xref: /petsc/src/mat/impls/baij/mpi/baijov.c (revision 6831982abb6453c2f3e25efecb5d0951d333371e)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijov.c,v 1.38 1999/10/13 20:37:30 bsmith Exp bsmith $";
3 #endif
4 
5 /*
6    Routines to compute overlapping regions of a parallel MPI matrix
7   and to find submatrices that were shared across processors.
8 */
9 #include "src/mat/impls/baij/mpi/mpibaij.h"
10 #include "bitarray.h"
11 
12 static int MatIncreaseOverlap_MPIBAIJ_Once(Mat, int, IS *);
13 static int MatIncreaseOverlap_MPIBAIJ_Local(Mat , int , char **,int*, int**);
14 static int MatIncreaseOverlap_MPIBAIJ_Receive(Mat , int, int **, int**, int* );
15 extern int MatGetRow_MPIBAIJ(Mat,int,int*,int**,Scalar**);
16 extern int MatRestoreRow_MPIBAIJ(Mat,int,int*,int**,Scalar**);
17 
18 #undef __FUNC__
19 #define __FUNC__ "MatCompressIndicesGeneral_MPIBAIJ"
20 static int MatCompressIndicesGeneral_MPIBAIJ(Mat C, int imax, IS *is_in, IS *is_out)
21 {
22   Mat_MPIBAIJ  *baij = (Mat_MPIBAIJ *) C->data;
23   int          ierr,isz,bs = baij->bs,Nbs,n,i,j,*idx,*nidx,ival;
24   BTPetsc      table;
25 
26   PetscFunctionBegin;
27   Nbs   = baij->Nbs;
28   nidx  = (int *) PetscMalloc((Nbs+1)*sizeof(int));CHKPTRQ(nidx);
29   ierr  = PetscBTCreate(Nbs,table);CHKERRQ(ierr);
30 
31   for (i=0; i<imax; i++) {
32     isz  = 0;
33     ierr = PetscBTMemzero(Nbs,table);CHKERRQ(ierr);
34     ierr = ISGetIndices(is_in[i],&idx);CHKERRQ(ierr);
35     ierr = ISGetSize(is_in[i],&n);CHKERRQ(ierr);
36     for (j=0; j<n ; j++) {
37       ival = idx[j]/bs; /* convert the indices into block indices */
38       if (ival>Nbs) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,0,"index greater than mat-dim");
39       if(!PetscBTLoopupSet(table, ival)) { nidx[isz++] = ival;}
40     }
41     ierr = ISRestoreIndices(is_in[i],&idx);CHKERRQ(ierr);
42     ierr = ISCreateGeneral(PETSC_COMM_SELF, isz, nidx, (is_out+i));CHKERRQ(ierr);
43   }
44   ierr = PetscBTDestroy(table);CHKERRQ(ierr);
45   ierr = PetscFree(nidx);CHKERRQ(ierr);
46   PetscFunctionReturn(0);
47 }
48 
49 #undef __FUNC__
50 #define __FUNC__ "MatCompressIndicesSorted_MPIBAIJ"
51 static int MatCompressIndicesSorted_MPIBAIJ(Mat C, int imax, IS *is_in, IS *is_out)
52 {
53   Mat_MPIBAIJ  *baij = (Mat_MPIBAIJ *) C->data;
54   int          ierr,bs=baij->bs,i,j,k,val,n,*idx,*nidx,Nbs=baij->Nbs,*idx_local;
55   PetscTruth   flg;
56 
57   PetscFunctionBegin;
58   for (i=0; i<imax; i++) {
59     ierr = ISSorted(is_in[i],&flg);CHKERRQ(ierr);
60     if (!flg) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,0,"Indices are not sorted");
61   }
62   nidx  = (int *) PetscMalloc((Nbs+1)*sizeof(int));CHKPTRQ(nidx);
63   /* Now check if the indices are in block order */
64   for (i=0; i<imax; i++) {
65     ierr = ISGetIndices(is_in[i],&idx);CHKERRQ(ierr);
66     ierr = ISGetSize(is_in[i],&n);CHKERRQ(ierr);
67     if ( n%bs !=0 ) SETERRA(1,0,"Indices are not block ordered");
68 
69     n = n/bs; /* The reduced index size */
70     idx_local = idx;
71     for (j=0; j<n ; j++) {
72       val = idx_local[0];
73       if (val%bs != 0) SETERRA(1,0,"Indices are not block ordered");
74       for (k=0; k<bs; k++) {
75         if ( val+k != idx_local[k]) SETERRA(1,0,"Indices are not block ordered");
76       }
77       nidx[j] = val/bs;
78       idx_local +=bs;
79     }
80     ierr = ISRestoreIndices(is_in[i],&idx);CHKERRQ(ierr);
81     ierr = ISCreateGeneral(PETSC_COMM_SELF,n,nidx,(is_out+i));CHKERRQ(ierr);
82   }
83   ierr = PetscFree(nidx);CHKERRQ(ierr);
84   PetscFunctionReturn(0);
85 }
86 
87 #undef __FUNC__
88 #define __FUNC__ "MatExpandIndices_MPIBAIJ"
89 static int MatExpandIndices_MPIBAIJ(Mat C, int imax, IS *is_in, IS *is_out)
90 {
91   Mat_MPIBAIJ  *baij = (Mat_MPIBAIJ *) C->data;
92   int          ierr,bs = baij->bs,Nbs,n,i,j,k,*idx,*nidx;
93 
94   PetscFunctionBegin;
95   Nbs   = baij->Nbs;
96 
97   nidx  = (int *) PetscMalloc((Nbs*bs+1)*sizeof(int));CHKPTRQ(nidx);
98 
99   for ( i=0; i<imax; i++ ) {
100     ierr = ISGetIndices(is_in[i],&idx);CHKERRQ(ierr);
101     ierr = ISGetSize(is_in[i],&n);CHKERRQ(ierr);
102     for (j=0; j<n ; ++j){
103       for (k=0; k<bs; k++)
104         nidx[j*bs+k] = idx[j]*bs+k;
105     }
106     ierr = ISRestoreIndices(is_in[i],&idx);CHKERRQ(ierr);
107     ierr = ISCreateGeneral(PETSC_COMM_SELF, n*bs, nidx, (is_out+i));CHKERRQ(ierr);
108   }
109   ierr = PetscFree(nidx);CHKERRQ(ierr);
110   PetscFunctionReturn(0);
111 }
112 
113 
114 #undef __FUNC__
115 #define __FUNC__ "MatIncreaseOverlap_MPIBAIJ"
116 int MatIncreaseOverlap_MPIBAIJ(Mat C, int imax, IS *is, int ov)
117 {
118   int i, ierr;
119   IS  *is_new;
120 
121   PetscFunctionBegin;
122   is_new = (IS *)PetscMalloc(imax*sizeof(IS));CHKPTRQ(is_new);
123   /* Convert the indices into block format */
124   ierr = MatCompressIndicesGeneral_MPIBAIJ(C, imax, is,is_new);CHKERRQ(ierr);
125   if (ov < 0){ SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,0,"Negative overlap specified\n");}
126   for (i=0; i<ov; ++i) {
127     ierr = MatIncreaseOverlap_MPIBAIJ_Once(C, imax, is_new);CHKERRQ(ierr);
128   }
129   for (i=0; i<imax; i++) {ierr = ISDestroy(is[i]);CHKERRQ(ierr);}
130   ierr = MatExpandIndices_MPIBAIJ(C, imax, is_new,is);CHKERRQ(ierr);
131   for (i=0; i<imax; i++) {ierr = ISDestroy(is_new[i]);CHKERRQ(ierr);}
132   ierr = PetscFree(is_new);CHKERRQ(ierr);
133   PetscFunctionReturn(0);
134 }
135 
136 /*
137   Sample message format:
138   If a processor A wants processor B to process some elements corresponding
139   to index sets 1s[1], is[5]
140   mesg [0] = 2   ( no of index sets in the mesg)
141   -----------
142   mesg [1] = 1 => is[1]
143   mesg [2] = sizeof(is[1]);
144   -----------
145   mesg [5] = 5  => is[5]
146   mesg [6] = sizeof(is[5]);
147   -----------
148   mesg [7]
149   mesg [n]  datas[1]
150   -----------
151   mesg[n+1]
152   mesg[m]  data(is[5])
153   -----------
154 
155   Notes:
156   nrqs - no of requests sent (or to be sent out)
157   nrqr - no of requests recieved (which have to be or which have been processed
158 */
159 #undef __FUNC__
160 #define __FUNC__ "MatIncreaseOverlap_MPIBAIJ_Once"
161 static int MatIncreaseOverlap_MPIBAIJ_Once(Mat C, int imax, IS *is)
162 {
163   Mat_MPIBAIJ  *c = (Mat_MPIBAIJ *) C->data;
164   int         **idx, *n, *w1, *w2, *w3, *w4, *rtable,**data,len,*idx_i;
165   int         size,rank,Mbs,i,j,k,ierr,**rbuf,row,proc,nrqs,msz,**outdat,**ptr;
166   int         *ctr,*pa,tag,*tmp,bsz,nrqr,*isz,*isz1,**xdata,bsz1,**rbuf2;
167   BTPetsc     *table;
168   MPI_Comm    comm;
169   MPI_Request *s_waits1,*r_waits1,*s_waits2,*r_waits2;
170   MPI_Status  *s_status,*recv_status;
171 
172   PetscFunctionBegin;
173   comm   = C->comm;
174   tag    = C->tag;
175   size   = c->size;
176   rank   = c->rank;
177   Mbs      = c->Mbs;
178 
179   len    = (imax+1)*sizeof(int *) + (imax + Mbs)*sizeof(int);
180   idx    = (int **) PetscMalloc(len);CHKPTRQ(idx);
181   n      = (int *) (idx + imax);
182   rtable = n + imax;
183 
184   for (i=0; i<imax; i++) {
185     ierr = ISGetIndices(is[i],&idx[i]);CHKERRQ(ierr);
186     ierr = ISGetSize(is[i],&n[i]);CHKERRQ(ierr);
187   }
188 
189   /* Create hash table for the mapping :row -> proc*/
190   for (i=0,j=0; i<size; i++) {
191     len = c->rowners[i+1];
192     for (; j<len; j++) {
193       rtable[j] = i;
194     }
195   }
196 
197   /* evaluate communication - mesg to who, length of mesg, and buffer space
198      required. Based on this, buffers are allocated, and data copied into them*/
199   w1   = (int *)PetscMalloc(size*4*sizeof(int));CHKPTRQ(w1);/*  mesg size */
200   w2   = w1 + size;       /* if w2[i] marked, then a message to proc i*/
201   w3   = w2 + size;       /* no of IS that needs to be sent to proc i */
202   w4   = w3 + size;       /* temp work space used in determining w1, w2, w3 */
203   ierr = PetscMemzero(w1,size*3*sizeof(int));CHKERRQ(ierr); /* initialise work vector*/
204   for (i=0; i<imax; i++) {
205     ierr  = PetscMemzero(w4,size*sizeof(int));CHKERRQ(ierr); /* initialise work vector*/
206     idx_i = idx[i];
207     len   = n[i];
208     for (j=0; j<len; j++) {
209       row  = idx_i[j];
210       if (row < 0) {
211         SETERRQ(1,1,"Index set cannot have negative entries");
212       }
213       proc = rtable[row];
214       w4[proc]++;
215     }
216     for (j=0; j<size; j++){
217       if (w4[j]) { w1[j] += w4[j]; w3[j]++;}
218     }
219   }
220 
221   nrqs     = 0;              /* no of outgoing messages */
222   msz      = 0;              /* total mesg length (for all proc */
223   w1[rank] = 0;              /* no mesg sent to intself */
224   w3[rank] = 0;
225   for ( i=0; i<size; i++) {
226     if (w1[i])  {w2[i] = 1; nrqs++;} /* there exists a message to proc i */
227   }
228   /* pa - is list of processors to communicate with */
229   pa = (int *)PetscMalloc((nrqs+1)*sizeof(int));CHKPTRQ(pa);
230   for (i=0,j=0; i<size; i++) {
231     if (w1[i]) {pa[j] = i; j++;}
232   }
233 
234   /* Each message would have a header = 1 + 2*(no of IS) + data */
235   for (i=0; i<nrqs; i++) {
236     j      = pa[i];
237     w1[j] += w2[j] + 2*w3[j];
238     msz   += w1[j];
239   }
240 
241 
242   /* Do a global reduction to determine how many messages to expect*/
243   {
244     int *rw1;
245     rw1   = (int *) PetscMalloc(2*size*sizeof(int));CHKPTRQ(rw1);
246     ierr  = MPI_Allreduce(w1, rw1, 2*size, MPI_INT, PetscMaxSum_Op, comm);CHKERRQ(ierr);
247     bsz   = rw1[rank];
248     nrqr  = rw1[size+rank];
249     ierr  = PetscFree(rw1);CHKERRQ(ierr);
250   }
251 
252   /* Allocate memory for recv buffers . Prob none if nrqr = 0 ???? */
253   len     = (nrqr+1)*sizeof(int*) + nrqr*bsz*sizeof(int);
254   rbuf    = (int**) PetscMalloc(len);CHKPTRQ(rbuf);
255   rbuf[0] = (int *) (rbuf + nrqr);
256   for (i=1; i<nrqr; ++i) rbuf[i] = rbuf[i-1] + bsz;
257 
258   /* Post the receives */
259   r_waits1 = (MPI_Request *) PetscMalloc((nrqr+1)*sizeof(MPI_Request));CHKPTRQ(r_waits1);
260   for (i=0; i<nrqr; ++i) {
261     ierr = MPI_Irecv(rbuf[i],bsz,MPI_INT,MPI_ANY_SOURCE,tag,comm,r_waits1+i);CHKERRQ(ierr);
262   }
263 
264   /* Allocate Memory for outgoing messages */
265   len    = 2*size*sizeof(int*) + (size+msz)*sizeof(int);
266   outdat = (int **)PetscMalloc(len);CHKPTRQ(outdat);
267   ptr    = outdat + size;     /* Pointers to the data in outgoing buffers */
268   ierr   = PetscMemzero(outdat,2*size*sizeof(int*));CHKERRQ(ierr);
269   tmp    = (int *) (outdat + 2*size);
270   ctr    = tmp + msz;
271 
272   {
273     int *iptr = tmp,ict  = 0;
274     for (i=0; i<nrqs; i++) {
275       j         = pa[i];
276       iptr     +=  ict;
277       outdat[j] = iptr;
278       ict       = w1[j];
279     }
280   }
281 
282   /* Form the outgoing messages */
283   /*plug in the headers*/
284   for (i=0; i<nrqs; i++) {
285     j            = pa[i];
286     outdat[j][0] = 0;
287     ierr = PetscMemzero(outdat[j]+1,2*w3[j]*sizeof(int));CHKERRQ(ierr);
288     ptr[j]       = outdat[j] + 2*w3[j] + 1;
289   }
290 
291   /* Memory for doing local proc's work*/
292   {
293     int  *d_p;
294     char *t_p;
295 
296     len   = (imax)*(sizeof(BTPetsc) + sizeof(int *) + sizeof(int)) +
297       (Mbs)*imax*sizeof(int)  + (Mbs/BITSPERBYTE+1)*imax*sizeof(char) + 1;
298     table = (BTPetsc *)PetscMalloc(len);CHKPTRQ(table);
299     ierr  = PetscMemzero(table,len);CHKERRQ(ierr);
300     data  = (int **)(table + imax);
301     isz   = (int  *)(data  + imax);
302     d_p   = (int  *)(isz   + imax);
303     t_p   = (char *)(d_p   + Mbs*imax);
304     for (i=0; i<imax; i++) {
305       table[i] = t_p + (Mbs/BITSPERBYTE+1)*i;
306       data[i]  = d_p + (Mbs)*i;
307     }
308   }
309 
310   /* Parse the IS and update local tables and the outgoing buf with the data*/
311   {
312     int     n_i,*data_i,isz_i,*outdat_j,ctr_j;
313     BTPetsc table_i;
314 
315     for (i=0; i<imax; i++) {
316       ierr    = PetscMemzero(ctr,size*sizeof(int));CHKERRQ(ierr);
317       n_i     = n[i];
318       table_i = table[i];
319       idx_i   = idx[i];
320       data_i  = data[i];
321       isz_i   = isz[i];
322       for (j=0;  j<n_i; j++) {  /* parse the indices of each IS */
323         row  = idx_i[j];
324         proc = rtable[row];
325         if (proc != rank) { /* copy to the outgoing buffer */
326           ctr[proc]++;
327           *ptr[proc] = row;
328           ptr[proc]++;
329         }
330         else { /* Update the local table */
331           if (!PetscBTLoopupSet(table_i,row)) { data_i[isz_i++] = row;}
332         }
333       }
334       /* Update the headers for the current IS */
335       for (j=0; j<size; j++) { /* Can Optimise this loop by using pa[] */
336         if ((ctr_j = ctr[j])) {
337           outdat_j        = outdat[j];
338           k               = ++outdat_j[0];
339           outdat_j[2*k]   = ctr_j;
340           outdat_j[2*k-1] = i;
341         }
342       }
343       isz[i] = isz_i;
344     }
345   }
346 
347 
348 
349   /*  Now  post the sends */
350   s_waits1 = (MPI_Request *) PetscMalloc((nrqs+1)*sizeof(MPI_Request));CHKPTRQ(s_waits1);
351   for (i=0; i<nrqs; ++i) {
352     j    = pa[i];
353     ierr = MPI_Isend(outdat[j], w1[j], MPI_INT, j, tag, comm, s_waits1+i);CHKERRQ(ierr);
354   }
355 
356   /* No longer need the original indices*/
357   for (i=0; i<imax; ++i) {
358     ierr = ISRestoreIndices(is[i], idx+i);CHKERRQ(ierr);
359   }
360   ierr = PetscFree(idx);CHKERRQ(ierr);
361 
362   for (i=0; i<imax; ++i) {
363     ierr = ISDestroy(is[i]);CHKERRQ(ierr);
364   }
365 
366   /* Do Local work*/
367   ierr = MatIncreaseOverlap_MPIBAIJ_Local(C,imax,table,isz,data);CHKERRQ(ierr);
368 
369   /* Receive messages*/
370   {
371     int        index;
372 
373     recv_status = (MPI_Status *) PetscMalloc((nrqr+1)*sizeof(MPI_Status));CHKPTRQ(recv_status);
374     for (i=0; i<nrqr; ++i) {
375       ierr = MPI_Waitany(nrqr, r_waits1, &index, recv_status+i);CHKERRQ(ierr);
376     }
377 
378     s_status = (MPI_Status *) PetscMalloc((nrqs+1)*sizeof(MPI_Status));CHKPTRQ(s_status);
379     ierr     = MPI_Waitall(nrqs,s_waits1,s_status);CHKERRQ(ierr);
380   }
381 
382   /* Phase 1 sends are complete - deallocate buffers */
383   ierr = PetscFree(outdat);CHKERRQ(ierr);
384   ierr = PetscFree(w1);CHKERRQ(ierr);
385 
386   xdata = (int **)PetscMalloc((nrqr+1)*sizeof(int *));CHKPTRQ(xdata);
387   isz1  = (int *)PetscMalloc((nrqr+1)*sizeof(int));CHKPTRQ(isz1);
388   ierr  = MatIncreaseOverlap_MPIBAIJ_Receive(C,nrqr,rbuf,xdata,isz1);CHKERRQ(ierr);
389   ierr = PetscFree(rbuf);CHKERRQ(ierr);
390 
391   /* Send the data back*/
392   /* Do a global reduction to know the buffer space req for incoming messages*/
393   {
394     int *rw1, *rw2;
395 
396     rw1  = (int *)PetscMalloc(2*size*sizeof(int));CHKPTRQ(rw1);
397     ierr = PetscMemzero(rw1,2*size*sizeof(int));CHKERRQ(ierr);
398     rw2  = rw1+size;
399     for (i=0; i<nrqr; ++i) {
400       proc      = recv_status[i].MPI_SOURCE;
401       rw1[proc] = isz1[i];
402     }
403 
404     ierr   = MPI_Allreduce(rw1, rw2, size, MPI_INT, MPI_MAX, comm);CHKERRQ(ierr);
405     bsz1   = rw2[rank];
406     ierr = PetscFree(rw1);CHKERRQ(ierr);
407   }
408 
409   /* Allocate buffers*/
410 
411   /* Allocate memory for recv buffers. Prob none if nrqr = 0 ???? */
412   len      = (nrqs+1)*sizeof(int*) + nrqs*bsz1*sizeof(int);
413   rbuf2    = (int**) PetscMalloc(len);CHKPTRQ(rbuf2);
414   rbuf2[0] = (int *) (rbuf2 + nrqs);
415   for (i=1; i<nrqs; ++i) rbuf2[i] = rbuf2[i-1] + bsz1;
416 
417   /* Post the receives */
418   r_waits2 = (MPI_Request *)PetscMalloc((nrqs+1)*sizeof(MPI_Request));CHKPTRQ(r_waits2);
419   for (i=0; i<nrqs; ++i) {
420     ierr = MPI_Irecv(rbuf2[i], bsz1, MPI_INT, MPI_ANY_SOURCE, tag, comm, r_waits2+i);CHKERRQ(ierr);
421   }
422 
423   /*  Now  post the sends */
424   s_waits2 = (MPI_Request *) PetscMalloc((nrqr+1)*sizeof(MPI_Request));CHKPTRQ(s_waits2);
425   for (i=0; i<nrqr; ++i) {
426     j    = recv_status[i].MPI_SOURCE;
427     ierr = MPI_Isend( xdata[i], isz1[i], MPI_INT, j, tag, comm, s_waits2+i);CHKERRQ(ierr);
428   }
429 
430   /* receive work done on other processors*/
431   {
432     int         index, is_no, ct1, max,*rbuf2_i,isz_i,*data_i,jmax;
433     BTPetsc     table_i;
434     MPI_Status  *status2;
435 
436     status2 = (MPI_Status *) PetscMalloc((nrqs+1)*sizeof(MPI_Status));CHKPTRQ(status2);
437 
438     for (i=0; i<nrqs; ++i) {
439       ierr = MPI_Waitany(nrqs, r_waits2, &index, status2+i);CHKERRQ(ierr);
440       /* Process the message*/
441       rbuf2_i = rbuf2[index];
442       ct1     = 2*rbuf2_i[0]+1;
443       jmax    = rbuf2[index][0];
444       for (j=1; j<=jmax; j++) {
445         max     = rbuf2_i[2*j];
446         is_no   = rbuf2_i[2*j-1];
447         isz_i   = isz[is_no];
448         data_i  = data[is_no];
449         table_i = table[is_no];
450         for (k=0; k<max; k++,ct1++) {
451           row = rbuf2_i[ct1];
452           if (!PetscBTLoopupSet(table_i,row)) { data_i[isz_i++] = row;}
453         }
454         isz[is_no] = isz_i;
455       }
456     }
457     ierr = MPI_Waitall(nrqr,s_waits2,status2);CHKERRQ(ierr);
458     ierr = PetscFree(status2); CHKERRQ(ierr);
459   }
460 
461   for (i=0; i<imax; ++i) {
462     ierr = ISCreateGeneral(PETSC_COMM_SELF, isz[i], data[i], is+i);CHKERRQ(ierr);
463   }
464 
465   ierr = PetscFree(pa);CHKERRQ(ierr);
466   ierr = PetscFree(rbuf2);CHKERRQ(ierr);
467   ierr = PetscFree(s_waits1);CHKERRQ(ierr);
468   ierr = PetscFree(r_waits1);CHKERRQ(ierr);
469   ierr = PetscFree(s_waits2);CHKERRQ(ierr);
470   ierr = PetscFree(r_waits2);CHKERRQ(ierr);
471   ierr = PetscFree(table);CHKERRQ(ierr);
472   ierr = PetscFree(s_status);CHKERRQ(ierr);
473   ierr = PetscFree(recv_status);CHKERRQ(ierr);
474   ierr = PetscFree(xdata[0]);CHKERRQ(ierr);
475   ierr = PetscFree(xdata);CHKERRQ(ierr);
476   ierr = PetscFree(isz1);CHKERRQ(ierr);
477   PetscFunctionReturn(0);
478 }
479 
480 #undef __FUNC__
481 #define __FUNC__ "MatIncreaseOverlap_MPIBAIJ_Local"
482 /*
483    MatIncreaseOverlap_MPIBAIJ_Local - Called by MatincreaseOverlap, to do
484        the work on the local processor.
485 
486      Inputs:
487       C      - MAT_MPIBAIJ;
488       imax - total no of index sets processed at a time;
489       table  - an array of char - size = Mbs bits.
490 
491      Output:
492       isz    - array containing the count of the solution elements correspondign
493                to each index set;
494       data   - pointer to the solutions
495 */
496 static int MatIncreaseOverlap_MPIBAIJ_Local(Mat C,int imax,BTPetsc *table,int *isz,int **data)
497 {
498   Mat_MPIBAIJ *c = (Mat_MPIBAIJ *) C->data;
499   Mat         A = c->A, B = c->B;
500   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)B->data;
501   int         start, end, val, max, rstart,cstart,*ai, *aj;
502   int         *bi, *bj, *garray, i, j, k, row,*data_i,isz_i;
503   BTPetsc     table_i;
504 
505   PetscFunctionBegin;
506   rstart = c->rstart;
507   cstart = c->cstart;
508   ai     = a->i;
509   aj     = a->j;
510   bi     = b->i;
511   bj     = b->j;
512   garray = c->garray;
513 
514 
515   for (i=0; i<imax; i++) {
516     data_i  = data[i];
517     table_i = table[i];
518     isz_i   = isz[i];
519     for (j=0, max=isz[i]; j<max; j++) {
520       row   = data_i[j] - rstart;
521       start = ai[row];
522       end   = ai[row+1];
523       for (k=start; k<end; k++) { /* Amat */
524         val = aj[k] + cstart;
525         if (!PetscBTLoopupSet(table_i,val)) { data_i[isz_i++] = val;}
526       }
527       start = bi[row];
528       end   = bi[row+1];
529       for (k=start; k<end; k++) { /* Bmat */
530         val = garray[bj[k]];
531         if (!PetscBTLoopupSet(table_i,val)) { data_i[isz_i++] = val;}
532       }
533     }
534     isz[i] = isz_i;
535   }
536   PetscFunctionReturn(0);
537 }
538 #undef __FUNC__
539 #define __FUNC__ "MatIncreaseOverlap_MPIBAIJ_Receive"
540 /*
541       MatIncreaseOverlap_MPIBAIJ_Receive - Process the recieved messages,
542          and return the output
543 
544          Input:
545            C    - the matrix
546            nrqr - no of messages being processed.
547            rbuf - an array of pointers to the recieved requests
548 
549          Output:
550            xdata - array of messages to be sent back
551            isz1  - size of each message
552 
553   For better efficiency perhaps we should malloc seperately each xdata[i],
554 then if a remalloc is required we need only copy the data for that one row
555 rather then all previous rows as it is now where a single large chunck of
556 memory is used.
557 
558 */
559 static int MatIncreaseOverlap_MPIBAIJ_Receive(Mat C,int nrqr,int **rbuf,int **xdata, int * isz1)
560 {
561   Mat_MPIBAIJ *c = (Mat_MPIBAIJ *) C->data;
562   Mat         A = c->A, B = c->B;
563   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)B->data;
564   int         rstart,cstart,*ai, *aj, *bi, *bj, *garray, i, j, k;
565   int         row,total_sz,ct, ct1, ct2, ct3,mem_estimate, oct2, l, start, end;
566   int         val, max1, max2, rank, Mbs, no_malloc =0, *tmp, new_estimate, ctr;
567   int         *rbuf_i,kmax,rbuf_0,ierr;
568   BTPetsc     xtable;
569 
570   PetscFunctionBegin;
571   rank   = c->rank;
572   Mbs    = c->Mbs;
573   rstart = c->rstart;
574   cstart = c->cstart;
575   ai     = a->i;
576   aj     = a->j;
577   bi     = b->i;
578   bj     = b->j;
579   garray = c->garray;
580 
581 
582   for (i=0,ct=0,total_sz=0; i<nrqr; ++i) {
583     rbuf_i  =  rbuf[i];
584     rbuf_0  =  rbuf_i[0];
585     ct     += rbuf_0;
586     for (j=1; j<=rbuf_0; j++) { total_sz += rbuf_i[2*j]; }
587   }
588 
589   if (c->Mbs) max1 = ct*(a->nz +b->nz)/c->Mbs;
590   else        max1 = 1;
591   mem_estimate = 3*((total_sz > max1 ? total_sz : max1)+1);
592   xdata[0]     = (int *) PetscMalloc(mem_estimate*sizeof(int));CHKPTRQ(xdata[0]);
593   ++no_malloc;
594   ierr         = PetscBTCreate(Mbs,xtable);CHKERRQ(ierr);
595   ierr         = PetscMemzero(isz1,nrqr*sizeof(int));CHKERRQ(ierr);
596 
597   ct3 = 0;
598   for (i=0; i<nrqr; i++) { /* for easch mesg from proc i */
599     rbuf_i =  rbuf[i];
600     rbuf_0 =  rbuf_i[0];
601     ct1    =  2*rbuf_0+1;
602     ct2    =  ct1;
603     ct3    += ct1;
604     for (j=1; j<=rbuf_0; j++) { /* for each IS from proc i*/
605       ierr = PetscBTMemzero(Mbs,xtable);CHKERRQ(ierr);
606       oct2 = ct2;
607       kmax = rbuf_i[2*j];
608       for (k=0; k<kmax; k++, ct1++) {
609         row = rbuf_i[ct1];
610         if (!PetscBTLoopupSet(xtable,row)) {
611           if (!(ct3 < mem_estimate)) {
612             new_estimate = (int)(1.5*mem_estimate)+1;
613             tmp          = (int*) PetscMalloc(new_estimate * sizeof(int));CHKPTRQ(tmp);
614             ierr = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(int));CHKERRQ(ierr);
615             ierr = PetscFree(xdata[0]);CHKERRQ(ierr);
616             xdata[0]     = tmp;
617             mem_estimate = new_estimate; ++no_malloc;
618             for (ctr=1; ctr<=i; ctr++) { xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];}
619           }
620           xdata[i][ct2++] = row;
621           ct3++;
622         }
623       }
624       for (k=oct2,max2=ct2; k<max2; k++)  {
625         row   = xdata[i][k] - rstart;
626         start = ai[row];
627         end   = ai[row+1];
628         for (l=start; l<end; l++) {
629           val = aj[l] + cstart;
630           if (!PetscBTLoopupSet(xtable,val)) {
631             if (!(ct3 < mem_estimate)) {
632               new_estimate = (int)(1.5*mem_estimate)+1;
633               tmp          = (int*) PetscMalloc(new_estimate * sizeof(int));CHKPTRQ(tmp);
634               ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(int));CHKERRQ(ierr);
635               ierr = PetscFree(xdata[0]);CHKERRQ(ierr);
636               xdata[0]     = tmp;
637               mem_estimate = new_estimate; ++no_malloc;
638               for (ctr=1; ctr<=i; ctr++) { xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];}
639             }
640             xdata[i][ct2++] = val;
641             ct3++;
642           }
643         }
644         start = bi[row];
645         end   = bi[row+1];
646         for (l=start; l<end; l++) {
647           val = garray[bj[l]];
648           if (!PetscBTLoopupSet(xtable,val)) {
649             if (!(ct3 < mem_estimate)) {
650               new_estimate = (int)(1.5*mem_estimate)+1;
651               tmp          = (int*) PetscMalloc(new_estimate * sizeof(int));CHKPTRQ(tmp);
652               ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(int));CHKERRQ(ierr);
653               ierr = PetscFree(xdata[0]);CHKERRQ(ierr);
654               xdata[0]     = tmp;
655               mem_estimate = new_estimate; ++no_malloc;
656               for (ctr =1; ctr <=i; ctr++) { xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];}
657             }
658             xdata[i][ct2++] = val;
659             ct3++;
660           }
661         }
662       }
663       /* Update the header*/
664       xdata[i][2*j]   = ct2 - oct2; /* Undo the vector isz1 and use only a var*/
665       xdata[i][2*j-1] = rbuf_i[2*j-1];
666     }
667     xdata[i][0] = rbuf_0;
668     xdata[i+1]  = xdata[i] + ct2;
669     isz1[i]     = ct2; /* size of each message */
670   }
671   ierr = PetscBTDestroy(xtable);CHKERRQ(ierr);
672   PLogInfo(0,"MatIncreaseOverlap_MPIBAIJ:[%d] Allocated %d bytes, required %d, no of mallocs = %d\n",rank,mem_estimate,ct3,no_malloc);
673   PetscFunctionReturn(0);
674 }
675 
676 static int MatGetSubMatrices_MPIBAIJ_local(Mat,int,IS *,IS *,MatReuse,Mat *);
677 
678 #undef __FUNC__
679 #define __FUNC__ "MatGetSubMatrices_MPIBAIJ"
680 int MatGetSubMatrices_MPIBAIJ(Mat C,int ismax,IS *isrow,IS *iscol,
681                              MatReuse scall,Mat **submat)
682 {
683   IS          *isrow_new,*iscol_new;
684   Mat_MPIBAIJ *c = (Mat_MPIBAIJ *) C->data;
685   int         nmax,nstages_local,nstages,i,pos,max_no,ierr;
686 
687   PetscFunctionBegin;
688   /* The compression and expansion should be avoided. Does'nt point
689      out errors might change the indices hence buggey */
690 
691   isrow_new = (IS *)PetscMalloc(2*(ismax+1)*sizeof(IS));CHKPTRQ(isrow_new);
692   iscol_new = isrow_new + ismax;
693   ierr = MatCompressIndicesSorted_MPIBAIJ(C, ismax, isrow,isrow_new);CHKERRQ(ierr);
694   ierr = MatCompressIndicesSorted_MPIBAIJ(C, ismax, iscol,iscol_new);CHKERRQ(ierr);
695 
696   /* Allocate memory to hold all the submatrices */
697   if (scall != MAT_REUSE_MATRIX) {
698     *submat = (Mat *)PetscMalloc((ismax+1)*sizeof(Mat));CHKPTRQ(*submat);
699   }
700   /* Determine the number of stages through which submatrices are done */
701   nmax          = 20*1000000 / (c->Nbs * sizeof(int));
702   if (nmax == 0) nmax = 1;
703   nstages_local = ismax/nmax + ((ismax % nmax)?1:0);
704 
705   /* Make sure every porcessor loops through the nstages */
706   ierr = MPI_Allreduce(&nstages_local,&nstages,1,MPI_INT,MPI_MAX,C->comm);CHKERRQ(ierr);
707 
708   for ( i=0,pos=0; i<nstages; i++ ) {
709     if (pos+nmax <= ismax) max_no = nmax;
710     else if (pos == ismax) max_no = 0;
711     else                   max_no = ismax-pos;
712     ierr = MatGetSubMatrices_MPIBAIJ_local(C,max_no,isrow_new+pos,iscol_new+pos,scall,*submat+pos);CHKERRQ(ierr);
713     pos += max_no;
714   }
715 
716   for (i=0; i<ismax; i++) {
717     ierr = ISDestroy(isrow_new[i]);CHKERRQ(ierr);
718     ierr = ISDestroy(iscol_new[i]);CHKERRQ(ierr);
719   }
720   ierr = PetscFree(isrow_new);CHKERRQ(ierr);
721   PetscFunctionReturn(0);
722 }
723 
724 /* -------------------------------------------------------------------------*/
725 #undef __FUNC__
726 #define __FUNC__ "MatGetSubMatrices_MPIBAIJ_local"
727 static int MatGetSubMatrices_MPIBAIJ_local(Mat C,int ismax,IS *isrow,IS *iscol,
728                              MatReuse scall,Mat *submats)
729 {
730   Mat_MPIBAIJ *c = (Mat_MPIBAIJ *) C->data;
731   Mat         A = c->A;
732   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data, *b = (Mat_SeqBAIJ*)c->B->data, *mat;
733   int         **irow,**icol,*nrow,*ncol,*w1,*w2,*w3,*w4,*rtable,start,end,size;
734   int         **sbuf1,**sbuf2, rank, Mbs,i,j,k,l,ct1,ct2,ierr, **rbuf1,row,proc;
735   int         nrqs, msz, **ptr,index,*req_size,*ctr,*pa,*tmp,tcol,bsz,nrqr;
736   int         **rbuf3,*req_source,**sbuf_aj, **rbuf2, max1,max2,**rmap;
737   int         **cmap,**lens,is_no,ncols,*cols,mat_i,*mat_j,tmp2,jmax,*irow_i;
738   int         len,ctr_j,*sbuf1_j,*sbuf_aj_i,*rbuf1_i,kmax,*cmap_i,*lens_i;
739   int         *rmap_i,bs=c->bs,bs2=c->bs2,*a_j=a->j,*b_j=b->j,*cworkA, *cworkB;
740   int         cstart = c->cstart,nzA,nzB,*a_i=a->i,*b_i=b->i,imark;
741   int         *bmap = c->garray,ctmp,rstart=c->rstart,tag0,tag1,tag2,tag3;
742   MPI_Request *s_waits1,*r_waits1,*s_waits2,*r_waits2,*r_waits3;
743   MPI_Request *r_waits4,*s_waits3,*s_waits4;
744   MPI_Status  *r_status1,*r_status2,*s_status1,*s_status3,*s_status2;
745   MPI_Status  *r_status3,*r_status4,*s_status4;
746   MPI_Comm    comm;
747   Scalar      **rbuf4,**sbuf_aa,*vals,*mat_a,*sbuf_aa_i,*vworkA,*vworkB;
748   Scalar      *a_a=a->a,*b_a=b->a;
749   PetscTruth  flag;
750 
751   PetscFunctionBegin;
752   comm   = C->comm;
753   tag0    = C->tag;
754   size   = c->size;
755   rank   = c->rank;
756   Mbs      = c->Mbs;
757 
758   /* Get some new tags to keep the communication clean */
759   ierr = PetscObjectGetNewTag((PetscObject)C,&tag1);CHKERRQ(ierr);
760   ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
761   ierr = PetscObjectGetNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
762 
763   /* Check if the col indices are sorted */
764   for (i=0; i<ismax; i++) {
765     ierr = ISSorted(iscol[i],(PetscTruth*)&j);CHKERRQ(ierr);
766     if (!j) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,0,"IS is not sorted");
767   }
768 
769   len    = (2*ismax+1)*(sizeof(int *) + sizeof(int)) + (Mbs+1)*sizeof(int);
770   irow   = (int **)PetscMalloc(len);CHKPTRQ(irow);
771   icol   = irow + ismax;
772   nrow   = (int *) (icol + ismax);
773   ncol   = nrow + ismax;
774   rtable = ncol + ismax;
775 
776   for (i=0; i<ismax; i++) {
777     ierr = ISGetIndices(isrow[i],&irow[i]);CHKERRQ(ierr);
778     ierr = ISGetIndices(iscol[i],&icol[i]);CHKERRQ(ierr);
779     ierr = ISGetSize(isrow[i],&nrow[i]);CHKERRQ(ierr);
780     ierr = ISGetSize(iscol[i],&ncol[i]);CHKERRQ(ierr);
781   }
782 
783   /* Create hash table for the mapping :row -> proc*/
784   for (i=0,j=0; i<size; i++) {
785     jmax = c->rowners[i+1];
786     for (; j<jmax; j++) {
787       rtable[j] = i;
788     }
789   }
790 
791   /* evaluate communication - mesg to who, length of mesg, and buffer space
792      required. Based on this, buffers are allocated, and data copied into them*/
793   w1     = (int *)PetscMalloc(size*4*sizeof(int));CHKPTRQ(w1); /* mesg size */
794   w2     = w1 + size;      /* if w2[i] marked, then a message to proc i*/
795   w3     = w2 + size;      /* no of IS that needs to be sent to proc i */
796   w4     = w3 + size;      /* temp work space used in determining w1, w2, w3 */
797   ierr   = PetscMemzero(w1,size*3*sizeof(int));CHKERRQ(ierr); /* initialise work vector*/
798   for (i=0; i<ismax; i++) {
799     ierr   = PetscMemzero(w4,size*sizeof(int));CHKERRQ(ierr); /* initialise work vector*/
800     jmax   = nrow[i];
801     irow_i = irow[i];
802     for (j=0; j<jmax; j++) {
803       row  = irow_i[j];
804       proc = rtable[row];
805       w4[proc]++;
806     }
807     for (j=0; j<size; j++) {
808       if (w4[j]) { w1[j] += w4[j];  w3[j]++;}
809     }
810   }
811 
812   nrqs     = 0;              /* no of outgoing messages */
813   msz      = 0;              /* total mesg length for all proc */
814   w1[rank] = 0;              /* no mesg sent to intself */
815   w3[rank] = 0;
816   for (i=0; i<size; i++) {
817     if (w1[i])  { w2[i] = 1; nrqs++;} /* there exists a message to proc i */
818   }
819   pa = (int *)PetscMalloc((nrqs+1)*sizeof(int));CHKPTRQ(pa); /*(proc -array)*/
820   for (i=0, j=0; i<size; i++) {
821     if (w1[i]) { pa[j] = i; j++; }
822   }
823 
824   /* Each message would have a header = 1 + 2*(no of IS) + data */
825   for (i=0; i<nrqs; i++) {
826     j     = pa[i];
827     w1[j] += w2[j] + 2* w3[j];
828     msz   += w1[j];
829   }
830   /* Do a global reduction to determine how many messages to expect*/
831   {
832     int *rw1;
833     rw1  = (int *)PetscMalloc(2*size*sizeof(int));CHKPTRQ(rw1);
834     ierr = MPI_Allreduce(w1, rw1, 2*size, MPI_INT, PetscMaxSum_Op, comm);CHKERRQ(ierr);
835     bsz  = rw1[rank];
836     nrqr = rw1[size+rank];
837     ierr = PetscFree(rw1);CHKERRQ(ierr);
838   }
839 
840   /* Allocate memory for recv buffers . Prob none if nrqr = 0 ???? */
841   len      = (nrqr+1)*sizeof(int*) + nrqr*bsz*sizeof(int);
842   rbuf1    = (int**) PetscMalloc(len);CHKPTRQ(rbuf1);
843   rbuf1[0] = (int *) (rbuf1 + nrqr);
844   for (i=1; i<nrqr; ++i) rbuf1[i] = rbuf1[i-1] + bsz;
845 
846   /* Post the receives */
847   r_waits1 = (MPI_Request *) PetscMalloc((nrqr+1)*sizeof(MPI_Request));CHKPTRQ(r_waits1);
848   for (i=0; i<nrqr; ++i) {
849     ierr = MPI_Irecv(rbuf1[i],bsz,MPI_INT,MPI_ANY_SOURCE,tag0,comm,r_waits1+i);CHKERRQ(ierr);
850   }
851 
852   /* Allocate Memory for outgoing messages */
853   len      = 2*size*sizeof(int*) + 2*msz*sizeof(int) + size*sizeof(int);
854   sbuf1    = (int **)PetscMalloc(len);CHKPTRQ(sbuf1);
855   ptr      = sbuf1 + size;   /* Pointers to the data in outgoing buffers */
856   ierr     = PetscMemzero(sbuf1,2*size*sizeof(int*));CHKERRQ(ierr);
857   /* allocate memory for outgoing data + buf to receive the first reply */
858   tmp      = (int *) (ptr + size);
859   ctr      = tmp + 2*msz;
860 
861   {
862     int *iptr = tmp,ict = 0;
863     for (i=0; i<nrqs; i++) {
864       j         = pa[i];
865       iptr     += ict;
866       sbuf1[j]  = iptr;
867       ict       = w1[j];
868     }
869   }
870 
871   /* Form the outgoing messages */
872   /* Initialise the header space */
873   for (i=0; i<nrqs; i++) {
874     j           = pa[i];
875     sbuf1[j][0] = 0;
876     ierr        = PetscMemzero(sbuf1[j]+1, 2*w3[j]*sizeof(int));CHKERRQ(ierr);
877     ptr[j]      = sbuf1[j] + 2*w3[j] + 1;
878   }
879 
880   /* Parse the isrow and copy data into outbuf */
881   for (i=0; i<ismax; i++) {
882     ierr   = PetscMemzero(ctr,size*sizeof(int));CHKERRQ(ierr);
883     irow_i = irow[i];
884     jmax   = nrow[i];
885     for (j=0; j<jmax; j++) {  /* parse the indices of each IS */
886       row  = irow_i[j];
887       proc = rtable[row];
888       if (proc != rank) { /* copy to the outgoing buf*/
889         ctr[proc]++;
890         *ptr[proc] = row;
891         ptr[proc]++;
892       }
893     }
894     /* Update the headers for the current IS */
895     for (j=0; j<size; j++) { /* Can Optimise this loop too */
896       if ((ctr_j = ctr[j])) {
897         sbuf1_j        = sbuf1[j];
898         k              = ++sbuf1_j[0];
899         sbuf1_j[2*k]   = ctr_j;
900         sbuf1_j[2*k-1] = i;
901       }
902     }
903   }
904 
905   /*  Now  post the sends */
906   s_waits1 = (MPI_Request *) PetscMalloc((nrqs+1)*sizeof(MPI_Request));CHKPTRQ(s_waits1);
907   for (i=0; i<nrqs; ++i) {
908     j = pa[i];
909     ierr = MPI_Isend( sbuf1[j], w1[j], MPI_INT, j, tag0, comm, s_waits1+i);CHKERRQ(ierr);
910   }
911 
912   /* Post Recieves to capture the buffer size */
913   r_waits2 = (MPI_Request *) PetscMalloc((nrqs+1)*sizeof(MPI_Request));CHKPTRQ(r_waits2);
914   rbuf2    = (int**)PetscMalloc((nrqs+1)*sizeof(int *));CHKPTRQ(rbuf2);
915   rbuf2[0] = tmp + msz;
916   for (i=1; i<nrqs; ++i) {
917     j        = pa[i];
918     rbuf2[i] = rbuf2[i-1]+w1[pa[i-1]];
919   }
920   for (i=0; i<nrqs; ++i) {
921     j    = pa[i];
922     ierr = MPI_Irecv( rbuf2[i], w1[j], MPI_INT, j, tag1, comm, r_waits2+i);CHKERRQ(ierr);
923   }
924 
925   /* Send to other procs the buf size they should allocate */
926 
927 
928   /* Receive messages*/
929   s_waits2   = (MPI_Request *) PetscMalloc((nrqr+1)*sizeof(MPI_Request));CHKPTRQ(s_waits2);
930   r_status1  = (MPI_Status *) PetscMalloc((nrqr+1)*sizeof(MPI_Status));CHKPTRQ(r_status1);
931   len        = 2*nrqr*sizeof(int) + (nrqr+1)*sizeof(int*);
932   sbuf2      = (int**) PetscMalloc(len);CHKPTRQ(sbuf2);
933   req_size   = (int *) (sbuf2 + nrqr);
934   req_source = req_size + nrqr;
935 
936   {
937     Mat_SeqBAIJ *sA = (Mat_SeqBAIJ*) c->A->data, *sB = (Mat_SeqBAIJ*) c->B->data;
938     int        *sAi = sA->i, *sBi = sB->i, id, *sbuf2_i;
939 
940     for (i=0; i<nrqr; ++i) {
941       ierr = MPI_Waitany(nrqr, r_waits1, &index, r_status1+i);CHKERRQ(ierr);
942       req_size[index] = 0;
943       rbuf1_i         = rbuf1[index];
944       start           = 2*rbuf1_i[0] + 1;
945       ierr = MPI_Get_count(r_status1+i,MPI_INT, &end);CHKERRQ(ierr);
946       sbuf2[index] = (int *)PetscMalloc(end*sizeof(int));CHKPTRQ(sbuf2[index]);
947       sbuf2_i      = sbuf2[index];
948       for (j=start; j<end; j++) {
949         id               = rbuf1_i[j] - rstart;
950         ncols            = sAi[id+1] - sAi[id] + sBi[id+1] - sBi[id];
951         sbuf2_i[j]       = ncols;
952         req_size[index] += ncols;
953       }
954       req_source[index] = r_status1[i].MPI_SOURCE;
955       /* form the header */
956       sbuf2_i[0]   = req_size[index];
957       for (j=1; j<start; j++) { sbuf2_i[j] = rbuf1_i[j]; }
958       ierr = MPI_Isend(sbuf2_i,end,MPI_INT,req_source[index],tag1,comm,s_waits2+i);CHKERRQ(ierr);
959     }
960   }
961   ierr = PetscFree(r_status1);CHKERRQ(ierr);
962   ierr = PetscFree(r_waits1);CHKERRQ(ierr);
963 
964   /*  recv buffer sizes */
965   /* Receive messages*/
966 
967   rbuf3     = (int**)PetscMalloc((nrqs+1)*sizeof(int*));CHKPTRQ(rbuf3);
968   rbuf4     = (Scalar**)PetscMalloc((nrqs+1)*sizeof(Scalar*));CHKPTRQ(rbuf4);
969   r_waits3  = (MPI_Request *) PetscMalloc((nrqs+1)*sizeof(MPI_Request));CHKPTRQ(r_waits3);
970   r_waits4  = (MPI_Request *) PetscMalloc((nrqs+1)*sizeof(MPI_Request));CHKPTRQ(r_waits4);
971   r_status2 = (MPI_Status *) PetscMalloc((nrqs+1)*sizeof(MPI_Status));CHKPTRQ(r_status2);
972 
973   for (i=0; i<nrqs; ++i) {
974     ierr = MPI_Waitany(nrqs, r_waits2, &index, r_status2+i);CHKERRQ(ierr);
975     rbuf3[index] = (int *)PetscMalloc(rbuf2[index][0]*sizeof(int));CHKPTRQ(rbuf3[index]);
976     rbuf4[index] = (Scalar *)PetscMalloc(rbuf2[index][0]*bs2*sizeof(Scalar));CHKPTRQ(rbuf4[index]);
977     ierr = MPI_Irecv(rbuf3[index],rbuf2[index][0], MPI_INT,
978                      r_status2[i].MPI_SOURCE, tag2, comm, r_waits3+index);CHKERRQ(ierr);
979     ierr = MPI_Irecv(rbuf4[index],rbuf2[index][0]*bs2, MPIU_SCALAR,
980                      r_status2[i].MPI_SOURCE, tag3, comm, r_waits4+index);CHKERRQ(ierr);
981   }
982   ierr = PetscFree(r_status2);CHKERRQ(ierr);
983   ierr = PetscFree(r_waits2);CHKERRQ(ierr);
984 
985   /* Wait on sends1 and sends2 */
986   s_status1 = (MPI_Status *) PetscMalloc((nrqs+1)*sizeof(MPI_Status));CHKPTRQ(s_status1);
987   s_status2 = (MPI_Status *) PetscMalloc((nrqr+1)*sizeof(MPI_Status));CHKPTRQ(s_status2);
988 
989   ierr = MPI_Waitall(nrqs,s_waits1,s_status1);CHKERRQ(ierr);
990   ierr = MPI_Waitall(nrqr,s_waits2,s_status2);CHKERRQ(ierr);
991   ierr = PetscFree(s_status1);CHKERRQ(ierr);
992   ierr = PetscFree(s_status2);CHKERRQ(ierr);
993   ierr = PetscFree(s_waits1);CHKERRQ(ierr);
994   ierr = PetscFree(s_waits2);CHKERRQ(ierr);
995 
996   /* Now allocate buffers for a->j, and send them off */
997   sbuf_aj = (int **)PetscMalloc((nrqr+1)*sizeof(int *));CHKPTRQ(sbuf_aj);
998   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
999   sbuf_aj[0] = (int*) PetscMalloc((j+1)*sizeof(int));CHKPTRQ(sbuf_aj[0]);
1000   for (i=1; i<nrqr; i++)  sbuf_aj[i] = sbuf_aj[i-1] + req_size[i-1];
1001 
1002   s_waits3 = (MPI_Request *) PetscMalloc((nrqr+1)*sizeof(MPI_Request));CHKPTRQ(s_waits3);
1003   {
1004      for (i=0; i<nrqr; i++) {
1005       rbuf1_i   = rbuf1[i];
1006       sbuf_aj_i = sbuf_aj[i];
1007       ct1       = 2*rbuf1_i[0] + 1;
1008       ct2       = 0;
1009       for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
1010         kmax = rbuf1[i][2*j];
1011         for (k=0; k<kmax; k++,ct1++) {
1012           row    = rbuf1_i[ct1] - rstart;
1013           nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
1014           ncols  = nzA + nzB;
1015           cworkA = a_j + a_i[row]; cworkB = b_j + b_i[row];
1016 
1017           /* load the column indices for this row into cols*/
1018           cols  = sbuf_aj_i + ct2;
1019           for (l=0; l<nzB; l++) {
1020             if ((ctmp = bmap[cworkB[l]]) < cstart)  cols[l] = ctmp;
1021             else break;
1022           }
1023           imark = l;
1024           for (l=0; l<nzA; l++)   cols[imark+l] = cstart + cworkA[l];
1025           for (l=imark; l<nzB; l++) cols[nzA+l] = bmap[cworkB[l]];
1026           ct2 += ncols;
1027         }
1028       }
1029       ierr = MPI_Isend(sbuf_aj_i,req_size[i],MPI_INT,req_source[i],tag2,comm,s_waits3+i);CHKERRQ(ierr);
1030     }
1031   }
1032   r_status3 = (MPI_Status *) PetscMalloc((nrqs+1)*sizeof(MPI_Status));CHKPTRQ(r_status3);
1033   s_status3 = (MPI_Status *) PetscMalloc((nrqr+1)*sizeof(MPI_Status));CHKPTRQ(s_status3);
1034 
1035   /* Allocate buffers for a->a, and send them off */
1036   sbuf_aa = (Scalar **)PetscMalloc((nrqr+1)*sizeof(Scalar *));CHKPTRQ(sbuf_aa);
1037   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
1038   sbuf_aa[0] = (Scalar*) PetscMalloc((j+1)*bs2*sizeof(Scalar));CHKPTRQ(sbuf_aa[0]);
1039   for (i=1; i<nrqr; i++)  sbuf_aa[i] = sbuf_aa[i-1] + req_size[i-1]*bs2;
1040 
1041   s_waits4 = (MPI_Request *) PetscMalloc((nrqr+1)*sizeof(MPI_Request));CHKPTRQ(s_waits4);
1042   {
1043     for (i=0; i<nrqr; i++) {
1044       rbuf1_i   = rbuf1[i];
1045       sbuf_aa_i = sbuf_aa[i];
1046       ct1       = 2*rbuf1_i[0]+1;
1047       ct2       = 0;
1048       for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
1049         kmax = rbuf1_i[2*j];
1050         for (k=0; k<kmax; k++,ct1++) {
1051           row    = rbuf1_i[ct1] - rstart;
1052           nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
1053           ncols  = nzA + nzB;
1054           cworkA = a_j + a_i[row];     cworkB = b_j + b_i[row];
1055           vworkA = a_a + a_i[row]*bs2; vworkB = b_a + b_i[row]*bs2;
1056 
1057           /* load the column values for this row into vals*/
1058           vals  = sbuf_aa_i+ct2*bs2;
1059           for (l=0; l<nzB; l++) {
1060             if ((bmap[cworkB[l]]) < cstart) {
1061               ierr = PetscMemcpy(vals+l*bs2,vworkB+l*bs2,bs2*sizeof(Scalar));CHKERRQ(ierr);
1062             }
1063             else break;
1064           }
1065           imark = l;
1066           for (l=0; l<nzA; l++) {
1067             ierr = PetscMemcpy(vals+(imark+l)*bs2,vworkA+l*bs2,bs2*sizeof(Scalar));CHKERRQ(ierr);
1068           }
1069           for (l=imark; l<nzB; l++) {
1070             ierr = PetscMemcpy(vals+(nzA+l)*bs2,vworkB+l*bs2,bs2*sizeof(Scalar));CHKERRQ(ierr);
1071           }
1072           ct2 += ncols;
1073         }
1074       }
1075       ierr = MPI_Isend(sbuf_aa_i,req_size[i]*bs2,MPIU_SCALAR,req_source[i],tag3,comm,s_waits4+i);CHKERRQ(ierr);
1076     }
1077   }
1078   r_status4 = (MPI_Status *) PetscMalloc((nrqs+1)*sizeof(MPI_Status));CHKPTRQ(r_status4);
1079   s_status4 = (MPI_Status *) PetscMalloc((nrqr+1)*sizeof(MPI_Status));CHKPTRQ(s_status4);
1080   ierr = PetscFree(rbuf1);CHKERRQ(ierr);
1081 
1082   /* Form the matrix */
1083   /* create col map */
1084   {
1085     int *icol_i;
1086 
1087     len     = (1+ismax)*sizeof(int *) + ismax*c->Nbs*sizeof(int);
1088     cmap    = (int **)PetscMalloc(len);CHKPTRQ(cmap);
1089     cmap[0] = (int *)(cmap + ismax);
1090     ierr    = PetscMemzero(cmap[0],(1+ismax*c->Nbs)*sizeof(int));CHKERRQ(ierr);
1091     for (i=1; i<ismax; i++) { cmap[i] = cmap[i-1] + c->Nbs; }
1092     for (i=0; i<ismax; i++) {
1093       jmax   = ncol[i];
1094       icol_i = icol[i];
1095       cmap_i = cmap[i];
1096       for (j=0; j<jmax; j++) {
1097         cmap_i[icol_i[j]] = j+1;
1098       }
1099     }
1100   }
1101 
1102 
1103   /* Create lens which is required for MatCreate... */
1104   for (i=0,j=0; i<ismax; i++) { j += nrow[i]; }
1105   len     = (1+ismax)*sizeof(int *) + j*sizeof(int);
1106   lens    = (int **)PetscMalloc(len);CHKPTRQ(lens);
1107   lens[0] = (int *)(lens + ismax);
1108   ierr    = PetscMemzero(lens[0], j*sizeof(int));CHKERRQ(ierr);
1109   for (i=1; i<ismax; i++) { lens[i] = lens[i-1] + nrow[i-1]; }
1110 
1111   /* Update lens from local data */
1112   for (i=0; i<ismax; i++) {
1113     jmax   = nrow[i];
1114     cmap_i = cmap[i];
1115     irow_i = irow[i];
1116     lens_i = lens[i];
1117     for (j=0; j<jmax; j++) {
1118       row  = irow_i[j];
1119       proc = rtable[row];
1120       if (proc == rank) {
1121         /* Get indices from matA and then from matB */
1122         row    = row - rstart;
1123         nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
1124         cworkA =  a_j + a_i[row]; cworkB = b_j + b_i[row];
1125         for (k=0; k<nzA; k++) {
1126           if (cmap_i[cstart + cworkA[k]]) { lens_i[j]++;}
1127         }
1128         for (k=0; k<nzB; k++) {
1129           if (cmap_i[bmap[cworkB[k]]]) { lens_i[j]++;}
1130         }
1131       }
1132     }
1133   }
1134 
1135   /* Create row map*/
1136   len     = (1+ismax)*sizeof(int *) + ismax*c->Mbs*sizeof(int);
1137   rmap    = (int **)PetscMalloc(len);CHKPTRQ(rmap);
1138   rmap[0] = (int *)(rmap + ismax);
1139   ierr    = PetscMemzero(rmap[0],ismax*c->Mbs*sizeof(int));CHKERRQ(ierr);
1140   for (i=1; i<ismax; i++) { rmap[i] = rmap[i-1] + c->Mbs;}
1141   for (i=0; i<ismax; i++) {
1142     rmap_i = rmap[i];
1143     irow_i = irow[i];
1144     jmax   = nrow[i];
1145     for (j=0; j<jmax; j++) {
1146       rmap_i[irow_i[j]] = j;
1147     }
1148   }
1149 
1150   /* Update lens from offproc data */
1151   {
1152     int *rbuf2_i, *rbuf3_i, *sbuf1_i;
1153 
1154     for (tmp2=0; tmp2<nrqs; tmp2++) {
1155       ierr    = MPI_Waitany(nrqs, r_waits3, &i, r_status3+tmp2);CHKERRQ(ierr);
1156       index   = pa[i];
1157       sbuf1_i = sbuf1[index];
1158       jmax    = sbuf1_i[0];
1159       ct1     = 2*jmax+1;
1160       ct2     = 0;
1161       rbuf2_i = rbuf2[i];
1162       rbuf3_i = rbuf3[i];
1163       for (j=1; j<=jmax; j++) {
1164         is_no   = sbuf1_i[2*j-1];
1165         max1    = sbuf1_i[2*j];
1166         lens_i  = lens[is_no];
1167         cmap_i  = cmap[is_no];
1168         rmap_i  = rmap[is_no];
1169         for (k=0; k<max1; k++,ct1++) {
1170           row  = rmap_i[sbuf1_i[ct1]]; /* the val in the new matrix to be */
1171           max2 = rbuf2_i[ct1];
1172           for (l=0; l<max2; l++,ct2++) {
1173             if (cmap_i[rbuf3_i[ct2]]) {
1174               lens_i[row]++;
1175             }
1176           }
1177         }
1178       }
1179     }
1180   }
1181   ierr = PetscFree(r_status3);CHKERRQ(ierr);
1182   ierr = PetscFree(r_waits3);CHKERRQ(ierr);
1183   ierr = MPI_Waitall(nrqr,s_waits3,s_status3);CHKERRQ(ierr);
1184   ierr = PetscFree(s_status3);CHKERRQ(ierr);
1185   ierr = PetscFree(s_waits3);CHKERRQ(ierr);
1186 
1187   /* Create the submatrices */
1188   if (scall == MAT_REUSE_MATRIX) {
1189     /*
1190         Assumes new rows are same length as the old rows, hence bug!
1191     */
1192     for (i=0; i<ismax; i++) {
1193       mat = (Mat_SeqBAIJ *)(submats[i]->data);
1194       if ((mat->mbs != nrow[i]) || (mat->nbs != ncol[i] || mat->bs != bs)) {
1195         SETERRQ(PETSC_ERR_ARG_SIZ,0,"Cannot reuse matrix. wrong size");
1196       }
1197       ierr = PetscMemcmp(mat->ilen,lens[i], mat->mbs *sizeof(int),&flag);CHKERRQ(ierr);
1198       if (flag == PETSC_FALSE) {
1199         SETERRQ(PETSC_ERR_ARG_INCOMP,0,"Cannot reuse matrix. wrong no of nonzeros");
1200       }
1201       /* Initial matrix as if empty */
1202       ierr = PetscMemzero(mat->ilen,mat->mbs*sizeof(int));CHKERRQ(ierr);
1203       submats[i]->factor = C->factor;
1204     }
1205   } else {
1206     for (i=0; i<ismax; i++) {
1207       ierr = MatCreateSeqBAIJ(PETSC_COMM_SELF,a->bs,nrow[i]*bs,ncol[i]*bs,0,lens[i],submats+i);CHKERRQ(ierr);
1208     }
1209   }
1210 
1211   /* Assemble the matrices */
1212   /* First assemble the local rows */
1213   {
1214     int    ilen_row,*imat_ilen, *imat_j, *imat_i;
1215     Scalar *imat_a;
1216 
1217     for (i=0; i<ismax; i++) {
1218       mat       = (Mat_SeqBAIJ *) submats[i]->data;
1219       imat_ilen = mat->ilen;
1220       imat_j    = mat->j;
1221       imat_i    = mat->i;
1222       imat_a    = mat->a;
1223       cmap_i    = cmap[i];
1224       rmap_i    = rmap[i];
1225       irow_i    = irow[i];
1226       jmax      = nrow[i];
1227       for (j=0; j<jmax; j++) {
1228         row      = irow_i[j];
1229         proc     = rtable[row];
1230         if (proc == rank) {
1231           row      = row - rstart;
1232           nzA      = a_i[row+1] - a_i[row];
1233           nzB      = b_i[row+1] - b_i[row];
1234           cworkA   = a_j + a_i[row];
1235           cworkB   = b_j + b_i[row];
1236           vworkA   = a_a + a_i[row]*bs2;
1237           vworkB   = b_a + b_i[row]*bs2;
1238 
1239           row      = rmap_i[row + rstart];
1240           mat_i    = imat_i[row];
1241           mat_a    = imat_a + mat_i*bs2;
1242           mat_j    = imat_j + mat_i;
1243           ilen_row = imat_ilen[row];
1244 
1245           /* load the column indices for this row into cols*/
1246           for (l=0; l<nzB; l++) {
1247             if ((ctmp = bmap[cworkB[l]]) < cstart) {
1248               if ((tcol = cmap_i[ctmp])) {
1249                 *mat_j++ = tcol - 1;
1250                 ierr     = PetscMemcpy(mat_a,vworkB+l*bs2,bs2*sizeof(Scalar));CHKERRQ(ierr);
1251                 mat_a   += bs2;
1252                 ilen_row++;
1253               }
1254             } else break;
1255           }
1256           imark = l;
1257           for (l=0; l<nzA; l++) {
1258             if ((tcol = cmap_i[cstart + cworkA[l]])) {
1259               *mat_j++ = tcol - 1;
1260               ierr     = PetscMemcpy(mat_a,vworkA+l*bs2,bs2*sizeof(Scalar));CHKERRQ(ierr);
1261               mat_a   += bs2;
1262               ilen_row++;
1263             }
1264           }
1265           for (l=imark; l<nzB; l++) {
1266             if ((tcol = cmap_i[bmap[cworkB[l]]])) {
1267               *mat_j++ = tcol - 1;
1268               ierr     = PetscMemcpy(mat_a,vworkB+l*bs2,bs2*sizeof(Scalar));CHKERRQ(ierr);
1269               mat_a   += bs2;
1270               ilen_row++;
1271             }
1272           }
1273           imat_ilen[row] = ilen_row;
1274         }
1275       }
1276 
1277     }
1278   }
1279 
1280   /*   Now assemble the off proc rows*/
1281   {
1282     int    *sbuf1_i,*rbuf2_i,*rbuf3_i,*imat_ilen,ilen;
1283     int    *imat_j,*imat_i;
1284     Scalar *imat_a,*rbuf4_i;
1285 
1286     for (tmp2=0; tmp2<nrqs; tmp2++) {
1287       ierr    = MPI_Waitany(nrqs, r_waits4, &i, r_status4+tmp2);CHKERRQ(ierr);
1288       index   = pa[i];
1289       sbuf1_i = sbuf1[index];
1290       jmax    = sbuf1_i[0];
1291       ct1     = 2*jmax + 1;
1292       ct2     = 0;
1293       rbuf2_i = rbuf2[i];
1294       rbuf3_i = rbuf3[i];
1295       rbuf4_i = rbuf4[i];
1296       for (j=1; j<=jmax; j++) {
1297         is_no     = sbuf1_i[2*j-1];
1298         rmap_i    = rmap[is_no];
1299         cmap_i    = cmap[is_no];
1300         mat       = (Mat_SeqBAIJ *) submats[is_no]->data;
1301         imat_ilen = mat->ilen;
1302         imat_j    = mat->j;
1303         imat_i    = mat->i;
1304         imat_a    = mat->a;
1305         max1      = sbuf1_i[2*j];
1306         for (k=0; k<max1; k++, ct1++) {
1307           row   = sbuf1_i[ct1];
1308           row   = rmap_i[row];
1309           ilen  = imat_ilen[row];
1310           mat_i = imat_i[row];
1311           mat_a = imat_a + mat_i*bs2;
1312           mat_j = imat_j + mat_i;
1313           max2 = rbuf2_i[ct1];
1314           for (l=0; l<max2; l++,ct2++) {
1315             if ((tcol = cmap_i[rbuf3_i[ct2]])) {
1316               *mat_j++    = tcol - 1;
1317               /* *mat_a++= rbuf4_i[ct2]; */
1318               ierr        = PetscMemcpy(mat_a,rbuf4_i+ct2*bs2,bs2*sizeof(Scalar));CHKERRQ(ierr);
1319               mat_a      += bs2;
1320               ilen++;
1321             }
1322           }
1323           imat_ilen[row] = ilen;
1324         }
1325       }
1326     }
1327   }
1328   ierr = PetscFree(r_status4);CHKERRQ(ierr);
1329   ierr = PetscFree(r_waits4);CHKERRQ(ierr);
1330   ierr = MPI_Waitall(nrqr,s_waits4,s_status4);CHKERRQ(ierr);
1331   ierr = PetscFree(s_waits4);CHKERRQ(ierr);
1332   ierr = PetscFree(s_status4);CHKERRQ(ierr);
1333 
1334   /* Restore the indices */
1335   for (i=0; i<ismax; i++) {
1336     ierr = ISRestoreIndices(isrow[i], irow+i);CHKERRQ(ierr);
1337     ierr = ISRestoreIndices(iscol[i], icol+i);CHKERRQ(ierr);
1338   }
1339 
1340   /* Destroy allocated memory */
1341   ierr = PetscFree(irow);CHKERRQ(ierr);
1342   ierr = PetscFree(w1);CHKERRQ(ierr);
1343   ierr = PetscFree(pa);CHKERRQ(ierr);
1344 
1345   ierr = PetscFree(sbuf1);CHKERRQ(ierr);
1346   ierr = PetscFree(rbuf2);CHKERRQ(ierr);
1347   for (i=0; i<nrqr; ++i) {
1348     ierr = PetscFree(sbuf2[i]);CHKERRQ(ierr);
1349   }
1350   for (i=0; i<nrqs; ++i) {
1351     ierr = PetscFree(rbuf3[i]);CHKERRQ(ierr);
1352     ierr = PetscFree(rbuf4[i]);CHKERRQ(ierr);
1353   }
1354 
1355   ierr = PetscFree(sbuf2);CHKERRQ(ierr);
1356   ierr = PetscFree(rbuf3);CHKERRQ(ierr);
1357   ierr = PetscFree(rbuf4 );CHKERRQ(ierr);
1358   ierr = PetscFree(sbuf_aj[0]);CHKERRQ(ierr);
1359   ierr = PetscFree(sbuf_aj);CHKERRQ(ierr);
1360   ierr = PetscFree(sbuf_aa[0]);CHKERRQ(ierr);
1361   ierr = PetscFree(sbuf_aa);CHKERRQ(ierr);
1362 
1363   ierr = PetscFree(cmap);CHKERRQ(ierr);
1364   ierr = PetscFree(rmap);CHKERRQ(ierr);
1365   ierr = PetscFree(lens);CHKERRQ(ierr);
1366 
1367   for (i=0; i<ismax; i++) {
1368     ierr = MatAssemblyBegin(submats[i], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1369     ierr = MatAssemblyEnd(submats[i], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1370   }
1371 
1372   ierr = PetscObjectRestoreNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
1373   ierr = PetscObjectRestoreNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
1374   ierr = PetscObjectRestoreNewTag((PetscObject)C,&tag1);CHKERRQ(ierr);
1375 
1376   PetscFunctionReturn(0);
1377 }
1378 
1379 
1380