_MPIAIJ(Mat,Vec,Vec,Vec);
1048 
1049 static int MatSetOption_MPIAIJ(Mat A,MatOption op)
1050 {
1051   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
1052 
1053   if (op == NO_NEW_NONZERO_LOCATIONS ||
1054       op == YES_NEW_NONZERO_LOCATIONS ||
1055       op == COLUMNS_SORTED ||
1056       op == ROW_ORIENTED) {
1057         MatSetOption(a->A,op);
1058         MatSetOption(a->B,op);
1059   }
1060   else if (op == ROWS_SORTED ||
1061            op == SYMMETRIC_MATRIX ||
1062            op == STRUCTURALLY_SYMMETRIC_MATRIX ||
1063            op == YES_NEW_DIAGONALS)
1064     PLogInfo(A,"Info:MatSetOption_MPIAIJ:Option ignored\n");
1065   else if (op == COLUMN_ORIENTED) {
1066     a->roworiented = 0;
1067     MatSetOption(a->A,op);
1068     MatSetOption(a->B,op);
1069   }
1070   else if (op == NO_NEW_DIAGONALS)
1071     {SETERRQ(PETSC_ERR_SUP,"MatSetOption_MPIAIJ:NO_NEW_DIAGONALS");}
1072   else
1073     {SETERRQ(PETSC_ERR_SUP,"MatSetOption_MPIAIJ:unknown option");}
1074   return 0;
1075 }
1076 
1077 static int MatGetSize_MPIAIJ(Mat matin,int *m,int *n)
1078 {
1079   Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
1080   *m = mat->M; *n = mat->N;
1081   return 0;
1082 }
1083 
1084 static int MatGetLocalSize_MPIAIJ(Mat matin,int *m,int *n)
1085 {
1086   Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
1087   *m = mat->m; *n = mat->N;
1088   return 0;
1089 }
1090 
1091 static int MatGetOwnershipRange_MPIAIJ(Mat matin,int *m,int *n)
1092 {
1093   Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
1094   *m = mat->rstart; *n = mat->rend;
1095   return 0;
1096 }
1097 
1098 extern int MatGetRow_SeqAIJ(Mat,int,int*,int**,Scalar**);
1099 extern int MatRestoreRow_SeqAIJ(Mat,int,int*,int**,Scalar**);
1100 
1101 int MatGetRow_MPIAIJ(Mat matin,int row,int *nz,int **idx,Scalar **v)
1102 {
1103   Mat_MPIAIJ *mat = (Mat_MPIAIJ *) matin->data;
1104   Scalar     *vworkA, *vworkB, **pvA, **pvB,*v_p;
1105   int        i, ierr, *cworkA, *cworkB, **pcA, **pcB, cstart = mat->cstart;
1106   int        nztot, nzA, nzB, lrow, rstart = mat->rstart, rend = mat->rend;
1107   int        *cmap, *idx_p;
1108 
1109   if (mat->getrowactive == PETSC_TRUE) SETERRQ(1,"MatGetRow_MPIAIJ:Already active");
1110   mat->getrowactive = PETSC_TRUE;
1111 
1112   if (!mat->rowvalues && (idx || v)) {
1113     /*
1114         allocate enough space to hold information from the longest row.
1115     */
1116     Mat_SeqAIJ *Aa = (Mat_SeqAIJ *) mat->A->data,*Ba = (Mat_SeqAIJ *) mat->B->data;
1117     int     max = 1,n = mat->n,tmp;
1118     for ( i=0; i<n; i++ ) {
1119       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1120       if (max < tmp) { max = tmp; }
1121     }
1122     mat->rowvalues = (Scalar *) PetscMalloc( max*(sizeof(int)+sizeof(Scalar)));
1123     CHKPTRQ(mat->rowvalues);
1124     mat->rowindices = (int *) (mat->rowvalues + max);
1125   }
1126 
1127 
1128   if (row < rstart || row >= rend) SETERRQ(1,"MatGetRow_MPIAIJ:Only local rows")
1129   lrow = row - rstart;
1130 
1131   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1132   if (!v)   {pvA = 0; pvB = 0;}
1133   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1134   ierr = (*mat->A->ops.getrow)(mat->A,lrow,&nzA,pcA,pvA); CHKERRQ(ierr);
1135   ierr = (*mat->B->ops.getrow)(mat->B,lrow,&nzB,pcB,pvB); CHKERRQ(ierr);
1136   nztot = nzA + nzB;
1137 
1138   cmap  = mat->garray;
1139   if (v  || idx) {
1140     if (nztot) {
1141       /* Sort by increasing column numbers, assuming A and B already sorted */
1142       int imark = -1;
1143       if (v) {
1144         *v = v_p = mat->rowvalues;
1145         for ( i=0; i<nzB; i++ ) {
1146           if (cmap[cworkB[i]] < cstart)   v_p[i] = vworkB[i];
1147           else break;
1148         }
1149         imark = i;
1150         for ( i=0; i<nzA; i++ )     v_p[imark+i] = vworkA[i];
1151         for ( i=imark; i<nzB; i++ ) v_p[nzA+i]   = vworkB[i];
1152       }
1153       if (idx) {
1154         *idx = idx_p = mat->rowindices;
1155         if (imark > -1) {
1156           for ( i=0; i<imark; i++ ) {
1157             idx_p[i] = cmap[cworkB[i]];
1158           }
1159         } else {
1160           for ( i=0; i<nzB; i++ ) {
1161             if (cmap[cworkB[i]] < cstart)   idx_p[i] = cmap[cworkB[i]];
1162             else break;
1163           }
1164           imark = i;
1165         }
1166         for ( i=0; i<nzA; i++ )     idx_p[imark+i] = cstart + cworkA[i];
1167         for ( i=imark; i<nzB; i++ ) idx_p[nzA+i]   = cmap[cworkB[i]];
1168       }
1169     }
1170     else {*idx = 0; *v=0;}
1171   }
1172   *nz = nztot;
1173   ierr = (*mat->A->ops.restorerow)(mat->A,lrow,&nzA,pcA,pvA); CHKERRQ(ierr);
1174   ierr = (*mat->B->ops.restorerow)(mat->B,lrow,&nzB,pcB,pvB); CHKERRQ(ierr);
1175   return 0;
1176 }
1177 
1178 int MatRestoreRow_MPIAIJ(Mat mat,int row,int *nz,int **idx,Scalar **v)
1179 {
1180   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
1181   if (aij->getrowactive == PETSC_FALSE) {
1182     SETERRQ(1,"MatRestoreRow_MPIAIJ:MatGetRow not called");
1183   }
1184   aij->getrowactive = PETSC_FALSE;
1185   return 0;
1186 }
1187 
1188 static int MatNorm_MPIAIJ(Mat mat,NormType type,double *norm)
1189 {
1190   Mat_MPIAIJ *aij = (Mat_MPIAIJ *) mat->data;
1191   Mat_SeqAIJ *amat = (Mat_SeqAIJ*) aij->A->data, *bmat = (Mat_SeqAIJ*) aij->B->data;
1192   int        ierr, i, j, cstart = aij->cstart,shift = amat->indexshift;
1193   double     sum = 0.0;
1194   Scalar     *v;
1195 
1196   if (aij->size == 1) {
1197     ierr =  MatNorm(aij->A,type,norm); CHKERRQ(ierr);
1198   } else {
1199     if (type == NORM_FROBENIUS) {
1200       v = amat->a;
1201       for (i=0; i<amat->nz; i++ ) {
1202 #if defined(PETSC_COMPLEX)
1203         sum += real(conj(*v)*(*v)); v++;
1204 #else
1205         sum += (*v)*(*v); v++;
1206 #endif
1207       }
1208       v = bmat->a;
1209       for (i=0; i<bmat->nz; i++ ) {
1210 #if defined(PETSC_COMPLEX)
1211         sum += real(conj(*v)*(*v)); v++;
1212 #else
1213         sum += (*v)*(*v); v++;
1214 #endif
1215       }
1216       MPI_Allreduce(&sum,norm,1,MPI_DOUBLE,MPI_SUM,mat->comm);
1217       *norm = sqrt(*norm);
1218     }
1219     else if (type == NORM_1) { /* max column norm */
1220       double *tmp, *tmp2;
1221       int    *jj, *garray = aij->garray;
1222       tmp  = (double *) PetscMalloc( aij->N*sizeof(double) ); CHKPTRQ(tmp);
1223       tmp2 = (double *) PetscMalloc( aij->N*sizeof(double) ); CHKPTRQ(tmp2);
1224       PetscMemzero(tmp,aij->N*sizeof(double));
1225       *norm = 0.0;
1226       v = amat->a; jj = amat->j;
1227       for ( j=0; j<amat->nz; j++ ) {
1228         tmp[cstart + *jj++ + shift] += PetscAbsScalar(*v);  v++;
1229       }
1230       v = bmat->a; jj = bmat->j;
1231       for ( j=0; j<bmat->nz; j++ ) {
1232         tmp[garray[*jj++ + shift]] += PetscAbsScalar(*v); v++;
1233       }
1234       MPI_Allreduce(tmp,tmp2,aij->N,MPI_DOUBLE,MPI_SUM,mat->comm);
1235       for ( j=0; j<aij->N; j++ ) {
1236         if (tmp2[j] > *norm) *norm = tmp2[j];
1237       }
1238       PetscFree(tmp); PetscFree(tmp2);
1239     }
1240     else if (type == NORM_INFINITY) { /* max row norm */
1241       double ntemp = 0.0;
1242       for ( j=0; j<amat->m; j++ ) {
1243         v = amat->a + amat->i[j] + shift;
1244         sum = 0.0;
1245         for ( i=0; i<amat->i[j+1]-amat->i[j]; i++ ) {
1246           sum += PetscAbsScalar(*v); v++;
1247         }
1248         v = bmat->a + bmat->i[j] + shift;
1249         for ( i=0; i<bmat->i[j+1]-bmat->i[j]; i++ ) {
1250           sum += PetscAbsScalar(*v); v++;
1251         }
1252         if (sum > ntemp) ntemp = sum;
1253       }
1254       MPI_Allreduce(&ntemp,norm,1,MPI_DOUBLE,MPI_MAX,mat->comm);
1255     }
1256     else {
1257       SETERRQ(1,"MatNorm_MPIAIJ:No support for two norm");
1258     }
1259   }
1260   return 0;
1261 }
1262 
1263 static int MatTranspose_MPIAIJ(Mat A,Mat *matout)
1264 {
1265   Mat_MPIAIJ *a = (Mat_MPIAIJ *) A->data;
1266   Mat_SeqAIJ *Aloc = (Mat_SeqAIJ *) a->A->data;
1267   int        ierr,shift = Aloc->indexshift;
1268   Mat        B;
1269   int        M = a->M, N = a->N,m,*ai,*aj,row,*cols,i,*ct;
1270   Scalar     *array;
1271 
1272   if (matout == PETSC_NULL && M != N)
1273     SETERRQ(1,"MatTranspose_MPIAIJ:Square matrix only for in-place");
1274   ierr = MatCreateMPIAIJ(A->comm,PETSC_DECIDE,PETSC_DECIDE,N,M,0,PETSC_NULL,0,
1275          PETSC_NULL,&B); CHKERRQ(ierr);
1276 
1277   /* copy over the A part */
1278   Aloc = (Mat_SeqAIJ*) a->A->data;
1279   m = Aloc->m; ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
1280   row = a->rstart;
1281   for ( i=0; i<ai[m]+shift; i++ ) {aj[i] += a->cstart + shift;}
1282   for ( i=0; i<m; i++ ) {
1283     ierr = MatSetValues(B,ai[i+1]-ai[i],aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1284     row++; array += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1285   }
1286   aj = Aloc->j;
1287   for ( i=0; i<ai[m]+shift; i++ ) {aj[i] -= a->cstart + shift;}
1288 
1289   /* copy over the B part */
1290   Aloc = (Mat_SeqAIJ*) a->B->data;
1291   m = Aloc->m;  ai = Aloc->i; aj = Aloc->j; array = Aloc->a;
1292   row = a->rstart;
1293   ct = cols = (int *) PetscMalloc( (1+ai[m]-shift)*sizeof(int) ); CHKPTRQ(cols);
1294   for ( i=0; i<ai[m]+shift; i++ ) {cols[i] = a->garray[aj[i]+shift];}
1295   for ( i=0; i<m; i++ ) {
1296     ierr = MatSetValues(B,ai[i+1]-ai[i],cols,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1297     row++; array += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1298   }
1299   PetscFree(ct);
1300   ierr = MatAssemblyBegin(B,FINAL_ASSEMBLY); CHKERRQ(ierr);
1301   ierr = MatAssemblyEnd(B,FINAL_ASSEMBLY); CHKERRQ(ierr);
1302   if (matout != PETSC_NULL) {
1303     *matout = B;
1304   } else {
1305     /* This isn't really an in-place transpose .... but free data structures from a */
1306     PetscFree(a->rowners);
1307     ierr = MatDestroy(a->A); CHKERRQ(ierr);
1308     ierr = MatDestroy(a->B); CHKERRQ(ierr);
1309     if (a->colmap) PetscFree(a->colmap);
1310     if (a->garray) PetscFree(a->garray);
1311     if (a->lvec) VecDestroy(a->lvec);
1312     if (a->Mvctx) VecScatterDestroy(a->Mvctx);
1313     PetscFree(a);
1314     PetscMemcpy(A,B,sizeof(struct _Mat));
1315     PetscHeaderDestroy(B);
1316   }
1317   return 0;
1318 }
1319 
1320 extern int MatPrintHelp_SeqAIJ(Mat);
1321 static int MatPrintHelp_MPIAIJ(Mat A)
1322 {
1323   Mat_MPIAIJ *a   = (Mat_MPIAIJ*) A->data;
1324 
1325   if (!a->rank) return MatPrintHelp_SeqAIJ(a->A);
1326   else return 0;
1327 }
1328 
1329 extern int MatConvert_MPIAIJ(Mat,MatType,Mat *);
1330 static int MatConvertSameType_MPIAIJ(Mat,Mat *,int);
1331 extern int MatIncreaseOverlap_MPIAIJ(Mat , int, IS *, int);
1332 int MatGetSubMatrices_MPIAIJ (Mat ,int , IS *,IS *,MatGetSubMatrixCall,Mat **);
1333 /* -------------------------------------------------------------------*/
1334 static struct _MatOps MatOps = {MatSetValues_MPIAIJ,
1335        MatGetRow_MPIAIJ,MatRestoreRow_MPIAIJ,
1336        MatMult_MPIAIJ,MatMultAdd_MPIAIJ,
1337        MatMultTrans_MPIAIJ,MatMultTransAdd_MPIAIJ,
1338        MatSolve_MPIAIJ,MatSolveAdd_MPIAIJ,
1339        MatSolveTrans_MPIAIJ,MatSolveTransAdd_MPIAIJ,
1340        MatLUFactor_MPIAIJ,0,
1341        MatRelax_MPIAIJ,
1342        MatTranspose_MPIAIJ,
1343        MatGetInfo_MPIAIJ,0,
1344        MatGetDiagonal_MPIAIJ,0,MatNorm_MPIAIJ,
1345        MatAssemblyBegin_MPIAIJ,MatAssemblyEnd_MPIAIJ,
1346        0,
1347        MatSetOption_MPIAIJ,MatZeroEntries_MPIAIJ,MatZeroRows_MPIAIJ,
1348        MatGetReordering_MPIAIJ,
1349        MatLUFactorSymbolic_MPIAIJ,MatLUFactorNumeric_MPIAIJ,0,0,
1350        MatGetSize_MPIAIJ,MatGetLocalSize_MPIAIJ,MatGetOwnershipRange_MPIAIJ,
1351        MatILUFactorSymbolic_MPIAIJ,0,
1352        0,0,MatConvert_MPIAIJ,0,0,MatConvertSameType_MPIAIJ,0,0,
1353        0,0,0,
1354        MatGetSubMatrices_MPIAIJ,MatIncreaseOverlap_MPIAIJ,MatGetValues_MPIAIJ,0,
1355        MatPrintHelp_MPIAIJ,
1356        MatScale_MPIAIJ};
1357 
1358 /*@C
1359    MatCreateMPIAIJ - Creates a sparse parallel matrix in AIJ format
1360    (the default parallel PETSc format).  For good matrix assembly performance
1361    the user should preallocate the matrix storage by setting the parameters
1362    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
1363    performance can be increased by more than a factor of 50.
1364 
1365    Input Parameters:
1366 .  comm - MPI communicator
1367 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
1368 .  n - number of local columns (or PETSC_DECIDE to have calculated
1369            if N is given)
1370 .  M - number of global rows (or PETSC_DECIDE to have calculated if m is given)
1371 .  N - number of global columns (or PETSC_DECIDE to have calculated
1372            if n is given)
1373 .  d_nz - number of nonzeros per row in diagonal portion of local submatrix
1374            (same for all local rows)
1375 .  d_nzz - array containing the number of nonzeros in the various rows of the
1376            diagonal portion of local submatrix (possibly different for each row)
1377            or PETSC_NULL. You must leave room for the diagonal entry even if
1378            it is zero.
1379 .  o_nz - number of nonzeros per row in the off-diagonal portion of local
1380            submatrix (same for all local rows).
1381 .  o_nzz - array containing the number of nonzeros in the various rows of the
1382            off-diagonal portion of the local submatrix (possibly different for
1383            each row) or PETSC_NULL.
1384 
1385    Output Parameter:
1386 .  A - the matrix
1387 
1388    Notes:
1389    The AIJ format (also called the Yale sparse matrix format or
1390    compressed row storage), is fully compatible with standard Fortran 77
1391    storage.  That is, the stored row and column indices can begin at
1392    either one (as in Fortran) or zero.  See the users manual for details.
1393 
1394    The user MUST specify either the local or global matrix dimensions
1395    (possibly both).
1396 
1397    By default, this format uses inodes (identical nodes) when possible.
1398    We search for consecutive rows with the same nonzero structure, thereby
1399    reusing matrix information to achieve increased efficiency.
1400 
1401    Options Database Keys:
1402 $    -mat_aij_no_inode  - Do not use inodes
1403 $    -mat_aij_inode_limit <limit> - Set inode limit.
1404 $        (max limit=5)
1405 $    -mat_aij_oneindex - Internally use indexing starting at 1
1406 $        rather than 0.  Note: When calling MatSetValues(),
1407 $        the user still MUST index entries starting at 0!
1408 
1409    Storage Information:
1410    For a square global matrix we define each processor's diagonal portion
1411    to be its local rows and the corresponding columns (a square submatrix);
1412    each processor's off-diagonal portion encompasses the remainder of the
1413    local matrix (a rectangular submatrix).
1414 
1415    The user can specify preallocated storage for the diagonal part of
1416    the local submatrix with either d_nz or d_nnz (not both).  Set
1417    d_nz=PETSC_DEFAULT and d_nnz=PETSC_NULL for PETSc to control dynamic
1418    memory allocation.  Likewise, specify preallocated storage for the
1419    off-diagonal part of the local submatrix with o_nz or o_nnz (not both).
1420 
1421    Consider a processor that owns rows 3, 4 and 5 of a parallel matrix. In
1422    the figure below we depict these three local rows and all columns (0-11).
1423 
1424 $          0 1 2 3 4 5 6 7 8 9 10 11
1425 $         -------------------
1426 $  row 3  |  o o o d d d o o o o o o
1427 $  row 4  |  o o o d d d o o o o o o
1428 $  row 5  |  o o o d d d o o o o o o
1429 $         -------------------
1430 $
1431 
1432    Thus, any entries in the d locations are stored in the d (diagonal)
1433    submatrix, and any entries in the o locations are stored in the
1434    o (off-diagonal) submatrix.  Note that the d and the o submatrices are
1435    stored simply in the MATSEQAIJ format for compressed row storage.
1436 
1437    Now d_nz should indicate the number of nonzeros per row in the d matrix,
1438    and o_nz should indicate the number of nonzeros per row in the o matrix.
1439    In general, for PDE problems in which most nonzeros are near the diagonal,
1440    one expects d_nz >> o_nz.   For additional details, see the users manual
1441    chapter on matrices and the file $(PETSC_DIR)/Performance.
1442 
1443 .keywords: matrix, aij, compressed row, sparse, parallel
1444 
1445 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues()
1446 @*/
1447 int MatCreateMPIAIJ(MPI_Comm comm,int m,int n,int M,int N,
1448                     int d_nz,int *d_nnz,int o_nz,int *o_nnz,Mat *A)
1449 {
1450   Mat          B;
1451   Mat_MPIAIJ   *b;
1452   int          ierr, i,sum[2],work[2];
1453 
1454   *A = 0;
1455   PetscHeaderCreate(B,_Mat,MAT_COOKIE,MATMPIAIJ,comm);
1456   PLogObjectCreate(B);
1457   B->data       = (void *) (b = PetscNew(Mat_MPIAIJ)); CHKPTRQ(b);
1458   PetscMemzero(b,sizeof(Mat_MPIAIJ));
1459   PetscMemcpy(&B->ops,&MatOps,sizeof(struct _MatOps));
1460   B->destroy    = MatDestroy_MPIAIJ;
1461   B->view       = MatView_MPIAIJ;
1462   B->factor     = 0;
1463   B->assembled  = PETSC_FALSE;
1464 
1465   b->insertmode = NOT_SET_VALUES;
1466   MPI_Comm_rank(comm,&b->rank);
1467   MPI_Comm_size(comm,&b->size);
1468 
1469   if (m == PETSC_DECIDE && (d_nnz != PETSC_NULL || o_nnz != PETSC_NULL))
1470     SETERRQ(1,"MatCreateMPIAIJ:Cannot have PETSC_DECIDE rows but set d_nnz or o_nnz");
1471 
1472   if (M == PETSC_DECIDE || N == PETSC_DECIDE) {
1473     work[0] = m; work[1] = n;
1474     MPI_Allreduce( work, sum,2,MPI_INT,MPI_SUM,comm );
1475     if (M == PETSC_DECIDE) M = sum[0];
1476     if (N == PETSC_DECIDE) N = sum[1];
1477   }
1478   if (m == PETSC_DECIDE) {m = M/b->size + ((M % b->size) > b->rank);}
1479   if (n == PETSC_DECIDE) {n = N/b->size + ((N % b->size) > b->rank);}
1480   b->m = m; B->m = m;
1481   b->n = n; B->n = n;
1482   b->N = N; B->N = N;
1483   b->M = M; B->M = M;
1484 
1485   /* build local table of row and column ownerships */
1486   b->rowners = (int *) PetscMalloc(2*(b->size+2)*sizeof(int)); CHKPTRQ(b->rowners);
1487   PLogObjectMemory(B,2*(b->size+2)*sizeof(int)+sizeof(struct _Mat)+sizeof(Mat_MPIAIJ));
1488   b->cowners = b->rowners + b->size + 1;
1489   MPI_Allgather(&m,1,MPI_INT,b->rowners+1,1,MPI_INT,comm);
1490   b->rowners[0] = 0;
1491   for ( i=2; i<=b->size; i++ ) {
1492     b->rowners[i] += b->rowners[i-1];
1493   }
1494   b->rstart = b->rowners[b->rank];
1495   b->rend   = b->rowners[b->rank+1];
1496   MPI_Allgather(&n,1,MPI_INT,b->cowners+1,1,MPI_INT,comm);
1497   b->cowners[0] = 0;
1498   for ( i=2; i<=b->size; i++ ) {
1499     b->cowners[i] += b->cowners[i-1];
1500   }
1501   b->cstart = b->cowners[b->rank];
1502   b->cend   = b->cowners[b->rank+1];
1503 
1504   if (d_nz == PETSC_DEFAULT) d_nz = 5;
1505   ierr = MatCreateSeqAIJ(MPI_COMM_SELF,m,n,d_nz,d_nnz,&b->A); CHKERRQ(ierr);
1506   PLogObjectParent(B,b->A);
1507   if (o_nz == PETSC_DEFAULT) o_nz = 0;
1508   ierr = MatCreateSeqAIJ(MPI_COMM_SELF,m,N,o_nz,o_nnz,&b->B); CHKERRQ(ierr);
1509   PLogObjectParent(B,b->B);
1510 
1511   /* build cache for off array entries formed */
1512   ierr = StashBuild_Private(&b->stash); CHKERRQ(ierr);
1513   b->colmap      = 0;
1514   b->garray      = 0;
1515   b->roworiented = 1;
1516 
1517   /* stuff used for matrix vector multiply */
1518   b->lvec      = 0;
1519   b->Mvctx     = 0;
1520 
1521   /* stuff for MatGetRow() */
1522   b->rowindices   = 0;
1523   b->rowvalues    = 0;
1524   b->getrowactive = PETSC_FALSE;
1525 
1526   *A = B;
1527   return 0;
1528 }
1529 
1530 static int MatConvertSameType_MPIAIJ(Mat matin,Mat *newmat,int cpvalues)
1531 {
1532   Mat        mat;
1533   Mat_MPIAIJ *a,*oldmat = (Mat_MPIAIJ *) matin->data;
1534   int        ierr, len=0, flg;
1535 
1536   *newmat       = 0;
1537   PetscHeaderCreate(mat,_Mat,MAT_COOKIE,MATMPIAIJ,matin->comm);
1538   PLogObjectCreate(mat);
1539   mat->data       = (void *) (a = PetscNew(Mat_MPIAIJ)); CHKPTRQ(a);
1540   PetscMemcpy(&mat->ops,&MatOps,sizeof(struct _MatOps));
1541   mat->destroy    = MatDestroy_MPIAIJ;
1542   mat->view       = MatView_MPIAIJ;
1543   mat->factor     = matin->factor;
1544   mat->assembled  = PETSC_TRUE;
1545 
1546   a->m = mat->m   = oldmat->m;
1547   a->n = mat->n   = oldmat->n;
1548   a->M = mat->M   = oldmat->M;
1549   a->N = mat->N   = oldmat->N;
1550 
1551   a->rstart       = oldmat->rstart;
1552   a->rend         = oldmat->rend;
1553   a->cstart       = oldmat->cstart;
1554   a->cend         = oldmat->cend;
1555   a->size         = oldmat->size;
1556   a->rank         = oldmat->rank;
1557   a->insertmode   = NOT_SET_VALUES;
1558   a->rowvalues    = 0;
1559   a->getrowactive = PETSC_FALSE;
1560 
1561   a->rowners = (int *) PetscMalloc((a->size+1)*sizeof(int)); CHKPTRQ(a->rowners);
1562   PLogObjectMemory(mat,(a->size+1)*sizeof(int)+sizeof(struct _Mat)+sizeof(Mat_MPIAIJ));
1563   PetscMemcpy(a->rowners,oldmat->rowners,(a->size+1)*sizeof(int));
1564   ierr = StashInitialize_Private(&a->stash); CHKERRQ(ierr);
1565   if (oldmat->colmap) {
1566     a->colmap = (int *) PetscMalloc((a->N)*sizeof(int));CHKPTRQ(a->colmap);
1567     PLogObjectMemory(mat,(a->N)*sizeof(int));
1568     PetscMemcpy(a->colmap,oldmat->colmap,(a->N)*sizeof(int));
1569   } else a->colmap = 0;
1570   if (oldmat->garray && (len = ((Mat_SeqAIJ *) (oldmat->B->data))->n)) {
1571     a->garray = (int *) PetscMalloc(len*sizeof(int)); CHKPTRQ(a->garray);
1572     PLogObjectMemory(mat,len*sizeof(int));
1573     PetscMemcpy(a->garray,oldmat->garray,len*sizeof(int));
1574   } else a->garray = 0;
1575 
1576   ierr =  VecDuplicate(oldmat->lvec,&a->lvec); CHKERRQ(ierr);
1577   PLogObjectParent(mat,a->lvec);
1578   ierr =  VecScatterCopy(oldmat->Mvctx,&a->Mvctx); CHKERRQ(ierr);
1579   PLogObjectParent(mat,a->Mvctx);
1580   ierr =  MatConvert(oldmat->A,MATSAME,&a->A); CHKERRQ(ierr);
1581   PLogObjectParent(mat,a->A);
1582   ierr =  MatConvert(oldmat->B,MATSAME,&a->B); CHKERRQ(ierr);
1583   PLogObjectParent(mat,a->B);
1584   ierr = OptionsHasName(PETSC_NULL,"-help",&flg); CHKERRQ(ierr);
1585   if (flg) {
1586     ierr = MatPrintHelp(mat); CHKERRQ(ierr);
1587   }
1588   *newmat = mat;
1589   return 0;
1590 }
1591 
1592 #include "sys.h"
1593 
1594 int MatLoad_MPIAIJ(Viewer viewer,MatType type,Mat *newmat)
1595 {
1596   Mat          A;
1597   int          i, nz, ierr, j,rstart, rend, fd;
1598   Scalar       *vals,*svals;
1599   MPI_Comm     comm = ((PetscObject)viewer)->comm;
1600   MPI_Status   status;
1601   int          header[4],rank,size,*rowlengths = 0,M,N,m,*rowners,maxnz,*cols;
1602   int          *ourlens,*sndcounts = 0,*procsnz = 0, *offlens,jj,*mycols,*smycols;
1603   int          tag = ((PetscObject)viewer)->tag;
1604 
1605   MPI_Comm_size(comm,&size); MPI_Comm_rank(comm,&rank);
1606   if (!rank) {
1607     ierr = ViewerBinaryGetDescriptor(viewer,&fd); CHKERRQ(ierr);
1608     ierr = PetscBinaryRead(fd,(char *)header,4,BINARY_INT); CHKERRQ(ierr);
1609     if (header[0] != MAT_COOKIE) SETERRQ(1,"MatLoad_MPIAIJ:not matrix object");
1610   }
1611 
1612   MPI_Bcast(header+1,3,MPI_INT,0,comm);
1613   M = header[1]; N = header[2];
1614   /* determine ownership of all rows */
1615   m = M/size + ((M % size) > rank);
1616   rowners = (int *) PetscMalloc((size+2)*sizeof(int)); CHKPTRQ(rowners);
1617   MPI_Allgather(&m,1,MPI_INT,rowners+1,1,MPI_INT,comm);
1618   rowners[0] = 0;
1619   for ( i=2; i<=size; i++ ) {
1620     rowners[i] += rowners[i-1];
1621   }
1622   rstart = rowners[rank];
1623   rend   = rowners[rank+1];
1624 
1625   /* distribute row lengths to all processors */
1626   ourlens = (int*) PetscMalloc( 2*(rend-rstart)*sizeof(int) ); CHKPTRQ(ourlens);
1627   offlens = ourlens + (rend-rstart);
1628   if (!rank) {
1629     rowlengths = (int*) PetscMalloc( M*sizeof(int) ); CHKPTRQ(rowlengths);
1630     ierr = PetscBinaryRead(fd,rowlengths,M,BINARY_INT); CHKERRQ(ierr);
1631     sndcounts = (int*) PetscMalloc( size*sizeof(int) ); CHKPTRQ(sndcounts);
1632     for ( i=0; i<size; i++ ) sndcounts[i] = rowners[i+1] - rowners[i];
1633     MPI_Scatterv(rowlengths,sndcounts,rowners,MPI_INT,ourlens,rend-rstart,MPI_INT,0,comm);
1634     PetscFree(sndcounts);
1635   }
1636   else {
1637     MPI_Scatterv(0,0,0,MPI_INT,ourlens,rend-rstart,MPI_INT, 0,comm);
1638   }
1639 
1640   if (!rank) {
1641     /* calculate the number of nonzeros on each processor */
1642     procsnz = (int*) PetscMalloc( size*sizeof(int) ); CHKPTRQ(procsnz);
1643     PetscMemzero(procsnz,size*sizeof(int));
1644     for ( i=0; i<size; i++ ) {
1645       for ( j=rowners[i]; j< rowners[i+1]; j++ ) {
1646         procsnz[i] += rowlengths[j];
1647       }
1648     }
1649     PetscFree(rowlengths);
1650 
1651     /* determine max buffer needed and allocate it */
1652     maxnz = 0;
1653     for ( i=0; i<size; i++ ) {
1654       maxnz = PetscMax(maxnz,procsnz[i]);
1655     }
1656     cols = (int *) PetscMalloc( maxnz*sizeof(int) ); CHKPTRQ(cols);
1657 
1658     /* read in my part of the matrix column indices  */
1659     nz = procsnz[0];
1660     mycols = (int *) PetscMalloc( nz*sizeof(int) ); CHKPTRQ(mycols);
1661     ierr = PetscBinaryRead(fd,mycols,nz,BINARY_INT); CHKERRQ(ierr);
1662 
1663     /* read in every one elses and ship off */
1664     for ( i=1; i<size; i++ ) {
1665       nz = procsnz[i];
1666       ierr = PetscBinaryRead(fd,cols,nz,BINARY_INT); CHKERRQ(ierr);
1667       MPI_Send(cols,nz,MPI_INT,i,tag,comm);
1668     }
1669     PetscFree(cols);
1670   }
1671   else {
1672     /* determine buffer space needed for message */
1673     nz = 0;
1674     for ( i=0; i<m; i++ ) {
1675       nz += ourlens[i];
1676     }
1677     mycols = (int*) PetscMalloc( nz*sizeof(int) ); CHKPTRQ(mycols);
1678 
1679     /* receive message of column indices*/
1680     MPI_Recv(mycols,nz,MPI_INT,0,tag,comm,&status);
1681     MPI_Get_count(&status,MPI_INT,&maxnz);
1682     if (maxnz != nz) SETERRQ(1,"MatLoad_MPIAIJ:something is wrong with file");
1683   }
1684 
1685   /* loop over local rows, determining number of off diagonal entries */
1686   PetscMemzero(offlens,m*sizeof(int));
1687   jj = 0;
1688   for ( i=0; i<m; i++ ) {
1689     for ( j=0; j<ourlens[i]; j++ ) {
1690       if (mycols[jj] < rstart || mycols[jj] >= rend) offlens[i]++;
1691       jj++;
1692     }
1693   }
1694 
1695   /* create our matrix */
1696   for ( i=0; i<m; i++ ) {
1697     ourlens[i] -= offlens[i];
1698   }
1699   ierr = MatCreateMPIAIJ(comm,m,PETSC_DECIDE,M,N,0,ourlens,0,offlens,newmat);CHKERRQ(ierr);
1700   A = *newmat;
1701   MatSetOption(A,COLUMNS_SORTED);
1702   for ( i=0; i<m; i++ ) {
1703     ourlens[i] += offlens[i];
1704   }
1705 
1706   if (!rank) {
1707     vals = (Scalar *) PetscMalloc( maxnz*sizeof(Scalar) ); CHKPTRQ(vals);
1708 
1709     /* read in my part of the matrix numerical values  */
1710     nz = procsnz[0];
1711     ierr = PetscBinaryRead(fd,vals,nz,BINARY_SCALAR); CHKERRQ(ierr);
1712 
1713     /* insert into matrix */
1714     jj      = rstart;
1715     smycols = mycols;
1716     svals   = vals;
1717     for ( i=0; i<m; i++ ) {
1718       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1719       smycols += ourlens[i];
1720       svals   += ourlens[i];
1721       jj++;
1722     }
1723 
1724     /* read in other processors and ship out */
1725     for ( i=1; i<size; i++ ) {
1726       nz = procsnz[i];
1727       ierr = PetscBinaryRead(fd,vals,nz,BINARY_SCALAR); CHKERRQ(ierr);
1728       MPI_Send(vals,nz,MPIU_SCALAR,i,A->tag,comm);
1729     }
1730     PetscFree(procsnz);
1731   }
1732   else {
1733     /* receive numeric values */
1734     vals = (Scalar*) PetscMalloc( nz*sizeof(Scalar) ); CHKPTRQ(vals);
1735 
1736     /* receive message of values*/
1737     MPI_Recv(vals,nz,MPIU_SCALAR,0,A->tag,comm,&status);
1738     MPI_Get_count(&status,MPIU_SCALAR,&maxnz);
1739     if (maxnz != nz) SETERRQ(1,"MatLoad_MPIAIJ:something is wrong with file");
1740 
1741     /* insert into matrix */
1742     jj      = rstart;
1743     smycols = mycols;
1744     svals   = vals;
1745     for ( i=0; i<m; i++ ) {
1746       ierr = MatSetValues(A,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
1747       smycols += ourlens[i];
1748       svals   += ourlens[i];
1749       jj++;
1750     }
1751   }
1752   PetscFree(ourlens); PetscFree(vals); PetscFree(mycols); PetscFree(rowners);
1753 
1754   ierr = MatAssemblyBegin(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
1755   ierr = MatAssemblyEnd(A,FINAL_ASSEMBLY); CHKERRQ(ierr);
1756   return 0;
1757 }
1758