xref: /petsc/src/mat/impls/aij/mpi/mpiov.c (revision 255698d24a1f06d3cfea1aeba52a689a8c41e046)
1 /*
2    Routines to compute overlapping regions of a parallel MPI matrix
3   and to find submatrices that were shared across processors.
4 */
5 #include <../src/mat/impls/aij/seq/aij.h>
6 #include <../src/mat/impls/aij/mpi/mpiaij.h>
7 #include <petscbt.h>
8 #include <petscsf.h>
9 
10 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once(Mat,PetscInt,IS*);
11 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local(Mat,PetscInt,char**,PetscInt*,PetscInt**,PetscTable*);
12 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive(Mat,PetscInt,PetscInt**,PetscInt**,PetscInt*);
13 extern PetscErrorCode MatGetRow_MPIAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);
14 extern PetscErrorCode MatRestoreRow_MPIAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);
15 
16 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once_Scalable(Mat,PetscInt,IS*);
17 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local_Scalable(Mat,PetscInt,IS*);
18 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Send_Scalable(Mat,PetscInt,PetscMPIInt,PetscMPIInt *,PetscInt *, PetscInt *,PetscInt **,PetscInt **);
19 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive_Scalable(Mat,PetscInt,IS*,PetscInt,PetscInt *);
20 
21 
22 PetscErrorCode MatIncreaseOverlap_MPIAIJ(Mat C,PetscInt imax,IS is[],PetscInt ov)
23 {
24   PetscErrorCode ierr;
25   PetscInt       i;
26 
27   PetscFunctionBegin;
28   if (ov < 0) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap specified");
29   for (i=0; i<ov; ++i) {
30     ierr = MatIncreaseOverlap_MPIAIJ_Once(C,imax,is);CHKERRQ(ierr);
31   }
32   PetscFunctionReturn(0);
33 }
34 
35 PetscErrorCode MatIncreaseOverlap_MPIAIJ_Scalable(Mat C,PetscInt imax,IS is[],PetscInt ov)
36 {
37   PetscErrorCode ierr;
38   PetscInt       i;
39 
40   PetscFunctionBegin;
41   if (ov < 0) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap specified");
42   for (i=0; i<ov; ++i) {
43     ierr = MatIncreaseOverlap_MPIAIJ_Once_Scalable(C,imax,is);CHKERRQ(ierr);
44   }
45   PetscFunctionReturn(0);
46 }
47 
48 
49 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once_Scalable(Mat mat,PetscInt nidx,IS is[])
50 {
51   PetscErrorCode   ierr;
52   MPI_Comm         comm;
53   PetscInt        *length,length_i,tlength,*remoterows,nrrows,reducednrrows,*rrow_ranks,*rrow_isids,i,j,owner;
54   PetscInt         *tosizes,*tosizes_temp,*toffsets,*fromsizes,*todata,*fromdata;
55   PetscInt         nrecvrows,*sbsizes = 0,*sbdata = 0;
56   const PetscInt  *indices_i,**indices;
57   PetscLayout      rmap;
58   PetscMPIInt      rank,size,*toranks,*fromranks,nto,nfrom;
59   PetscSF          sf;
60   PetscSFNode     *remote;
61 
62   PetscFunctionBegin;
63   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
64   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
65   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
66   /* get row map to determine where rows should be going */
67   ierr = MatGetLayouts(mat,&rmap,NULL);CHKERRQ(ierr);
68   /* retrieve IS data and put all together so that we
69    * can optimize communication
70    *  */
71   ierr = PetscCalloc2(nidx,(PetscInt ***)&indices,nidx,&length);CHKERRQ(ierr);
72   for (i=0,tlength=0; i<nidx; i++){
73     ierr = ISGetLocalSize(is[i],&length[i]);CHKERRQ(ierr);
74     tlength += length[i];
75     ierr = ISGetIndices(is[i],&indices[i]);CHKERRQ(ierr);
76   }
77   /* find these rows on remote processors */
78   ierr = PetscCalloc3(tlength,&remoterows,tlength,&rrow_ranks,tlength,&rrow_isids);CHKERRQ(ierr);
79   ierr = PetscCalloc3(size,&toranks,2*size,&tosizes,size,&tosizes_temp);CHKERRQ(ierr);
80   nrrows = 0;
81   for (i=0; i<nidx; i++){
82     length_i     = length[i];
83     indices_i    = indices[i];
84     for (j=0; j<length_i; j++){
85       owner = -1;
86       ierr = PetscLayoutFindOwner(rmap,indices_i[j],&owner);CHKERRQ(ierr);
87       /* remote processors */
88       if (owner != rank){
89         tosizes_temp[owner]++; /* number of rows to owner */
90         rrow_ranks[nrrows]  = owner; /* processor */
91         rrow_isids[nrrows]   = i; /* is id */
92         remoterows[nrrows++] = indices_i[j]; /* row */
93       }
94     }
95     ierr = ISRestoreIndices(is[i],&indices[i]);CHKERRQ(ierr);
96   }
97   ierr = PetscFree2(indices,length);CHKERRQ(ierr);
98   /* test if we need to exchange messages
99    * generally speaking, we do not need to exchange
100    * data when overlap is 1
101    * */
102   ierr = MPIU_Allreduce(&nrrows,&reducednrrows,1,MPIU_INT,MPIU_MAX,comm);CHKERRQ(ierr);
103   /* we do not have any messages
104    * It usually corresponds to overlap 1
105    * */
106   if (!reducednrrows){
107     ierr = PetscFree3(toranks,tosizes,tosizes_temp);CHKERRQ(ierr);
108     ierr = PetscFree3(remoterows,rrow_ranks,rrow_isids);CHKERRQ(ierr);
109     ierr = MatIncreaseOverlap_MPIAIJ_Local_Scalable(mat,nidx,is);CHKERRQ(ierr);
110     PetscFunctionReturn(0);
111   }
112   nto = 0;
113   /* send sizes and ranks for building a two-sided communcation */
114   for (i=0; i<size; i++){
115    if (tosizes_temp[i]){
116      tosizes[nto*2]  = tosizes_temp[i]*2; /* size */
117      tosizes_temp[i] = nto; /* a map from processor to index */
118      toranks[nto++]  = i; /* processor */
119    }
120   }
121   ierr = PetscCalloc1(nto+1,&toffsets);CHKERRQ(ierr);
122   for (i=0; i<nto; i++){
123     toffsets[i+1]  = toffsets[i]+tosizes[2*i]; /* offsets */
124     tosizes[2*i+1] = toffsets[i]; /* offsets to send */
125   }
126   /* send information to other processors */
127   ierr = PetscCommBuildTwoSided(comm,2,MPIU_INT,nto,toranks,tosizes,&nfrom,&fromranks,&fromsizes);CHKERRQ(ierr);
128   nrecvrows = 0;
129   for (i=0; i<nfrom; i++) nrecvrows += fromsizes[2*i];
130   ierr = PetscMalloc1(nrecvrows,&remote);CHKERRQ(ierr);
131   nrecvrows = 0;
132   for (i=0; i<nfrom; i++){
133     for (j=0; j<fromsizes[2*i]; j++){
134       remote[nrecvrows].rank    = fromranks[i];
135       remote[nrecvrows++].index = fromsizes[2*i+1]+j;
136     }
137   }
138   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
139   ierr = PetscSFSetGraph(sf,nrecvrows,nrecvrows,NULL,PETSC_OWN_POINTER,remote,PETSC_OWN_POINTER);CHKERRQ(ierr);
140   /* use two-sided communication by default since OPENMPI has some bugs for one-sided one */
141   ierr = PetscSFSetType(sf,PETSCSFBASIC);CHKERRQ(ierr);
142   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
143   /* message pair <no of is, row>  */
144   ierr = PetscCalloc2(2*nrrows,&todata,nrecvrows,&fromdata);CHKERRQ(ierr);
145   for (i=0; i<nrrows; i++){
146     owner = rrow_ranks[i]; /* processor */
147     j     = tosizes_temp[owner]; /* index */
148     todata[toffsets[j]++] = rrow_isids[i];
149     todata[toffsets[j]++] = remoterows[i];
150   }
151   ierr = PetscFree3(toranks,tosizes,tosizes_temp);CHKERRQ(ierr);
152   ierr = PetscFree3(remoterows,rrow_ranks,rrow_isids);CHKERRQ(ierr);
153   ierr = PetscFree(toffsets);CHKERRQ(ierr);
154   ierr = PetscSFBcastBegin(sf,MPIU_INT,todata,fromdata);CHKERRQ(ierr);
155   ierr = PetscSFBcastEnd(sf,MPIU_INT,todata,fromdata);CHKERRQ(ierr);
156   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
157   /* send rows belonging to the remote so that then we could get the overlapping data back */
158   ierr = MatIncreaseOverlap_MPIAIJ_Send_Scalable(mat,nidx,nfrom,fromranks,fromsizes,fromdata,&sbsizes,&sbdata);CHKERRQ(ierr);
159   ierr = PetscFree2(todata,fromdata);CHKERRQ(ierr);
160   ierr = PetscFree(fromsizes);CHKERRQ(ierr);
161   ierr = PetscCommBuildTwoSided(comm,2,MPIU_INT,nfrom,fromranks,sbsizes,&nto,&toranks,&tosizes);CHKERRQ(ierr);
162   ierr = PetscFree(fromranks);CHKERRQ(ierr);
163   nrecvrows = 0;
164   for (i=0; i<nto; i++) nrecvrows += tosizes[2*i];
165   ierr = PetscCalloc1(nrecvrows,&todata);CHKERRQ(ierr);
166   ierr = PetscMalloc1(nrecvrows,&remote);CHKERRQ(ierr);
167   nrecvrows = 0;
168   for (i=0; i<nto; i++){
169     for (j=0; j<tosizes[2*i]; j++){
170       remote[nrecvrows].rank    = toranks[i];
171       remote[nrecvrows++].index = tosizes[2*i+1]+j;
172     }
173   }
174   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
175   ierr = PetscSFSetGraph(sf,nrecvrows,nrecvrows,NULL,PETSC_OWN_POINTER,remote,PETSC_OWN_POINTER);CHKERRQ(ierr);
176   /* use two-sided communication by default since OPENMPI has some bugs for one-sided one */
177   ierr = PetscSFSetType(sf,PETSCSFBASIC);CHKERRQ(ierr);
178   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
179   /* overlap communication and computation */
180   ierr = PetscSFBcastBegin(sf,MPIU_INT,sbdata,todata);CHKERRQ(ierr);
181   ierr = MatIncreaseOverlap_MPIAIJ_Local_Scalable(mat,nidx,is);CHKERRQ(ierr);
182   ierr = PetscSFBcastEnd(sf,MPIU_INT,sbdata,todata);CHKERRQ(ierr);
183   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
184   ierr = PetscFree2(sbdata,sbsizes);CHKERRQ(ierr);
185   ierr = MatIncreaseOverlap_MPIAIJ_Receive_Scalable(mat,nidx,is,nrecvrows,todata);CHKERRQ(ierr);
186   ierr = PetscFree(toranks);CHKERRQ(ierr);
187   ierr = PetscFree(tosizes);CHKERRQ(ierr);
188   ierr = PetscFree(todata);CHKERRQ(ierr);
189   PetscFunctionReturn(0);
190 }
191 
192 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive_Scalable(Mat mat,PetscInt nidx, IS is[], PetscInt nrecvs, PetscInt *recvdata)
193 {
194   PetscInt         *isz,isz_i,i,j,is_id, data_size;
195   PetscInt          col,lsize,max_lsize,*indices_temp, *indices_i;
196   const PetscInt   *indices_i_temp;
197   PetscErrorCode    ierr;
198 
199   PetscFunctionBegin;
200   max_lsize = 0;
201   ierr = PetscMalloc1(nidx,&isz);CHKERRQ(ierr);
202   for (i=0; i<nidx; i++){
203     ierr = ISGetLocalSize(is[i],&lsize);CHKERRQ(ierr);
204     max_lsize = lsize>max_lsize ? lsize:max_lsize;
205     isz[i]    = lsize;
206   }
207   ierr = PetscMalloc1((max_lsize+nrecvs)*nidx,&indices_temp);CHKERRQ(ierr);
208   for (i=0; i<nidx; i++){
209     ierr = ISGetIndices(is[i],&indices_i_temp);CHKERRQ(ierr);
210     ierr = PetscMemcpy(indices_temp+i*(max_lsize+nrecvs),indices_i_temp, sizeof(PetscInt)*isz[i]);CHKERRQ(ierr);
211     ierr = ISRestoreIndices(is[i],&indices_i_temp);CHKERRQ(ierr);
212     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
213   }
214   /* retrieve information to get row id and its overlap */
215   for (i=0; i<nrecvs; ){
216     is_id      = recvdata[i++];
217     data_size  = recvdata[i++];
218     indices_i  = indices_temp+(max_lsize+nrecvs)*is_id;
219     isz_i      = isz[is_id];
220     for (j=0; j< data_size; j++){
221       col = recvdata[i++];
222       indices_i[isz_i++] = col;
223     }
224     isz[is_id] = isz_i;
225   }
226   /* remove duplicate entities */
227   for (i=0; i<nidx; i++){
228     indices_i  = indices_temp+(max_lsize+nrecvs)*i;
229     isz_i      = isz[i];
230     ierr = PetscSortRemoveDupsInt(&isz_i,indices_i);CHKERRQ(ierr);
231     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz_i,indices_i,PETSC_COPY_VALUES,&is[i]);CHKERRQ(ierr);
232   }
233   ierr = PetscFree(isz);CHKERRQ(ierr);
234   ierr = PetscFree(indices_temp);CHKERRQ(ierr);
235   PetscFunctionReturn(0);
236 }
237 
238 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Send_Scalable(Mat mat,PetscInt nidx, PetscMPIInt nfrom,PetscMPIInt *fromranks,PetscInt *fromsizes, PetscInt *fromrows, PetscInt **sbrowsizes, PetscInt **sbrows)
239 {
240   PetscLayout       rmap,cmap;
241   PetscInt          i,j,k,l,*rows_i,*rows_data_ptr,**rows_data,max_fszs,rows_pos,*rows_pos_i;
242   PetscInt          is_id,tnz,an,bn,rstart,cstart,row,start,end,col,totalrows,*sbdata;
243   PetscInt         *indv_counts,indvc_ij,*sbsizes,*indices_tmp,*offsets;
244   const PetscInt   *gcols,*ai,*aj,*bi,*bj;
245   Mat               amat,bmat;
246   PetscMPIInt       rank;
247   PetscBool         done;
248   MPI_Comm          comm;
249   PetscErrorCode    ierr;
250 
251   PetscFunctionBegin;
252   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
253   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
254   ierr = MatMPIAIJGetSeqAIJ(mat,&amat,&bmat,&gcols);CHKERRQ(ierr);
255   /* Even if the mat is symmetric, we still assume it is not symmetric */
256   ierr = MatGetRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
257   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
258   ierr = MatGetRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
259   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
260   /* total number of nonzero values is used to estimate the memory usage in the next step */
261   tnz  = ai[an]+bi[bn];
262   ierr = MatGetLayouts(mat,&rmap,&cmap);CHKERRQ(ierr);
263   ierr = PetscLayoutGetRange(rmap,&rstart,NULL);CHKERRQ(ierr);
264   ierr = PetscLayoutGetRange(cmap,&cstart,NULL);CHKERRQ(ierr);
265   /* to find the longest message */
266   max_fszs = 0;
267   for (i=0; i<nfrom; i++) max_fszs = fromsizes[2*i]>max_fszs ? fromsizes[2*i]:max_fszs;
268   /* better way to estimate number of nonzero in the mat??? */
269   ierr = PetscCalloc5(max_fszs*nidx,&rows_data_ptr,nidx,&rows_data,nidx,&rows_pos_i,nfrom*nidx,&indv_counts,tnz,&indices_tmp);CHKERRQ(ierr);
270   for (i=0; i<nidx; i++) rows_data[i] = rows_data_ptr+max_fszs*i;
271   rows_pos  = 0;
272   totalrows = 0;
273   for (i=0; i<nfrom; i++){
274     ierr = PetscMemzero(rows_pos_i,sizeof(PetscInt)*nidx);CHKERRQ(ierr);
275     /* group data together */
276     for (j=0; j<fromsizes[2*i]; j+=2){
277       is_id                       = fromrows[rows_pos++];/* no of is */
278       rows_i                      = rows_data[is_id];
279       rows_i[rows_pos_i[is_id]++] = fromrows[rows_pos++];/* row */
280     }
281     /* estimate a space to avoid multiple allocations  */
282     for (j=0; j<nidx; j++){
283       indvc_ij = 0;
284       rows_i   = rows_data[j];
285       for (l=0; l<rows_pos_i[j]; l++){
286         row    = rows_i[l]-rstart;
287         start  = ai[row];
288         end    = ai[row+1];
289         for (k=start; k<end; k++){ /* Amat */
290           col = aj[k] + cstart;
291           indices_tmp[indvc_ij++] = col;/* do not count the rows from the original rank */
292         }
293         start = bi[row];
294         end   = bi[row+1];
295         for (k=start; k<end; k++) { /* Bmat */
296           col = gcols[bj[k]];
297           indices_tmp[indvc_ij++] = col;
298         }
299       }
300       ierr = PetscSortRemoveDupsInt(&indvc_ij,indices_tmp);CHKERRQ(ierr);
301       indv_counts[i*nidx+j] = indvc_ij;
302       totalrows            += indvc_ij;
303     }
304   }
305   /* message triple <no of is, number of rows, rows> */
306   ierr = PetscCalloc2(totalrows+nidx*nfrom*2,&sbdata,2*nfrom,&sbsizes);CHKERRQ(ierr);
307   totalrows = 0;
308   rows_pos  = 0;
309   /* use this code again */
310   for (i=0;i<nfrom;i++){
311     ierr = PetscMemzero(rows_pos_i,sizeof(PetscInt)*nidx);CHKERRQ(ierr);
312     for (j=0; j<fromsizes[2*i]; j+=2){
313       is_id                       = fromrows[rows_pos++];
314       rows_i                      = rows_data[is_id];
315       rows_i[rows_pos_i[is_id]++] = fromrows[rows_pos++];
316     }
317     /* add data  */
318     for (j=0; j<nidx; j++){
319       if (!indv_counts[i*nidx+j]) continue;
320       indvc_ij = 0;
321       sbdata[totalrows++] = j;
322       sbdata[totalrows++] = indv_counts[i*nidx+j];
323       sbsizes[2*i]       += 2;
324       rows_i              = rows_data[j];
325       for (l=0; l<rows_pos_i[j]; l++){
326         row   = rows_i[l]-rstart;
327         start = ai[row];
328         end   = ai[row+1];
329         for (k=start; k<end; k++){ /* Amat */
330           col = aj[k] + cstart;
331           indices_tmp[indvc_ij++] = col;
332         }
333         start = bi[row];
334         end   = bi[row+1];
335         for (k=start; k<end; k++) { /* Bmat */
336           col = gcols[bj[k]];
337           indices_tmp[indvc_ij++] = col;
338         }
339       }
340       ierr = PetscSortRemoveDupsInt(&indvc_ij,indices_tmp);CHKERRQ(ierr);
341       sbsizes[2*i]  += indvc_ij;
342       ierr = PetscMemcpy(sbdata+totalrows,indices_tmp,sizeof(PetscInt)*indvc_ij);CHKERRQ(ierr);
343       totalrows += indvc_ij;
344     }
345   }
346   ierr = PetscCalloc1(nfrom+1,&offsets);CHKERRQ(ierr);
347   for (i=0; i<nfrom; i++){
348     offsets[i+1]   = offsets[i] + sbsizes[2*i];
349     sbsizes[2*i+1] = offsets[i];
350   }
351   ierr = PetscFree(offsets);CHKERRQ(ierr);
352   if (sbrowsizes) *sbrowsizes = sbsizes;
353   if (sbrows) *sbrows = sbdata;
354   ierr = PetscFree5(rows_data_ptr,rows_data,rows_pos_i,indv_counts,indices_tmp);CHKERRQ(ierr);
355   ierr = MatRestoreRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
356   ierr = MatRestoreRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
357   PetscFunctionReturn(0);
358 }
359 
360 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local_Scalable(Mat mat,PetscInt nidx, IS is[])
361 {
362   const PetscInt   *gcols,*ai,*aj,*bi,*bj, *indices;
363   PetscInt          tnz,an,bn,i,j,row,start,end,rstart,cstart,col,k,*indices_temp;
364   PetscInt          lsize,lsize_tmp,owner;
365   PetscMPIInt       rank;
366   Mat               amat,bmat;
367   PetscBool         done;
368   PetscLayout       cmap,rmap;
369   MPI_Comm          comm;
370   PetscErrorCode    ierr;
371 
372   PetscFunctionBegin;
373   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
374   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
375   ierr = MatMPIAIJGetSeqAIJ(mat,&amat,&bmat,&gcols);CHKERRQ(ierr);
376   ierr = MatGetRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
377   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
378   ierr = MatGetRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
379   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
380   /* is it a safe way to compute number of nonzero values ? */
381   tnz  = ai[an]+bi[bn];
382   ierr = MatGetLayouts(mat,&rmap,&cmap);CHKERRQ(ierr);
383   ierr = PetscLayoutGetRange(rmap,&rstart,NULL);CHKERRQ(ierr);
384   ierr = PetscLayoutGetRange(cmap,&cstart,NULL);CHKERRQ(ierr);
385   /* it is a better way to estimate memory than the old implementation
386    * where global size of matrix is used
387    * */
388   ierr = PetscMalloc1(tnz,&indices_temp);CHKERRQ(ierr);
389   for (i=0; i<nidx; i++) {
390     ierr = ISGetLocalSize(is[i],&lsize);CHKERRQ(ierr);
391     ierr = ISGetIndices(is[i],&indices);CHKERRQ(ierr);
392     lsize_tmp = 0;
393     for (j=0; j<lsize; j++) {
394       owner = -1;
395       row   = indices[j];
396       ierr = PetscLayoutFindOwner(rmap,row,&owner);CHKERRQ(ierr);
397       if (owner != rank) continue;
398       /* local number */
399       row  -= rstart;
400       start = ai[row];
401       end   = ai[row+1];
402       for (k=start; k<end; k++) { /* Amat */
403         col = aj[k] + cstart;
404         indices_temp[lsize_tmp++] = col;
405       }
406       start = bi[row];
407       end   = bi[row+1];
408       for (k=start; k<end; k++) { /* Bmat */
409         col = gcols[bj[k]];
410         indices_temp[lsize_tmp++] = col;
411       }
412     }
413    ierr = ISRestoreIndices(is[i],&indices);CHKERRQ(ierr);
414    ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
415    ierr = PetscSortRemoveDupsInt(&lsize_tmp,indices_temp);CHKERRQ(ierr);
416    ierr = ISCreateGeneral(PETSC_COMM_SELF,lsize_tmp,indices_temp,PETSC_COPY_VALUES,&is[i]);CHKERRQ(ierr);
417   }
418   ierr = PetscFree(indices_temp);CHKERRQ(ierr);
419   ierr = MatRestoreRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
420   ierr = MatRestoreRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
421   PetscFunctionReturn(0);
422 }
423 
424 
425 /*
426   Sample message format:
427   If a processor A wants processor B to process some elements corresponding
428   to index sets is[1],is[5]
429   mesg [0] = 2   (no of index sets in the mesg)
430   -----------
431   mesg [1] = 1 => is[1]
432   mesg [2] = sizeof(is[1]);
433   -----------
434   mesg [3] = 5  => is[5]
435   mesg [4] = sizeof(is[5]);
436   -----------
437   mesg [5]
438   mesg [n]  datas[1]
439   -----------
440   mesg[n+1]
441   mesg[m]  data(is[5])
442   -----------
443 
444   Notes:
445   nrqs - no of requests sent (or to be sent out)
446   nrqr - no of requests recieved (which have to be or which have been processed
447 */
448 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once(Mat C,PetscInt imax,IS is[])
449 {
450   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
451   PetscMPIInt    *w1,*w2,nrqr,*w3,*w4,*onodes1,*olengths1,*onodes2,*olengths2;
452   const PetscInt **idx,*idx_i;
453   PetscInt       *n,**data,len;
454 #if defined(PETSC_USE_CTABLE)
455   PetscTable     *table_data,table_data_i;
456   PetscInt       *tdata,tcount,tcount_max;
457 #else
458   PetscInt       *data_i,*d_p;
459 #endif
460   PetscErrorCode ierr;
461   PetscMPIInt    size,rank,tag1,tag2;
462   PetscInt       M,i,j,k,**rbuf,row,proc = 0,nrqs,msz,**outdat,**ptr;
463   PetscInt       *ctr,*pa,*tmp,*isz,*isz1,**xdata,**rbuf2;
464   PetscBT        *table;
465   MPI_Comm       comm;
466   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2;
467   MPI_Status     *s_status,*recv_status;
468   char           *t_p;
469 
470   PetscFunctionBegin;
471   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
472   size = c->size;
473   rank = c->rank;
474   M    = C->rmap->N;
475 
476   ierr = PetscObjectGetNewTag((PetscObject)C,&tag1);CHKERRQ(ierr);
477   ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
478 
479   ierr = PetscMalloc2(imax,&idx,imax,&n);CHKERRQ(ierr);
480 
481   for (i=0; i<imax; i++) {
482     ierr = ISGetIndices(is[i],&idx[i]);CHKERRQ(ierr);
483     ierr = ISGetLocalSize(is[i],&n[i]);CHKERRQ(ierr);
484   }
485 
486   /* evaluate communication - mesg to who,length of mesg, and buffer space
487      required. Based on this, buffers are allocated, and data copied into them  */
488   ierr = PetscMalloc4(size,&w1,size,&w2,size,&w3,size,&w4);CHKERRQ(ierr);
489   ierr = PetscMemzero(w1,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
490   ierr = PetscMemzero(w2,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
491   ierr = PetscMemzero(w3,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
492   for (i=0; i<imax; i++) {
493     ierr  = PetscMemzero(w4,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
494     idx_i = idx[i];
495     len   = n[i];
496     for (j=0; j<len; j++) {
497       row = idx_i[j];
498       if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Index set cannot have negative entries");
499       ierr = PetscLayoutFindOwner(C->rmap,row,&proc);CHKERRQ(ierr);
500       w4[proc]++;
501     }
502     for (j=0; j<size; j++) {
503       if (w4[j]) { w1[j] += w4[j]; w3[j]++;}
504     }
505   }
506 
507   nrqs     = 0;              /* no of outgoing messages */
508   msz      = 0;              /* total mesg length (for all proc */
509   w1[rank] = 0;              /* no mesg sent to intself */
510   w3[rank] = 0;
511   for (i=0; i<size; i++) {
512     if (w1[i])  {w2[i] = 1; nrqs++;} /* there exists a message to proc i */
513   }
514   /* pa - is list of processors to communicate with */
515   ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr);
516   for (i=0,j=0; i<size; i++) {
517     if (w1[i]) {pa[j] = i; j++;}
518   }
519 
520   /* Each message would have a header = 1 + 2*(no of IS) + data */
521   for (i=0; i<nrqs; i++) {
522     j      = pa[i];
523     w1[j] += w2[j] + 2*w3[j];
524     msz   += w1[j];
525   }
526 
527   /* Determine the number of messages to expect, their lengths, from from-ids */
528   ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
529   ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
530 
531   /* Now post the Irecvs corresponding to these messages */
532   ierr = PetscPostIrecvInt(comm,tag1,nrqr,onodes1,olengths1,&rbuf,&r_waits1);CHKERRQ(ierr);
533 
534   /* Allocate Memory for outgoing messages */
535   ierr = PetscMalloc4(size,&outdat,size,&ptr,msz,&tmp,size,&ctr);CHKERRQ(ierr);
536   ierr = PetscMemzero(outdat,size*sizeof(PetscInt*));CHKERRQ(ierr);
537   ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
538 
539   {
540     PetscInt *iptr = tmp,ict  = 0;
541     for (i=0; i<nrqs; i++) {
542       j         = pa[i];
543       iptr     +=  ict;
544       outdat[j] = iptr;
545       ict       = w1[j];
546     }
547   }
548 
549   /* Form the outgoing messages */
550   /* plug in the headers */
551   for (i=0; i<nrqs; i++) {
552     j            = pa[i];
553     outdat[j][0] = 0;
554     ierr         = PetscMemzero(outdat[j]+1,2*w3[j]*sizeof(PetscInt));CHKERRQ(ierr);
555     ptr[j]       = outdat[j] + 2*w3[j] + 1;
556   }
557 
558   /* Memory for doing local proc's work */
559   {
560     PetscInt M_BPB_imax = 0;
561 #if defined(PETSC_USE_CTABLE)
562     ierr = PetscIntMultError((M/PETSC_BITS_PER_BYTE+1),imax, &M_BPB_imax);CHKERRQ(ierr);
563     ierr = PetscMalloc1(imax,&table_data);CHKERRQ(ierr);
564     for (i=0; i<imax; i++) {
565       ierr = PetscTableCreate(n[i]+1,M+1,&table_data[i]);CHKERRQ(ierr);
566     }
567     ierr = PetscCalloc4(imax,&table, imax,&data, imax,&isz, M_BPB_imax,&t_p);CHKERRQ(ierr);
568     for (i=0; i<imax; i++) {
569       table[i] = t_p + (M/PETSC_BITS_PER_BYTE+1)*i;
570     }
571 #else
572     PetscInt Mimax = 0;
573     ierr = PetscIntMultError(M,imax, &Mimax);CHKERRQ(ierr);
574     ierr = PetscIntMultError((M/PETSC_BITS_PER_BYTE+1),imax, &M_BPB_imax);CHKERRQ(ierr);
575     ierr = PetscCalloc5(imax,&table, imax,&data, imax,&isz, Mimax,&d_p, M_BPB_imax,&t_p);CHKERRQ(ierr);
576     for (i=0; i<imax; i++) {
577       table[i] = t_p + (M/PETSC_BITS_PER_BYTE+1)*i;
578       data[i]  = d_p + M*i;
579     }
580 #endif
581   }
582 
583   /* Parse the IS and update local tables and the outgoing buf with the data */
584   {
585     PetscInt n_i,isz_i,*outdat_j,ctr_j;
586     PetscBT  table_i;
587 
588     for (i=0; i<imax; i++) {
589       ierr    = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
590       n_i     = n[i];
591       table_i = table[i];
592       idx_i   = idx[i];
593 #if defined(PETSC_USE_CTABLE)
594       table_data_i = table_data[i];
595 #else
596       data_i  = data[i];
597 #endif
598       isz_i   = isz[i];
599       for (j=0; j<n_i; j++) {   /* parse the indices of each IS */
600         row  = idx_i[j];
601         ierr = PetscLayoutFindOwner(C->rmap,row,&proc);CHKERRQ(ierr);
602         if (proc != rank) { /* copy to the outgoing buffer */
603           ctr[proc]++;
604           *ptr[proc] = row;
605           ptr[proc]++;
606         } else if (!PetscBTLookupSet(table_i,row)) {
607 #if defined(PETSC_USE_CTABLE)
608           ierr = PetscTableAdd(table_data_i,row+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
609 #else
610           data_i[isz_i] = row; /* Update the local table */
611 #endif
612           isz_i++;
613         }
614       }
615       /* Update the headers for the current IS */
616       for (j=0; j<size; j++) { /* Can Optimise this loop by using pa[] */
617         if ((ctr_j = ctr[j])) {
618           outdat_j        = outdat[j];
619           k               = ++outdat_j[0];
620           outdat_j[2*k]   = ctr_j;
621           outdat_j[2*k-1] = i;
622         }
623       }
624       isz[i] = isz_i;
625     }
626   }
627 
628   /*  Now  post the sends */
629   ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
630   for (i=0; i<nrqs; ++i) {
631     j    = pa[i];
632     ierr = MPI_Isend(outdat[j],w1[j],MPIU_INT,j,tag1,comm,s_waits1+i);CHKERRQ(ierr);
633   }
634 
635   /* No longer need the original indices */
636   for (i=0; i<imax; ++i) {
637     ierr = ISRestoreIndices(is[i],idx+i);CHKERRQ(ierr);
638   }
639   ierr = PetscFree2(idx,n);CHKERRQ(ierr);
640 
641   for (i=0; i<imax; ++i) {
642     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
643   }
644 
645   /* Do Local work */
646 #if defined(PETSC_USE_CTABLE)
647   ierr = MatIncreaseOverlap_MPIAIJ_Local(C,imax,table,isz,NULL,table_data);CHKERRQ(ierr);
648 #else
649   ierr = MatIncreaseOverlap_MPIAIJ_Local(C,imax,table,isz,data,NULL);CHKERRQ(ierr);
650 #endif
651 
652   /* Receive messages */
653   ierr = PetscMalloc1(nrqr+1,&recv_status);CHKERRQ(ierr);
654   if (nrqr) {ierr = MPI_Waitall(nrqr,r_waits1,recv_status);CHKERRQ(ierr);}
655 
656   ierr = PetscMalloc1(nrqs+1,&s_status);CHKERRQ(ierr);
657   if (nrqs) {ierr = MPI_Waitall(nrqs,s_waits1,s_status);CHKERRQ(ierr);}
658 
659   /* Phase 1 sends are complete - deallocate buffers */
660   ierr = PetscFree4(outdat,ptr,tmp,ctr);CHKERRQ(ierr);
661   ierr = PetscFree4(w1,w2,w3,w4);CHKERRQ(ierr);
662 
663   ierr = PetscMalloc1(nrqr+1,&xdata);CHKERRQ(ierr);
664   ierr = PetscMalloc1(nrqr+1,&isz1);CHKERRQ(ierr);
665   ierr = MatIncreaseOverlap_MPIAIJ_Receive(C,nrqr,rbuf,xdata,isz1);CHKERRQ(ierr);
666   ierr = PetscFree(rbuf[0]);CHKERRQ(ierr);
667   ierr = PetscFree(rbuf);CHKERRQ(ierr);
668 
669 
670   /* Send the data back */
671   /* Do a global reduction to know the buffer space req for incoming messages */
672   {
673     PetscMPIInt *rw1;
674 
675     ierr = PetscCalloc1(size,&rw1);CHKERRQ(ierr);
676 
677     for (i=0; i<nrqr; ++i) {
678       proc = recv_status[i].MPI_SOURCE;
679 
680       if (proc != onodes1[i]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPI_SOURCE mismatch");
681       rw1[proc] = isz1[i];
682     }
683     ierr = PetscFree(onodes1);CHKERRQ(ierr);
684     ierr = PetscFree(olengths1);CHKERRQ(ierr);
685 
686     /* Determine the number of messages to expect, their lengths, from from-ids */
687     ierr = PetscGatherMessageLengths(comm,nrqr,nrqs,rw1,&onodes2,&olengths2);CHKERRQ(ierr);
688     ierr = PetscFree(rw1);CHKERRQ(ierr);
689   }
690   /* Now post the Irecvs corresponding to these messages */
691   ierr = PetscPostIrecvInt(comm,tag2,nrqs,onodes2,olengths2,&rbuf2,&r_waits2);CHKERRQ(ierr);
692 
693   /* Now  post the sends */
694   ierr = PetscMalloc1(nrqr+1,&s_waits2);CHKERRQ(ierr);
695   for (i=0; i<nrqr; ++i) {
696     j    = recv_status[i].MPI_SOURCE;
697     ierr = MPI_Isend(xdata[i],isz1[i],MPIU_INT,j,tag2,comm,s_waits2+i);CHKERRQ(ierr);
698   }
699 
700   /* receive work done on other processors */
701   {
702     PetscInt    is_no,ct1,max,*rbuf2_i,isz_i,jmax;
703     PetscMPIInt idex;
704     PetscBT     table_i;
705     MPI_Status  *status2;
706 
707     ierr = PetscMalloc1((PetscMax(nrqr,nrqs)+1),&status2);CHKERRQ(ierr);
708     for (i=0; i<nrqs; ++i) {
709       ierr = MPI_Waitany(nrqs,r_waits2,&idex,status2+i);CHKERRQ(ierr);
710       /* Process the message */
711       rbuf2_i = rbuf2[idex];
712       ct1     = 2*rbuf2_i[0]+1;
713       jmax    = rbuf2[idex][0];
714       for (j=1; j<=jmax; j++) {
715         max     = rbuf2_i[2*j];
716         is_no   = rbuf2_i[2*j-1];
717         isz_i   = isz[is_no];
718         table_i = table[is_no];
719 #if defined(PETSC_USE_CTABLE)
720         table_data_i = table_data[is_no];
721 #else
722         data_i  = data[is_no];
723 #endif
724         for (k=0; k<max; k++,ct1++) {
725           row = rbuf2_i[ct1];
726           if (!PetscBTLookupSet(table_i,row)) {
727 #if defined(PETSC_USE_CTABLE)
728             ierr = PetscTableAdd(table_data_i,row+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
729 #else
730             data_i[isz_i] = row;
731 #endif
732             isz_i++;
733           }
734         }
735         isz[is_no] = isz_i;
736       }
737     }
738 
739     if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits2,status2);CHKERRQ(ierr);}
740     ierr = PetscFree(status2);CHKERRQ(ierr);
741   }
742 
743 #if defined(PETSC_USE_CTABLE)
744   tcount_max = 0;
745   for (i=0; i<imax; ++i) {
746     table_data_i = table_data[i];
747     ierr = PetscTableGetCount(table_data_i,&tcount);CHKERRQ(ierr);
748     if (tcount_max < tcount) tcount_max = tcount;
749   }
750   ierr = PetscMalloc1(tcount_max+1,&tdata);CHKERRQ(ierr);
751 #endif
752 
753   for (i=0; i<imax; ++i) {
754 #if defined(PETSC_USE_CTABLE)
755     PetscTablePosition tpos;
756     table_data_i = table_data[i];
757 
758     ierr = PetscTableGetHeadPosition(table_data_i,&tpos);CHKERRQ(ierr);
759     while (tpos) {
760       ierr = PetscTableGetNext(table_data_i,&tpos,&k,&j);CHKERRQ(ierr);
761       tdata[--j] = --k;
762     }
763     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz[i],tdata,PETSC_COPY_VALUES,is+i);CHKERRQ(ierr);
764 #else
765     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz[i],data[i],PETSC_COPY_VALUES,is+i);CHKERRQ(ierr);
766 #endif
767   }
768 
769   ierr = PetscFree(onodes2);CHKERRQ(ierr);
770   ierr = PetscFree(olengths2);CHKERRQ(ierr);
771 
772   ierr = PetscFree(pa);CHKERRQ(ierr);
773   ierr = PetscFree(rbuf2[0]);CHKERRQ(ierr);
774   ierr = PetscFree(rbuf2);CHKERRQ(ierr);
775   ierr = PetscFree(s_waits1);CHKERRQ(ierr);
776   ierr = PetscFree(r_waits1);CHKERRQ(ierr);
777   ierr = PetscFree(s_waits2);CHKERRQ(ierr);
778   ierr = PetscFree(r_waits2);CHKERRQ(ierr);
779   ierr = PetscFree(s_status);CHKERRQ(ierr);
780   ierr = PetscFree(recv_status);CHKERRQ(ierr);
781   ierr = PetscFree(xdata[0]);CHKERRQ(ierr);
782   ierr = PetscFree(xdata);CHKERRQ(ierr);
783   ierr = PetscFree(isz1);CHKERRQ(ierr);
784 #if defined(PETSC_USE_CTABLE)
785   for (i=0; i<imax; i++) {
786     ierr = PetscTableDestroy((PetscTable*)&table_data[i]);CHKERRQ(ierr);
787   }
788   ierr = PetscFree(table_data);CHKERRQ(ierr);
789   ierr = PetscFree(tdata);CHKERRQ(ierr);
790   ierr = PetscFree4(table,data,isz,t_p);CHKERRQ(ierr);
791 #else
792   ierr = PetscFree5(table,data,isz,d_p,t_p);CHKERRQ(ierr);
793 #endif
794   PetscFunctionReturn(0);
795 }
796 
797 /*
798    MatIncreaseOverlap_MPIAIJ_Local - Called by MatincreaseOverlap, to do
799        the work on the local processor.
800 
801      Inputs:
802       C      - MAT_MPIAIJ;
803       imax - total no of index sets processed at a time;
804       table  - an array of char - size = m bits.
805 
806      Output:
807       isz    - array containing the count of the solution elements corresponding
808                to each index set;
809       data or table_data  - pointer to the solutions
810 */
811 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local(Mat C,PetscInt imax,PetscBT *table,PetscInt *isz,PetscInt **data,PetscTable *table_data)
812 {
813   Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
814   Mat        A  = c->A,B = c->B;
815   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
816   PetscInt   start,end,val,max,rstart,cstart,*ai,*aj;
817   PetscInt   *bi,*bj,*garray,i,j,k,row,isz_i;
818   PetscBT    table_i;
819 #if defined(PETSC_USE_CTABLE)
820   PetscTable         table_data_i;
821   PetscErrorCode     ierr;
822   PetscTablePosition tpos;
823   PetscInt           tcount,*tdata;
824 #else
825   PetscInt           *data_i;
826 #endif
827 
828   PetscFunctionBegin;
829   rstart = C->rmap->rstart;
830   cstart = C->cmap->rstart;
831   ai     = a->i;
832   aj     = a->j;
833   bi     = b->i;
834   bj     = b->j;
835   garray = c->garray;
836 
837   for (i=0; i<imax; i++) {
838 #if defined(PETSC_USE_CTABLE)
839     /* copy existing entries of table_data_i into tdata[] */
840     table_data_i = table_data[i];
841     ierr = PetscTableGetCount(table_data_i,&tcount);CHKERRQ(ierr);
842     if (tcount != isz[i]) SETERRQ3(PETSC_COMM_SELF,0," tcount %d != isz[%d] %d",tcount,i,isz[i]);
843 
844     ierr = PetscMalloc1(tcount,&tdata);CHKERRQ(ierr);
845     ierr = PetscTableGetHeadPosition(table_data_i,&tpos);CHKERRQ(ierr);
846     while (tpos) {
847       ierr = PetscTableGetNext(table_data_i,&tpos,&row,&j);CHKERRQ(ierr);
848       tdata[--j] = --row;
849       if (j > tcount - 1) SETERRQ2(PETSC_COMM_SELF,0," j %d >= tcount %d",j,tcount);
850     }
851 #else
852     data_i  = data[i];
853 #endif
854     table_i = table[i];
855     isz_i   = isz[i];
856     max     = isz[i];
857 
858     for (j=0; j<max; j++) {
859 #if defined(PETSC_USE_CTABLE)
860       row   = tdata[j] - rstart;
861 #else
862       row   = data_i[j] - rstart;
863 #endif
864       start = ai[row];
865       end   = ai[row+1];
866       for (k=start; k<end; k++) { /* Amat */
867         val = aj[k] + cstart;
868         if (!PetscBTLookupSet(table_i,val)) {
869 #if defined(PETSC_USE_CTABLE)
870           ierr = PetscTableAdd(table_data_i,val+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
871 #else
872           data_i[isz_i] = val;
873 #endif
874           isz_i++;
875         }
876       }
877       start = bi[row];
878       end   = bi[row+1];
879       for (k=start; k<end; k++) { /* Bmat */
880         val = garray[bj[k]];
881         if (!PetscBTLookupSet(table_i,val)) {
882 #if defined(PETSC_USE_CTABLE)
883           ierr = PetscTableAdd(table_data_i,val+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
884 #else
885           data_i[isz_i] = val;
886 #endif
887           isz_i++;
888         }
889       }
890     }
891     isz[i] = isz_i;
892 
893 #if defined(PETSC_USE_CTABLE)
894     ierr = PetscFree(tdata);CHKERRQ(ierr);
895 #endif
896   }
897   PetscFunctionReturn(0);
898 }
899 
900 /*
901       MatIncreaseOverlap_MPIAIJ_Receive - Process the recieved messages,
902          and return the output
903 
904          Input:
905            C    - the matrix
906            nrqr - no of messages being processed.
907            rbuf - an array of pointers to the recieved requests
908 
909          Output:
910            xdata - array of messages to be sent back
911            isz1  - size of each message
912 
913   For better efficiency perhaps we should malloc separately each xdata[i],
914 then if a remalloc is required we need only copy the data for that one row
915 rather then all previous rows as it is now where a single large chunck of
916 memory is used.
917 
918 */
919 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive(Mat C,PetscInt nrqr,PetscInt **rbuf,PetscInt **xdata,PetscInt * isz1)
920 {
921   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
922   Mat            A  = c->A,B = c->B;
923   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
924   PetscErrorCode ierr;
925   PetscInt       rstart,cstart,*ai,*aj,*bi,*bj,*garray,i,j,k;
926   PetscInt       row,total_sz,ct,ct1,ct2,ct3,mem_estimate,oct2,l,start,end;
927   PetscInt       val,max1,max2,m,no_malloc =0,*tmp,new_estimate,ctr;
928   PetscInt       *rbuf_i,kmax,rbuf_0;
929   PetscBT        xtable;
930 
931   PetscFunctionBegin;
932   m      = C->rmap->N;
933   rstart = C->rmap->rstart;
934   cstart = C->cmap->rstart;
935   ai     = a->i;
936   aj     = a->j;
937   bi     = b->i;
938   bj     = b->j;
939   garray = c->garray;
940 
941 
942   for (i=0,ct=0,total_sz=0; i<nrqr; ++i) {
943     rbuf_i =  rbuf[i];
944     rbuf_0 =  rbuf_i[0];
945     ct    += rbuf_0;
946     for (j=1; j<=rbuf_0; j++) total_sz += rbuf_i[2*j];
947   }
948 
949   if (C->rmap->n) max1 = ct*(a->nz + b->nz)/C->rmap->n;
950   else max1 = 1;
951   mem_estimate = 3*((total_sz > max1 ? total_sz : max1)+1);
952   ierr         = PetscMalloc1(mem_estimate,&xdata[0]);CHKERRQ(ierr);
953   ++no_malloc;
954   ierr = PetscBTCreate(m,&xtable);CHKERRQ(ierr);
955   ierr = PetscMemzero(isz1,nrqr*sizeof(PetscInt));CHKERRQ(ierr);
956 
957   ct3 = 0;
958   for (i=0; i<nrqr; i++) { /* for easch mesg from proc i */
959     rbuf_i =  rbuf[i];
960     rbuf_0 =  rbuf_i[0];
961     ct1    =  2*rbuf_0+1;
962     ct2    =  ct1;
963     ct3   += ct1;
964     for (j=1; j<=rbuf_0; j++) { /* for each IS from proc i*/
965       ierr = PetscBTMemzero(m,xtable);CHKERRQ(ierr);
966       oct2 = ct2;
967       kmax = rbuf_i[2*j];
968       for (k=0; k<kmax; k++,ct1++) {
969         row = rbuf_i[ct1];
970         if (!PetscBTLookupSet(xtable,row)) {
971           if (!(ct3 < mem_estimate)) {
972             new_estimate = (PetscInt)(1.5*mem_estimate)+1;
973             ierr         = PetscMalloc1(new_estimate,&tmp);CHKERRQ(ierr);
974             ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(PetscInt));CHKERRQ(ierr);
975             ierr         = PetscFree(xdata[0]);CHKERRQ(ierr);
976             xdata[0]     = tmp;
977             mem_estimate = new_estimate; ++no_malloc;
978             for (ctr=1; ctr<=i; ctr++) xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];
979           }
980           xdata[i][ct2++] = row;
981           ct3++;
982         }
983       }
984       for (k=oct2,max2=ct2; k<max2; k++) {
985         row   = xdata[i][k] - rstart;
986         start = ai[row];
987         end   = ai[row+1];
988         for (l=start; l<end; l++) {
989           val = aj[l] + cstart;
990           if (!PetscBTLookupSet(xtable,val)) {
991             if (!(ct3 < mem_estimate)) {
992               new_estimate = (PetscInt)(1.5*mem_estimate)+1;
993               ierr         = PetscMalloc1(new_estimate,&tmp);CHKERRQ(ierr);
994               ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(PetscInt));CHKERRQ(ierr);
995               ierr         = PetscFree(xdata[0]);CHKERRQ(ierr);
996               xdata[0]     = tmp;
997               mem_estimate = new_estimate; ++no_malloc;
998               for (ctr=1; ctr<=i; ctr++) xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];
999             }
1000             xdata[i][ct2++] = val;
1001             ct3++;
1002           }
1003         }
1004         start = bi[row];
1005         end   = bi[row+1];
1006         for (l=start; l<end; l++) {
1007           val = garray[bj[l]];
1008           if (!PetscBTLookupSet(xtable,val)) {
1009             if (!(ct3 < mem_estimate)) {
1010               new_estimate = (PetscInt)(1.5*mem_estimate)+1;
1011               ierr         = PetscMalloc1(new_estimate,&tmp);CHKERRQ(ierr);
1012               ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(PetscInt));CHKERRQ(ierr);
1013               ierr         = PetscFree(xdata[0]);CHKERRQ(ierr);
1014               xdata[0]     = tmp;
1015               mem_estimate = new_estimate; ++no_malloc;
1016               for (ctr =1; ctr <=i; ctr++) xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];
1017             }
1018             xdata[i][ct2++] = val;
1019             ct3++;
1020           }
1021         }
1022       }
1023       /* Update the header*/
1024       xdata[i][2*j]   = ct2 - oct2; /* Undo the vector isz1 and use only a var*/
1025       xdata[i][2*j-1] = rbuf_i[2*j-1];
1026     }
1027     xdata[i][0] = rbuf_0;
1028     xdata[i+1]  = xdata[i] + ct2;
1029     isz1[i]     = ct2; /* size of each message */
1030   }
1031   ierr = PetscBTDestroy(&xtable);CHKERRQ(ierr);
1032   ierr = PetscInfo3(C,"Allocated %D bytes, required %D bytes, no of mallocs = %D\n",mem_estimate,ct3,no_malloc);CHKERRQ(ierr);
1033   PetscFunctionReturn(0);
1034 }
1035 /* -------------------------------------------------------------------------*/
1036 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
1037 extern PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat,MatAssemblyType);
1038 /*
1039     Every processor gets the entire matrix
1040 */
1041 PetscErrorCode MatGetSubMatrix_MPIAIJ_All(Mat A,MatGetSubMatrixOption flag,MatReuse scall,Mat *Bin[])
1042 {
1043   Mat            B;
1044   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1045   Mat_SeqAIJ     *b,*ad = (Mat_SeqAIJ*)a->A->data,*bd = (Mat_SeqAIJ*)a->B->data;
1046   PetscErrorCode ierr;
1047   PetscMPIInt    size,rank,*recvcounts = 0,*displs = 0;
1048   PetscInt       sendcount,i,*rstarts = A->rmap->range,n,cnt,j;
1049   PetscInt       m,*b_sendj,*garray = a->garray,*lens,*jsendbuf,*a_jsendbuf,*b_jsendbuf;
1050   MatScalar      *sendbuf,*recvbuf,*a_sendbuf,*b_sendbuf;
1051 
1052   PetscFunctionBegin;
1053   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRQ(ierr);
1054   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
1055 
1056   if (scall == MAT_INITIAL_MATRIX) {
1057     /* ----------------------------------------------------------------
1058          Tell every processor the number of nonzeros per row
1059     */
1060     ierr = PetscMalloc1(A->rmap->N,&lens);CHKERRQ(ierr);
1061     for (i=A->rmap->rstart; i<A->rmap->rend; i++) {
1062       lens[i] = ad->i[i-A->rmap->rstart+1] - ad->i[i-A->rmap->rstart] + bd->i[i-A->rmap->rstart+1] - bd->i[i-A->rmap->rstart];
1063     }
1064     ierr      = PetscMalloc2(size,&recvcounts,size,&displs);CHKERRQ(ierr);
1065     for (i=0; i<size; i++) {
1066       recvcounts[i] = A->rmap->range[i+1] - A->rmap->range[i];
1067       displs[i]     = A->rmap->range[i];
1068     }
1069 #if defined(PETSC_HAVE_MPI_IN_PLACE)
1070     ierr = MPI_Allgatherv(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,lens,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1071 #else
1072     sendcount = A->rmap->rend - A->rmap->rstart;
1073     ierr = MPI_Allgatherv(lens+A->rmap->rstart,sendcount,MPIU_INT,lens,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1074 #endif
1075     /* ---------------------------------------------------------------
1076          Create the sequential matrix of the same type as the local block diagonal
1077     */
1078     ierr  = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
1079     ierr  = MatSetSizes(B,A->rmap->N,A->cmap->N,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1080     ierr  = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
1081     ierr  = MatSetType(B,((PetscObject)a->A)->type_name);CHKERRQ(ierr);
1082     ierr  = MatSeqAIJSetPreallocation(B,0,lens);CHKERRQ(ierr);
1083     ierr  = PetscMalloc1(1,Bin);CHKERRQ(ierr);
1084     **Bin = B;
1085     b     = (Mat_SeqAIJ*)B->data;
1086 
1087     /*--------------------------------------------------------------------
1088        Copy my part of matrix column indices over
1089     */
1090     sendcount  = ad->nz + bd->nz;
1091     jsendbuf   = b->j + b->i[rstarts[rank]];
1092     a_jsendbuf = ad->j;
1093     b_jsendbuf = bd->j;
1094     n          = A->rmap->rend - A->rmap->rstart;
1095     cnt        = 0;
1096     for (i=0; i<n; i++) {
1097 
1098       /* put in lower diagonal portion */
1099       m = bd->i[i+1] - bd->i[i];
1100       while (m > 0) {
1101         /* is it above diagonal (in bd (compressed) numbering) */
1102         if (garray[*b_jsendbuf] > A->rmap->rstart + i) break;
1103         jsendbuf[cnt++] = garray[*b_jsendbuf++];
1104         m--;
1105       }
1106 
1107       /* put in diagonal portion */
1108       for (j=ad->i[i]; j<ad->i[i+1]; j++) {
1109         jsendbuf[cnt++] = A->rmap->rstart + *a_jsendbuf++;
1110       }
1111 
1112       /* put in upper diagonal portion */
1113       while (m-- > 0) {
1114         jsendbuf[cnt++] = garray[*b_jsendbuf++];
1115       }
1116     }
1117     if (cnt != sendcount) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Corrupted PETSc matrix: nz given %D actual nz %D",sendcount,cnt);
1118 
1119     /*--------------------------------------------------------------------
1120        Gather all column indices to all processors
1121     */
1122     for (i=0; i<size; i++) {
1123       recvcounts[i] = 0;
1124       for (j=A->rmap->range[i]; j<A->rmap->range[i+1]; j++) {
1125         recvcounts[i] += lens[j];
1126       }
1127     }
1128     displs[0] = 0;
1129     for (i=1; i<size; i++) {
1130       displs[i] = displs[i-1] + recvcounts[i-1];
1131     }
1132 #if defined(PETSC_HAVE_MPI_IN_PLACE)
1133     ierr = MPI_Allgatherv(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,b->j,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1134 #else
1135     ierr = MPI_Allgatherv(jsendbuf,sendcount,MPIU_INT,b->j,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1136 #endif
1137     /*--------------------------------------------------------------------
1138         Assemble the matrix into useable form (note numerical values not yet set)
1139     */
1140     /* set the b->ilen (length of each row) values */
1141     ierr = PetscMemcpy(b->ilen,lens,A->rmap->N*sizeof(PetscInt));CHKERRQ(ierr);
1142     /* set the b->i indices */
1143     b->i[0] = 0;
1144     for (i=1; i<=A->rmap->N; i++) {
1145       b->i[i] = b->i[i-1] + lens[i-1];
1146     }
1147     ierr = PetscFree(lens);CHKERRQ(ierr);
1148     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1149     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1150 
1151   } else {
1152     B = **Bin;
1153     b = (Mat_SeqAIJ*)B->data;
1154   }
1155 
1156   /*--------------------------------------------------------------------
1157        Copy my part of matrix numerical values into the values location
1158   */
1159   if (flag == MAT_GET_VALUES) {
1160     sendcount = ad->nz + bd->nz;
1161     sendbuf   = b->a + b->i[rstarts[rank]];
1162     a_sendbuf = ad->a;
1163     b_sendbuf = bd->a;
1164     b_sendj   = bd->j;
1165     n         = A->rmap->rend - A->rmap->rstart;
1166     cnt       = 0;
1167     for (i=0; i<n; i++) {
1168 
1169       /* put in lower diagonal portion */
1170       m = bd->i[i+1] - bd->i[i];
1171       while (m > 0) {
1172         /* is it above diagonal (in bd (compressed) numbering) */
1173         if (garray[*b_sendj] > A->rmap->rstart + i) break;
1174         sendbuf[cnt++] = *b_sendbuf++;
1175         m--;
1176         b_sendj++;
1177       }
1178 
1179       /* put in diagonal portion */
1180       for (j=ad->i[i]; j<ad->i[i+1]; j++) {
1181         sendbuf[cnt++] = *a_sendbuf++;
1182       }
1183 
1184       /* put in upper diagonal portion */
1185       while (m-- > 0) {
1186         sendbuf[cnt++] = *b_sendbuf++;
1187         b_sendj++;
1188       }
1189     }
1190     if (cnt != sendcount) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Corrupted PETSc matrix: nz given %D actual nz %D",sendcount,cnt);
1191 
1192     /* -----------------------------------------------------------------
1193        Gather all numerical values to all processors
1194     */
1195     if (!recvcounts) {
1196       ierr = PetscMalloc2(size,&recvcounts,size,&displs);CHKERRQ(ierr);
1197     }
1198     for (i=0; i<size; i++) {
1199       recvcounts[i] = b->i[rstarts[i+1]] - b->i[rstarts[i]];
1200     }
1201     displs[0] = 0;
1202     for (i=1; i<size; i++) {
1203       displs[i] = displs[i-1] + recvcounts[i-1];
1204     }
1205     recvbuf = b->a;
1206 #if defined(PETSC_HAVE_MPI_IN_PLACE)
1207     ierr = MPI_Allgatherv(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,recvbuf,recvcounts,displs,MPIU_SCALAR,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1208 #else
1209     ierr = MPI_Allgatherv(sendbuf,sendcount,MPIU_SCALAR,recvbuf,recvcounts,displs,MPIU_SCALAR,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1210 #endif
1211   }  /* endof (flag == MAT_GET_VALUES) */
1212   ierr = PetscFree2(recvcounts,displs);CHKERRQ(ierr);
1213 
1214   if (A->symmetric) {
1215     ierr = MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
1216   } else if (A->hermitian) {
1217     ierr = MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
1218   } else if (A->structurally_symmetric) {
1219     ierr = MatSetOption(B,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
1220   }
1221   PetscFunctionReturn(0);
1222 }
1223 PetscErrorCode MatDestroy_MPIAIJ_MatGetSubmatrices(Mat C)
1224 {
1225   PetscErrorCode ierr;
1226   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
1227   Mat_SubMat     *submatj = c->submatis1;
1228   PetscInt       i;
1229 
1230   PetscFunctionBegin;
1231   ierr = submatj->destroy(C);CHKERRQ(ierr);
1232 
1233   ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
1234 
1235   for (i=0; i<submatj->nrqr; ++i) {
1236     ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
1237   }
1238   ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
1239 
1240   if (submatj->rbuf1) {
1241     ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
1242     ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
1243   }
1244 
1245   for (i=0; i<submatj->nrqs; ++i) {
1246     ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
1247   }
1248   ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
1249   ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
1250 
1251   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
1252 
1253 #if defined(PETSC_USE_CTABLE)
1254   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
1255   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
1256   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
1257 #else
1258   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
1259 #endif
1260 
1261   if (!submatj->allcolumns) {
1262 #if defined(PETSC_USE_CTABLE)
1263     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
1264 #else
1265     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
1266 #endif
1267   }
1268 
1269   ierr = PetscFree(submatj);CHKERRQ(ierr);
1270   PetscFunctionReturn(0);
1271 }
1272 
1273 PetscErrorCode MatGetSubMatrices_MPIAIJ_SingleIS_Local(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,PetscBool allcolumns,Mat *submats)
1274 {
1275   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
1276   Mat            submat,A = c->A,B = c->B;
1277   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data,*subc;
1278   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,nzA,nzB;
1279   PetscInt       cstart = C->cmap->rstart,cend = C->cmap->rend,rstart = C->rmap->rstart,*bmap = c->garray;
1280   const PetscInt *icol,*irow;
1281   PetscInt       nrow,ncol,start;
1282   PetscErrorCode ierr;
1283   PetscMPIInt    rank,size,tag1,tag2,tag3,tag4,*w1,*w2,nrqr;
1284   PetscInt       **sbuf1,**sbuf2,i,j,k,l,ct1,ct2,ct3,**rbuf1,row,proc;
1285   PetscInt       nrqs=0,msz,**ptr,*req_size,*ctr,*pa,*tmp,tcol,*iptr;
1286   PetscInt       **rbuf3,*req_source1,*req_source2,**sbuf_aj,**rbuf2,max1,nnz;
1287   PetscInt       *lens,rmax,ncols,*cols,Crow;
1288 #if defined(PETSC_USE_CTABLE)
1289   PetscTable     cmap,rmap;
1290   PetscInt       *cmap_loc,*rmap_loc;
1291 #else
1292   PetscInt       *cmap,*rmap;
1293 #endif
1294   PetscInt       ctr_j,*sbuf1_j,*sbuf_aj_i,*rbuf1_i,kmax,*sbuf1_i,*rbuf2_i,*rbuf3_i;
1295   PetscInt       *cworkB,lwrite,*subcols,*row2proc;
1296   PetscScalar    *vworkA,*vworkB,*a_a = a->a,*b_a = b->a,*subvals=NULL;
1297   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2,*r_waits3;
1298   MPI_Request    *r_waits4,*s_waits3 = NULL,*s_waits4;
1299   MPI_Status     *r_status1,*r_status2,*s_status1,*s_status3 = NULL,*s_status2;
1300   MPI_Status     *r_status3 = NULL,*r_status4,*s_status4;
1301   MPI_Comm       comm;
1302   PetscScalar    **rbuf4,**sbuf_aa,*vals,*sbuf_aa_i,*rbuf4_i;
1303   PetscMPIInt    *onodes1,*olengths1,idex,end;
1304   Mat_SubMat     *smatis1;
1305   PetscBool      isrowsorted;
1306 
1307   PetscFunctionBegin;
1308   if (ismax != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This routine only works when all processes have ismax=1");
1309 
1310   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1311   size = c->size;
1312   rank = c->rank;
1313 
1314   ierr = ISSorted(isrow[0],&isrowsorted);CHKERRQ(ierr);
1315   if (!isrowsorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow[0] must be sorted");
1316 
1317   ierr = ISGetIndices(isrow[0],&irow);CHKERRQ(ierr);
1318   ierr = ISGetLocalSize(isrow[0],&nrow);CHKERRQ(ierr);
1319   if (allcolumns) {
1320     icol = NULL;
1321     ncol = C->cmap->N;
1322   } else {
1323     ierr = ISGetIndices(iscol[0],&icol);CHKERRQ(ierr);
1324     ierr = ISGetLocalSize(iscol[0],&ncol);CHKERRQ(ierr);
1325   }
1326 
1327   if (scall == MAT_INITIAL_MATRIX) {
1328     PetscInt *sbuf2_i,*cworkA,lwrite,ctmp;
1329 
1330     /* Get some new tags to keep the communication clean */
1331     tag1 = ((PetscObject)C)->tag;
1332     ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
1333     ierr = PetscObjectGetNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
1334 
1335     /* evaluate communication - mesg to who, length of mesg, and buffer space
1336      required. Based on this, buffers are allocated, and data copied into them */
1337     ierr = PetscCalloc2(size,&w1,size,&w2);CHKERRQ(ierr);
1338     ierr = PetscMalloc1(nrow,&row2proc);CHKERRQ(ierr);
1339 
1340     /* w1[proc] = num of rows owned by proc -- to be requested */
1341     proc = 0;
1342     nrqs = 0; /* num of outgoing messages */
1343     for (j=0; j<nrow; j++) {
1344       row  = irow[j]; /* sorted! */
1345       while (row >= C->rmap->range[proc+1]) proc++;
1346       w1[proc]++;
1347       row2proc[j] = proc; /* map row index to proc */
1348 
1349       if (proc != rank && !w2[proc]) {
1350         w2[proc] = 1; nrqs++;
1351       }
1352     }
1353     w1[rank] = 0;  /* rows owned by self will not be requested */
1354 
1355     ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr); /*(proc -array)*/
1356     for (proc=0,j=0; proc<size; proc++) {
1357       if (w1[proc]) { pa[j++] = proc;}
1358     }
1359 
1360     /* Each message would have a header = 1 + 2*(num of IS) + data (here,num of IS = 1) */
1361     msz = 0;              /* total mesg length (for all procs) */
1362     for (i=0; i<nrqs; i++) {
1363       proc      = pa[i];
1364       w1[proc] += 3;
1365       msz      += w1[proc];
1366     }
1367     ierr = PetscInfo2(0,"Number of outgoing messages %D Total message length %D\n",nrqs,msz);CHKERRQ(ierr);
1368 
1369     /* Determine nrqr, the number of messages to expect, their lengths, from from-ids */
1370     /* if w2[proc]=1, a message of length w1[proc] will be sent to proc; */
1371     ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
1372 
1373     /* Input: nrqs: nsend; nrqr: nrecv; w1: msg length to be sent;
1374        Output: onodes1: recv node-ids; olengths1: corresponding recv message length */
1375     ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
1376 
1377     /* Now post the Irecvs corresponding to these messages */
1378     ierr = PetscPostIrecvInt(comm,tag1,nrqr,onodes1,olengths1,&rbuf1,&r_waits1);CHKERRQ(ierr);
1379 
1380     ierr = PetscFree(onodes1);CHKERRQ(ierr);
1381     ierr = PetscFree(olengths1);CHKERRQ(ierr);
1382 
1383     /* Allocate Memory for outgoing messages */
1384     ierr = PetscMalloc4(size,&sbuf1,size,&ptr,2*msz,&tmp,size,&ctr);CHKERRQ(ierr);
1385     ierr = PetscMemzero(sbuf1,size*sizeof(PetscInt*));CHKERRQ(ierr);
1386     ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
1387 
1388     /* subf1[pa[0]] = tmp, subf1[pa[i]] = subf1[pa[i-1]] + w1[pa[i-1]] */
1389     iptr = tmp;
1390     for (i=0; i<nrqs; i++) {
1391       proc        = pa[i];
1392       sbuf1[proc] = iptr;
1393       iptr       += w1[proc];
1394     }
1395 
1396     /* Form the outgoing messages */
1397     /* Initialize the header space */
1398     for (i=0; i<nrqs; i++) {
1399       proc      = pa[i];
1400       ierr      = PetscMemzero(sbuf1[proc],3*sizeof(PetscInt));CHKERRQ(ierr);
1401       ptr[proc] = sbuf1[proc] + 3;
1402     }
1403 
1404     /* Parse the isrow and copy data into outbuf */
1405     ierr = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
1406     for (j=0; j<nrow; j++) {  /* parse the indices of each IS */
1407       proc = row2proc[j];
1408       if (proc != rank) { /* copy to the outgoing buf*/
1409         *ptr[proc] = irow[j];
1410         ctr[proc]++; ptr[proc]++;
1411       }
1412     }
1413 
1414     /* Update the headers for the current IS */
1415     for (j=0; j<size; j++) { /* Can Optimise this loop too */
1416       if ((ctr_j = ctr[j])) {
1417         sbuf1_j        = sbuf1[j];
1418         k              = ++sbuf1_j[0];
1419         sbuf1_j[2*k]   = ctr_j;
1420         sbuf1_j[2*k-1] = 0;
1421       }
1422     }
1423 
1424     /* Now post the sends */
1425     ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
1426     for (i=0; i<nrqs; ++i) {
1427       proc = pa[i];
1428       ierr = MPI_Isend(sbuf1[proc],w1[proc],MPIU_INT,proc,tag1,comm,s_waits1+i);CHKERRQ(ierr);
1429     }
1430 
1431     /* Post Receives to capture the buffer size */
1432     ierr = PetscMalloc4(nrqs+1,&r_status2,nrqr+1,&s_waits2,nrqs+1,&r_waits2,nrqr+1,&s_status2);CHKERRQ(ierr);
1433     ierr = PetscMalloc3(nrqs+1,&req_source2,nrqs+1,&rbuf2,nrqs+1,&rbuf3);CHKERRQ(ierr);
1434 
1435     rbuf2[0] = tmp + msz;
1436     for (i=1; i<nrqs; ++i) rbuf2[i] = rbuf2[i-1] + w1[pa[i-1]];
1437 
1438     for (i=0; i<nrqs; ++i) {
1439       proc = pa[i];
1440       ierr = MPI_Irecv(rbuf2[i],w1[proc],MPIU_INT,proc,tag2,comm,r_waits2+i);CHKERRQ(ierr);
1441     }
1442 
1443     ierr = PetscFree2(w1,w2);CHKERRQ(ierr);
1444 
1445     /* Send to other procs the buf size they should allocate */
1446     /* Receive messages*/
1447     ierr = PetscMalloc1(nrqr+1,&r_status1);CHKERRQ(ierr);
1448     ierr = PetscMalloc3(nrqr,&sbuf2,nrqr,&req_size,nrqr,&req_source1);CHKERRQ(ierr);
1449 
1450     ierr = MPI_Waitall(nrqr,r_waits1,r_status1);CHKERRQ(ierr);
1451     for (i=0; i<nrqr; ++i) {
1452       req_size[i] = 0;
1453       rbuf1_i        = rbuf1[i];
1454       start          = 2*rbuf1_i[0] + 1;
1455       ierr           = MPI_Get_count(r_status1+i,MPIU_INT,&end);CHKERRQ(ierr);
1456       ierr           = PetscMalloc1(end+1,&sbuf2[i]);CHKERRQ(ierr);
1457       sbuf2_i        = sbuf2[i];
1458       for (j=start; j<end; j++) {
1459         k            = rbuf1_i[j] - rstart;
1460         ncols        = ai[k+1] - ai[k] + bi[k+1] - bi[k];
1461         sbuf2_i[j]   = ncols;
1462         req_size[i] += ncols;
1463       }
1464       req_source1[i] = r_status1[i].MPI_SOURCE;
1465 
1466       /* form the header */
1467       sbuf2_i[0] = req_size[i];
1468       for (j=1; j<start; j++) sbuf2_i[j] = rbuf1_i[j];
1469 
1470       ierr = MPI_Isend(sbuf2_i,end,MPIU_INT,req_source1[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
1471     }
1472 
1473     ierr = PetscFree(r_status1);CHKERRQ(ierr);
1474     ierr = PetscFree(r_waits1);CHKERRQ(ierr);
1475 
1476     /* rbuf2 is received, Post recv column indices a->j */
1477     ierr = MPI_Waitall(nrqs,r_waits2,r_status2);CHKERRQ(ierr);
1478 
1479     ierr = PetscMalloc4(nrqs+1,&r_waits3,nrqr+1,&s_waits3,nrqs+1,&r_status3,nrqr+1,&s_status3);CHKERRQ(ierr);
1480     for (i=0; i<nrqs; ++i) {
1481       ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf3[i]);CHKERRQ(ierr);
1482       req_source2[i] = r_status2[i].MPI_SOURCE;
1483       ierr = MPI_Irecv(rbuf3[i],rbuf2[i][0],MPIU_INT,req_source2[i],tag3,comm,r_waits3+i);CHKERRQ(ierr);
1484     }
1485 
1486     /* Wait on sends1 and sends2 */
1487     ierr = PetscMalloc1(nrqs+1,&s_status1);CHKERRQ(ierr);
1488     ierr = MPI_Waitall(nrqs,s_waits1,s_status1);CHKERRQ(ierr);
1489     ierr = PetscFree(s_waits1);CHKERRQ(ierr);
1490     ierr = PetscFree(s_status1);CHKERRQ(ierr);
1491 
1492     ierr = MPI_Waitall(nrqr,s_waits2,s_status2);CHKERRQ(ierr);
1493     ierr = PetscFree4(r_status2,s_waits2,r_waits2,s_status2);CHKERRQ(ierr);
1494 
1495     /* Now allocate sending buffers for a->j, and send them off */
1496     ierr = PetscMalloc1(nrqr+1,&sbuf_aj);CHKERRQ(ierr);
1497     for (i=0,j=0; i<nrqr; i++) j += req_size[i];
1498     ierr = PetscMalloc1(j+1,&sbuf_aj[0]);CHKERRQ(ierr);
1499     for (i=1; i<nrqr; i++) sbuf_aj[i] = sbuf_aj[i-1] + req_size[i-1];
1500 
1501     for (i=0; i<nrqr; i++) { /* for each requested message */
1502       rbuf1_i   = rbuf1[i];
1503       sbuf_aj_i = sbuf_aj[i];
1504       ct1       = 2*rbuf1_i[0] + 1;
1505       ct2       = 0;
1506       /* max1=rbuf1_i[0]; if (max1 != 1) SETERRQ1(PETSC_COMM_SELF,0,"max1 %d != 1",max1); */
1507 
1508       kmax = rbuf1[i][2];
1509       for (k=0; k<kmax; k++,ct1++) { /* for each row */
1510         row    = rbuf1_i[ct1] - rstart;
1511         nzA    = ai[row+1] - ai[row];
1512         nzB    = bi[row+1] - bi[row];
1513         ncols  = nzA + nzB;
1514         cworkA = aj + ai[row]; cworkB = bj + bi[row];
1515 
1516         /* load the column indices for this row into cols*/
1517         cols = sbuf_aj_i + ct2;
1518 
1519         lwrite = 0;
1520         for (l=0; l<nzB; l++) {
1521           if ((ctmp = bmap[cworkB[l]]) < cstart) cols[lwrite++] = ctmp;
1522         }
1523         for (l=0; l<nzA; l++) cols[lwrite++] = cstart + cworkA[l];
1524         for (l=0; l<nzB; l++) {
1525           if ((ctmp = bmap[cworkB[l]]) >= cend) cols[lwrite++] = ctmp;
1526         }
1527 
1528         ct2 += ncols;
1529       }
1530       ierr = MPI_Isend(sbuf_aj_i,req_size[i],MPIU_INT,req_source1[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
1531     }
1532 
1533     /* create column map (cmap): global col of C -> local col of submat */
1534 #if defined(PETSC_USE_CTABLE)
1535     if (!allcolumns) {
1536       ierr = PetscTableCreate(ncol+1,C->cmap->N+1,&cmap);CHKERRQ(ierr);
1537       ierr = PetscCalloc1(C->cmap->n,&cmap_loc);CHKERRQ(ierr);
1538       for (j=0; j<ncol; j++) { /* use array cmap_loc[] for local col indices */
1539         if (icol[j] >= cstart && icol[j] <cend) {
1540           cmap_loc[icol[j] - cstart] = j+1;
1541         } else { /* use PetscTable for non-local col indices */
1542           ierr = PetscTableAdd(cmap,icol[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
1543         }
1544       }
1545     } else {
1546       cmap     = NULL;
1547       cmap_loc = NULL;
1548     }
1549     ierr = PetscCalloc1(C->rmap->n,&rmap_loc);CHKERRQ(ierr);
1550 #else
1551     if (!allcolumns) {
1552       ierr   = PetscCalloc1(C->cmap->N,&cmap);CHKERRQ(ierr);
1553       for (j=0; j<ncol; j++) cmap[icol[j]] = j+1;
1554     } else {
1555       cmap = NULL;
1556     }
1557 #endif
1558 
1559     /* Create lens for MatSeqAIJSetPreallocation() */
1560     ierr = PetscCalloc1(nrow,&lens);CHKERRQ(ierr);
1561 
1562     /* Compute lens from local part of C */
1563     for (j=0; j<nrow; j++) {
1564       row  = irow[j];
1565       proc = row2proc[j];
1566       if (proc == rank) {
1567         /* diagonal part A = c->A */
1568         ncols = ai[row-rstart+1] - ai[row-rstart];
1569         cols  = aj + ai[row-rstart];
1570         if (!allcolumns) {
1571           for (k=0; k<ncols; k++) {
1572 #if defined(PETSC_USE_CTABLE)
1573             tcol = cmap_loc[cols[k]];
1574 #else
1575             tcol = cmap[cols[k]+cstart];
1576 #endif
1577             if (tcol) lens[j]++;
1578           }
1579         } else { /* allcolumns */
1580           lens[j] = ncols;
1581         }
1582 
1583         /* off-diagonal part B = c->B */
1584         ncols = bi[row-rstart+1] - bi[row-rstart];
1585         cols  = bj + bi[row-rstart];
1586         if (!allcolumns) {
1587           for (k=0; k<ncols; k++) {
1588 #if defined(PETSC_USE_CTABLE)
1589             ierr = PetscTableFind(cmap,bmap[cols[k]]+1,&tcol);CHKERRQ(ierr);
1590 #else
1591             tcol = cmap[bmap[cols[k]]];
1592 #endif
1593             if (tcol) lens[j]++;
1594           }
1595         } else { /* allcolumns */
1596           lens[j] += ncols;
1597         }
1598       }
1599     }
1600 
1601     /* Create row map (rmap): global row of C -> local row of submat */
1602 #if defined(PETSC_USE_CTABLE)
1603     ierr = PetscTableCreate(nrow+1,C->rmap->N+1,&rmap);CHKERRQ(ierr);
1604     for (j=0; j<nrow; j++) {
1605       row  = irow[j];
1606       proc = row2proc[j];
1607       if (proc == rank) { /* a local row */
1608         rmap_loc[row - rstart] = j;
1609       } else {
1610         ierr = PetscTableAdd(rmap,irow[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
1611       }
1612     }
1613 #else
1614     ierr = PetscCalloc1(C->rmap->N,&rmap);CHKERRQ(ierr);
1615     for (j=0; j<nrow; j++) {
1616       rmap[irow[j]] = j;
1617     }
1618 #endif
1619 
1620     /* Update lens from offproc data */
1621     /* recv a->j is done */
1622     ierr    = MPI_Waitall(nrqs,r_waits3,r_status3);CHKERRQ(ierr);
1623     for (i=0; i<nrqs; i++) {
1624       proc    = pa[i];
1625       sbuf1_i = sbuf1[proc];
1626       /* jmax    = sbuf1_i[0]; if (jmax != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"jmax !=1"); */
1627       ct1     = 2 + 1;
1628       ct2     = 0;
1629       rbuf2_i = rbuf2[i]; /* received length of C->j */
1630       rbuf3_i = rbuf3[i]; /* received C->j */
1631 
1632       /* is_no  = sbuf1_i[2*j-1]; if (is_no != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_no !=0"); */
1633       max1   = sbuf1_i[2];
1634       for (k=0; k<max1; k++,ct1++) {
1635 #if defined(PETSC_USE_CTABLE)
1636         ierr = PetscTableFind(rmap,sbuf1_i[ct1]+1,&row);CHKERRQ(ierr);
1637         row--;
1638         if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"row not found in table");
1639 #else
1640         row = rmap[sbuf1_i[ct1]]; /* the row index in submat */
1641 #endif
1642         /* Now, store row index of submat in sbuf1_i[ct1] */
1643         sbuf1_i[ct1] = row;
1644 
1645         nnz = rbuf2_i[ct1];
1646         if (!allcolumns) {
1647           for (l=0; l<nnz; l++,ct2++) {
1648 #if defined(PETSC_USE_CTABLE)
1649             if (rbuf3_i[ct2] >= cstart && rbuf3_i[ct2] <cend) {
1650               tcol = cmap_loc[rbuf3_i[ct2] - cstart];
1651             } else {
1652               ierr = PetscTableFind(cmap,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
1653             }
1654 #else
1655             tcol = cmap[rbuf3_i[ct2]]; /* column index in submat */
1656 #endif
1657             if (tcol) lens[row]++;
1658           }
1659         } else { /* allcolumns */
1660           lens[row] += nnz;
1661         }
1662       }
1663     }
1664     ierr = MPI_Waitall(nrqr,s_waits3,s_status3);CHKERRQ(ierr);
1665     ierr = PetscFree4(r_waits3,s_waits3,r_status3,s_status3);CHKERRQ(ierr);
1666 
1667     /* Create the submatrices */
1668     ierr = MatCreate(PETSC_COMM_SELF,&submat);CHKERRQ(ierr);
1669     ierr = MatSetSizes(submat,nrow,ncol,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1670 
1671     ierr = ISGetBlockSize(isrow[0],&i);CHKERRQ(ierr);
1672     ierr = ISGetBlockSize(iscol[0],&j);CHKERRQ(ierr);
1673     ierr = MatSetBlockSizes(submat,i,j);CHKERRQ(ierr);
1674     ierr = MatSetType(submat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1675     ierr = MatSeqAIJSetPreallocation(submat,0,lens);CHKERRQ(ierr);
1676 
1677     /* create struct Mat_SubMat and attached it to submat */
1678     ierr = PetscNew(&smatis1);CHKERRQ(ierr);
1679     subc = (Mat_SeqAIJ*)submat->data;
1680     subc->submatis1 = smatis1;
1681 
1682     smatis1->nrqs        = nrqs;
1683     smatis1->nrqr        = nrqr;
1684     smatis1->rbuf1       = rbuf1;
1685     smatis1->rbuf2       = rbuf2;
1686     smatis1->rbuf3       = rbuf3;
1687     smatis1->sbuf2       = sbuf2;
1688     smatis1->req_source2 = req_source2;
1689 
1690     smatis1->sbuf1       = sbuf1;
1691     smatis1->ptr         = ptr;
1692     smatis1->tmp         = tmp;
1693     smatis1->ctr         = ctr;
1694 
1695     smatis1->pa           = pa;
1696     smatis1->req_size     = req_size;
1697     smatis1->req_source1  = req_source1;
1698 
1699     smatis1->allcolumns  = allcolumns;
1700     smatis1->row2proc    = row2proc;
1701     smatis1->rmap        = rmap;
1702     smatis1->cmap        = cmap;
1703 #if defined(PETSC_USE_CTABLE)
1704     smatis1->rmap_loc    = rmap_loc;
1705     smatis1->cmap_loc    = cmap_loc;
1706 #endif
1707 
1708     smatis1->destroy     = submat->ops->destroy;
1709     submat->ops->destroy = MatDestroy_MPIAIJ_MatGetSubmatrices;
1710     submat->factortype   = C->factortype;
1711 
1712     /* compute rmax */
1713     rmax = 0;
1714     for (i=0; i<nrow; i++) rmax = PetscMax(rmax,lens[i]);
1715 
1716   } else { /* scall == MAT_REUSE_MATRIX */
1717     submat = submats[0];
1718     if (submat->rmap->n != nrow || submat->cmap->n != ncol) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
1719 
1720     subc    = (Mat_SeqAIJ*)submat->data;
1721     rmax    = subc->rmax;
1722     smatis1 = subc->submatis1;
1723     nrqs        = smatis1->nrqs;
1724     nrqr        = smatis1->nrqr;
1725     rbuf1       = smatis1->rbuf1;
1726     rbuf2       = smatis1->rbuf2;
1727     rbuf3       = smatis1->rbuf3;
1728     req_source2 = smatis1->req_source2;
1729 
1730     sbuf1     = smatis1->sbuf1;
1731     sbuf2     = smatis1->sbuf2;
1732     ptr       = smatis1->ptr;
1733     tmp       = smatis1->tmp;
1734     ctr       = smatis1->ctr;
1735 
1736     pa         = smatis1->pa;
1737     req_size   = smatis1->req_size;
1738     req_source1 = smatis1->req_source1;
1739 
1740     allcolumns = smatis1->allcolumns;
1741     row2proc   = smatis1->row2proc;
1742     rmap       = smatis1->rmap;
1743     cmap       = smatis1->cmap;
1744 #if defined(PETSC_USE_CTABLE)
1745     rmap_loc   = smatis1->rmap_loc;
1746     cmap_loc   = smatis1->cmap_loc;
1747 #endif
1748   }
1749 
1750   /* Post recv matrix values */
1751   ierr = PetscMalloc3(nrqs+1,&rbuf4, rmax,&subcols, rmax,&subvals);CHKERRQ(ierr);
1752   ierr = PetscMalloc4(nrqs+1,&r_waits4,nrqr+1,&s_waits4,nrqs+1,&r_status4,nrqr+1,&s_status4);CHKERRQ(ierr);
1753   ierr = PetscObjectGetNewTag((PetscObject)C,&tag4);CHKERRQ(ierr);
1754   for (i=0; i<nrqs; ++i) {
1755     ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf4[i]);CHKERRQ(ierr);
1756     ierr = MPI_Irecv(rbuf4[i],rbuf2[i][0],MPIU_SCALAR,req_source2[i],tag4,comm,r_waits4+i);CHKERRQ(ierr);
1757   }
1758 
1759   /* Allocate sending buffers for a->a, and send them off */
1760   ierr = PetscMalloc1(nrqr+1,&sbuf_aa);CHKERRQ(ierr);
1761   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
1762   ierr = PetscMalloc1(j+1,&sbuf_aa[0]);CHKERRQ(ierr);
1763   for (i=1; i<nrqr; i++) sbuf_aa[i] = sbuf_aa[i-1] + req_size[i-1];
1764 
1765   for (i=0; i<nrqr; i++) {
1766     rbuf1_i   = rbuf1[i];
1767     sbuf_aa_i = sbuf_aa[i];
1768     ct1       = 2*rbuf1_i[0]+1;
1769     ct2       = 0;
1770     /* max1=rbuf1_i[0]; if (max1 != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"max1 !=1"); */
1771 
1772     kmax = rbuf1_i[2];
1773     for (k=0; k<kmax; k++,ct1++) {
1774       row = rbuf1_i[ct1] - rstart;
1775       nzA = ai[row+1] - ai[row];
1776       nzB = bi[row+1] - bi[row];
1777       ncols  = nzA + nzB;
1778       cworkB = bj + bi[row];
1779       vworkA = a_a + ai[row];
1780       vworkB = b_a + bi[row];
1781 
1782       /* load the column values for this row into vals*/
1783       vals = sbuf_aa_i + ct2;
1784 
1785       lwrite = 0;
1786       for (l=0; l<nzB; l++) {
1787         if ((bmap[cworkB[l]]) < cstart) vals[lwrite++] = vworkB[l];
1788       }
1789       for (l=0; l<nzA; l++) vals[lwrite++] = vworkA[l];
1790       for (l=0; l<nzB; l++) {
1791         if ((bmap[cworkB[l]]) >= cend) vals[lwrite++] = vworkB[l];
1792       }
1793 
1794       ct2 += ncols;
1795     }
1796     ierr = MPI_Isend(sbuf_aa_i,req_size[i],MPIU_SCALAR,req_source1[i],tag4,comm,s_waits4+i);CHKERRQ(ierr);
1797   }
1798 
1799   /* Assemble submat */
1800   /* First assemble the local rows */
1801   for (j=0; j<nrow; j++) {
1802     row  = irow[j];
1803     proc = row2proc[j];
1804     if (proc == rank) {
1805       Crow = row - rstart;  /* local row index of C */
1806 #if defined(PETSC_USE_CTABLE)
1807       row = rmap_loc[Crow]; /* row index of submat */
1808 #else
1809       row = rmap[row];
1810 #endif
1811 
1812       if (allcolumns) {
1813         /* diagonal part A = c->A */
1814         ncols = ai[Crow+1] - ai[Crow];
1815         cols  = aj + ai[Crow];
1816         vals  = a->a + ai[Crow];
1817         i     = 0;
1818         for (k=0; k<ncols; k++) {
1819           subcols[i]   = cols[k] + cstart;
1820           subvals[i++] = vals[k];
1821         }
1822 
1823         /* off-diagonal part B = c->B */
1824         ncols = bi[Crow+1] - bi[Crow];
1825         cols  = bj + bi[Crow];
1826         vals  = b->a + bi[Crow];
1827         for (k=0; k<ncols; k++) {
1828           subcols[i]   = bmap[cols[k]];
1829           subvals[i++] = vals[k];
1830         }
1831 
1832         ierr = MatSetValues_SeqAIJ(submat,1,&row,i,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1833 
1834       } else { /* !allcolumns */
1835 #if defined(PETSC_USE_CTABLE)
1836         /* diagonal part A = c->A */
1837         ncols = ai[Crow+1] - ai[Crow];
1838         cols  = aj + ai[Crow];
1839         vals  = a->a + ai[Crow];
1840         i     = 0;
1841         for (k=0; k<ncols; k++) {
1842           tcol = cmap_loc[cols[k]];
1843           if (tcol) {
1844             subcols[i]   = --tcol;
1845             subvals[i++] = vals[k];
1846           }
1847         }
1848 
1849         /* off-diagonal part B = c->B */
1850         ncols = bi[Crow+1] - bi[Crow];
1851         cols  = bj + bi[Crow];
1852         vals  = b->a + bi[Crow];
1853         for (k=0; k<ncols; k++) {
1854           ierr = PetscTableFind(cmap,bmap[cols[k]]+1,&tcol);CHKERRQ(ierr);
1855           if (tcol) {
1856             subcols[i]   = --tcol;
1857             subvals[i++] = vals[k];
1858           }
1859         }
1860 #else
1861         /* diagonal part A = c->A */
1862         ncols = ai[Crow+1] - ai[Crow];
1863         cols  = aj + ai[Crow];
1864         vals  = a->a + ai[Crow];
1865         i     = 0;
1866         for (k=0; k<ncols; k++) {
1867           tcol = cmap[cols[k]+cstart];
1868           if (tcol) {
1869             subcols[i]   = --tcol;
1870             subvals[i++] = vals[k];
1871           }
1872         }
1873 
1874         /* off-diagonal part B = c->B */
1875         ncols = bi[Crow+1] - bi[Crow];
1876         cols  = bj + bi[Crow];
1877         vals  = b->a + bi[Crow];
1878         for (k=0; k<ncols; k++) {
1879           tcol = cmap[bmap[cols[k]]];
1880           if (tcol) {
1881             subcols[i]   = --tcol;
1882             subvals[i++] = vals[k];
1883           }
1884         }
1885 #endif
1886         ierr = MatSetValues_SeqAIJ(submat,1,&row,i,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1887       }
1888     }
1889   }
1890 
1891   /* Now assemble the off-proc rows */
1892   for (i=0; i<nrqs; i++) { /* for each requested message */
1893     /* recv values from other processes */
1894     ierr    = MPI_Waitany(nrqs,r_waits4,&idex,r_status4+i);CHKERRQ(ierr);
1895     proc    = pa[idex];
1896     sbuf1_i = sbuf1[proc];
1897     /* jmax    = sbuf1_i[0]; if (jmax != 1)SETERRQ1(PETSC_COMM_SELF,0,"jmax %d != 1",jmax); */
1898     ct1     = 2 + 1;
1899     ct2     = 0; /* count of received C->j */
1900     ct3     = 0; /* count of received C->j that will be inserted into submat */
1901     rbuf2_i = rbuf2[idex]; /* int** received length of C->j from other processes */
1902     rbuf3_i = rbuf3[idex]; /* int** received C->j from other processes */
1903     rbuf4_i = rbuf4[idex]; /* scalar** received C->a from other processes */
1904 
1905     /* is_no = sbuf1_i[2*j-1]; if (is_no != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_no !=0"); */
1906     max1 = sbuf1_i[2];             /* num of rows */
1907     for (k=0; k<max1; k++,ct1++) { /* for each recved row */
1908       row = sbuf1_i[ct1]; /* row index of submat */
1909       if (!allcolumns) {
1910         idex = 0;
1911         if (scall == MAT_INITIAL_MATRIX) {
1912           nnz  = rbuf2_i[ct1]; /* num of C entries in this row */
1913           for (l=0; l<nnz; l++,ct2++) { /* for each recved column */
1914 #if defined(PETSC_USE_CTABLE)
1915             if (rbuf3_i[ct2] >= cstart && rbuf3_i[ct2] <cend) {
1916               tcol = cmap_loc[rbuf3_i[ct2] - cstart];
1917             } else {
1918               ierr = PetscTableFind(cmap,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
1919             }
1920 #else
1921             tcol = cmap[rbuf3_i[ct2]];
1922 #endif
1923             if (tcol) {
1924               subcols[idex]   = --tcol;
1925               subvals[idex++] = rbuf4_i[ct2];
1926 
1927               /* We receive an entire column of C, but a subset of it needs to be inserted into submat.
1928                For reuse, we replace received C->j with index that should be inserted to submat */
1929               rbuf3_i[ct3++] = ct2;
1930             }
1931           }
1932           ierr = MatSetValues_SeqAIJ(submat,1,&row,idex,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1933 
1934         } else { /* scall == MAT_REUSE_MATRIX */
1935           submat = submats[0];
1936           subc   = (Mat_SeqAIJ*)submat->data;
1937 
1938           nnz = subc->i[row+1] - subc->i[row]; /* num of submat entries in this row */
1939           for (l=0; l<nnz; l++) {
1940             ct2 = rbuf3_i[ct3++]; /* index of rbuf4_i[] which needs to be inserted into submat */
1941             subvals[idex++] = rbuf4_i[ct2];
1942           }
1943 
1944           bj = subc->j + subc->i[row];
1945           ierr = MatSetValues_SeqAIJ(submat,1,&row,nnz,bj,subvals,INSERT_VALUES);CHKERRQ(ierr);
1946         }
1947       } else { /* allcolumns */
1948         nnz  = rbuf2_i[ct1]; /* num of C entries in this row */
1949         ierr = MatSetValues_SeqAIJ(submat,1,&row,nnz,rbuf3_i+ct2,rbuf4_i+ct2,INSERT_VALUES);CHKERRQ(ierr);
1950         ct2 += nnz;
1951       }
1952     }
1953   }
1954 
1955   /* sending a->a are done */
1956   ierr = MPI_Waitall(nrqr,s_waits4,s_status4);CHKERRQ(ierr);
1957   ierr = PetscFree4(r_waits4,s_waits4,r_status4,s_status4);CHKERRQ(ierr);
1958 
1959   ierr = MatAssemblyBegin(submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1960   ierr = MatAssemblyEnd(submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1961   submats[0] = submat;
1962 
1963   /* Restore the indices */
1964   ierr = ISRestoreIndices(isrow[0],&irow);CHKERRQ(ierr);
1965   if (!allcolumns) {
1966     ierr = ISRestoreIndices(iscol[0],&icol);CHKERRQ(ierr);
1967   }
1968 
1969   /* Destroy allocated memory */
1970   for (i=0; i<nrqs; ++i) {
1971     ierr = PetscFree3(rbuf4[i],subcols,subvals);CHKERRQ(ierr);
1972   }
1973   ierr = PetscFree3(rbuf4,subcols,subvals);CHKERRQ(ierr);
1974   ierr = PetscFree(sbuf_aa[0]);CHKERRQ(ierr);
1975   ierr = PetscFree(sbuf_aa);CHKERRQ(ierr);
1976 
1977   if (scall == MAT_INITIAL_MATRIX) {
1978     ierr = PetscFree(lens);CHKERRQ(ierr);
1979     ierr = PetscFree(sbuf_aj[0]);CHKERRQ(ierr);
1980     ierr = PetscFree(sbuf_aj);CHKERRQ(ierr);
1981   }
1982   PetscFunctionReturn(0);
1983 }
1984 
1985 PetscErrorCode MatGetSubMatrices_MPIAIJ_SingleIS(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
1986 {
1987   PetscErrorCode ierr;
1988   PetscInt       ncol;
1989   PetscBool      colflag,allcolumns=PETSC_FALSE;
1990 
1991   PetscFunctionBegin;
1992   /* Allocate memory to hold all the submatrices */
1993   if (scall == MAT_INITIAL_MATRIX) {
1994     ierr = PetscMalloc1(1,submat);CHKERRQ(ierr);
1995   }
1996 
1997   /* Check for special case: each processor gets entire matrix columns */
1998   ierr = ISIdentity(iscol[0],&colflag);CHKERRQ(ierr);
1999   ierr = ISGetLocalSize(iscol[0],&ncol);CHKERRQ(ierr);
2000   if (colflag && ncol == C->cmap->N) allcolumns = PETSC_TRUE;
2001 
2002   ierr = MatGetSubMatrices_MPIAIJ_SingleIS_Local(C,ismax,isrow,iscol,scall,allcolumns,*submat);CHKERRQ(ierr);
2003   PetscFunctionReturn(0);
2004 }
2005 
2006 PetscErrorCode MatGetSubMatrices_MPIAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
2007 {
2008   PetscErrorCode ierr;
2009   PetscInt       nmax,nstages_local,nstages,i,pos,max_no,nrow,ncol;
2010   PetscBool      rowflag,colflag,wantallmatrix=PETSC_FALSE,twantallmatrix,*allcolumns;
2011 
2012   PetscFunctionBegin;
2013 #if 0
2014   /* Check for special case: each processor gets entire matrix */
2015   if (C->submat_singleis) { /* flag is set in PCSetUp_ASM() to skip several MPIU_Allreduce() */
2016     ierr = MatGetSubMatrices_MPIAIJ_SingleIS(C,ismax,isrow,iscol,scall,submat);CHKERRQ(ierr);
2017     PetscFunctionReturn(0);
2018   }
2019 #endif
2020 
2021   if (ismax == 1 && C->rmap->N == C->cmap->N) {
2022     ierr = ISIdentity(*isrow,&rowflag);CHKERRQ(ierr);
2023     ierr = ISIdentity(*iscol,&colflag);CHKERRQ(ierr);
2024     ierr = ISGetLocalSize(*isrow,&nrow);CHKERRQ(ierr);
2025     ierr = ISGetLocalSize(*iscol,&ncol);CHKERRQ(ierr);
2026     if (rowflag && colflag && nrow == C->rmap->N && ncol == C->cmap->N) {
2027       wantallmatrix = PETSC_TRUE;
2028 
2029       ierr = PetscOptionsGetBool(((PetscObject)C)->options,((PetscObject)C)->prefix,"-use_fast_submatrix",&wantallmatrix,NULL);CHKERRQ(ierr);
2030     }
2031   }
2032   ierr = MPIU_Allreduce(&wantallmatrix,&twantallmatrix,1,MPIU_BOOL,MPI_MIN,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
2033   if (twantallmatrix) {
2034     ierr = MatGetSubMatrix_MPIAIJ_All(C,MAT_GET_VALUES,scall,submat);CHKERRQ(ierr);
2035     PetscFunctionReturn(0);
2036   }
2037 
2038   /* Allocate memory to hold all the submatrices */
2039   if (scall == MAT_INITIAL_MATRIX) {
2040     ierr = PetscMalloc1(ismax+1,submat);CHKERRQ(ierr);
2041   }
2042 
2043   /* Check for special case: each processor gets entire matrix columns */
2044   ierr = PetscMalloc1(ismax+1,&allcolumns);CHKERRQ(ierr);
2045   for (i=0; i<ismax; i++) {
2046     ierr = ISIdentity(iscol[i],&colflag);CHKERRQ(ierr);
2047     ierr = ISGetLocalSize(iscol[i],&ncol);CHKERRQ(ierr);
2048     if (colflag && ncol == C->cmap->N) {
2049       allcolumns[i] = PETSC_TRUE;
2050     } else {
2051       allcolumns[i] = PETSC_FALSE;
2052     }
2053   }
2054 
2055   /* Determine the number of stages through which submatrices are done */
2056   nmax = 20*1000000 / (C->cmap->N * sizeof(PetscInt));
2057 
2058   /*
2059      Each stage will extract nmax submatrices.
2060      nmax is determined by the matrix column dimension.
2061      If the original matrix has 20M columns, only one submatrix per stage is allowed, etc.
2062   */
2063   if (!nmax) nmax = 1;
2064   nstages_local = ismax/nmax + ((ismax % nmax) ? 1 : 0);
2065 
2066   /* Make sure every processor loops through the nstages */
2067   ierr = MPIU_Allreduce(&nstages_local,&nstages,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
2068 
2069   for (i=0,pos=0; i<nstages; i++) {
2070     if (pos+nmax <= ismax) max_no = nmax;
2071     else if (pos == ismax) max_no = 0;
2072     else                   max_no = ismax-pos;
2073     ierr = MatGetSubMatrices_MPIAIJ_Local(C,max_no,isrow+pos,iscol+pos,scall,allcolumns+pos,*submat+pos);CHKERRQ(ierr);
2074     pos += max_no;
2075   }
2076 
2077   ierr = PetscFree(allcolumns);CHKERRQ(ierr);
2078   PetscFunctionReturn(0);
2079 }
2080 
2081 /* -------------------------------------------------------------------------*/
2082 PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,PetscBool *allcolumns,Mat *submats)
2083 {
2084   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
2085   Mat            A  = c->A;
2086   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)c->B->data,*mat;
2087   const PetscInt **icol,**irow;
2088   PetscInt       *nrow,*ncol,start;
2089   PetscErrorCode ierr;
2090   PetscMPIInt    rank,size,tag0,tag1,tag2,tag3,*w1,*w2,*w3,*w4,nrqr;
2091   PetscInt       **sbuf1,**sbuf2,i,j,k,l,ct1,ct2,**rbuf1,row,proc;
2092   PetscInt       nrqs,msz,**ptr,*req_size,*ctr,*pa,*tmp,tcol;
2093   PetscInt       **rbuf3,*req_source,**sbuf_aj,**rbuf2,max1,max2;
2094   PetscInt       **lens,is_no,ncols,*cols,mat_i,*mat_j,tmp2,jmax;
2095 #if defined(PETSC_USE_CTABLE)
2096   PetscTable *cmap,cmap_i=NULL,*rmap,rmap_i;
2097 #else
2098   PetscInt **cmap,*cmap_i=NULL,**rmap,*rmap_i;
2099 #endif
2100   const PetscInt *irow_i;
2101   PetscInt       ctr_j,*sbuf1_j,*sbuf_aj_i,*rbuf1_i,kmax,*lens_i;
2102   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2,*r_waits3;
2103   MPI_Request    *r_waits4,*s_waits3,*s_waits4;
2104   MPI_Status     *r_status1,*r_status2,*s_status1,*s_status3,*s_status2;
2105   MPI_Status     *r_status3,*r_status4,*s_status4;
2106   MPI_Comm       comm;
2107   PetscScalar    **rbuf4,**sbuf_aa,*vals,*mat_a,*sbuf_aa_i;
2108   PetscMPIInt    *onodes1,*olengths1;
2109   PetscMPIInt    idex,idex2,end;
2110   PetscInt       **row2proc,*row2proc_i;
2111   Mat_SubMat     **smats,*smat_i;
2112   PetscBool      *issorted;
2113 
2114   PetscFunctionBegin;
2115   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2116   tag0 = ((PetscObject)C)->tag;
2117   size = c->size;
2118   rank = c->rank;
2119   //printf("[%d] MatGetSubMatrices_MPIAIJ_Local, scall %d\n",rank,scall);
2120 
2121   /* Get some new tags to keep the communication clean */
2122   ierr = PetscObjectGetNewTag((PetscObject)C,&tag1);CHKERRQ(ierr);
2123   ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
2124   ierr = PetscObjectGetNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
2125 
2126   ierr = PetscMalloc4(ismax,&irow,ismax,&icol,ismax,&nrow,ismax,&ncol);CHKERRQ(ierr);
2127   ierr = PetscMalloc1(ismax,&issorted);CHKERRQ(ierr);
2128 
2129   for (i=0; i<ismax; i++) {
2130     ierr = ISSorted(isrow[i],&issorted[i]);CHKERRQ(ierr);
2131 
2132     ierr = ISGetIndices(isrow[i],&irow[i]);CHKERRQ(ierr);
2133     ierr = ISGetLocalSize(isrow[i],&nrow[i]);CHKERRQ(ierr);
2134     if (allcolumns[i]) {
2135       icol[i] = NULL;
2136       ncol[i] = C->cmap->N;
2137     } else {
2138       ierr = ISGetIndices(iscol[i],&icol[i]);CHKERRQ(ierr);
2139       ierr = ISGetLocalSize(iscol[i],&ncol[i]);CHKERRQ(ierr);
2140     }
2141   }
2142 
2143 
2144   ierr = PetscMalloc1(ismax,&smats);CHKERRQ(ierr);
2145   ierr = PetscMalloc1(ismax,&row2proc);CHKERRQ(ierr);
2146 
2147   if (scall == MAT_REUSE_MATRIX) {
2148     //PetscInt  *req_source1,*req_source2;
2149 
2150     /* Assumes new rows are same length as the old rows,hence bug! */
2151     for (i=0; i<ismax; i++) {
2152       mat = (Mat_SeqAIJ*)(submats[i]->data);
2153       if ((submats[i]->rmap->n != nrow[i]) || (submats[i]->cmap->n != ncol[i])) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2154 
2155       /* Initial matrix as if empty -- rm later!!! */
2156       ierr = PetscMemzero(mat->ilen,submats[i]->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2157 
2158       /* Initial matrix as if empty */
2159       submats[i]->factortype = C->factortype;
2160 
2161       smat_i   = mat->submatis1;
2162       smats[i] = smat_i;
2163 
2164       nrqs        = smat_i->nrqs;
2165       nrqr        = smat_i->nrqr;
2166       rbuf1       = smat_i->rbuf1;
2167       rbuf2       = smat_i->rbuf2;
2168       rbuf3       = smat_i->rbuf3;
2169       //req_source2 = smat_i->req_source2;
2170 
2171       sbuf1     = smat_i->sbuf1;
2172       sbuf2     = smat_i->sbuf2;
2173       ptr       = smat_i->ptr;
2174       tmp       = smat_i->tmp;
2175       ctr       = smat_i->ctr;
2176 
2177       pa          = smat_i->pa;
2178       req_size    = smat_i->req_size;
2179       //req_source1 = smat_i->req_source1;
2180 
2181       allcolumns[i] = smat_i->allcolumns;
2182       row2proc[i]   = smat_i->row2proc;
2183       //rmap       = smat_i->rmap;
2184       //cmap       = smat_i->cmap;
2185 #if defined(PETSC_USE_CTABLE)
2186       //rmap_loc   = smat_i->rmap_loc;
2187       //cmap_loc   = smat_i->cmap_loc;
2188 #endif
2189     }
2190   }
2191 
2192   /* evaluate communication - mesg to who, length of mesg, and buffer space
2193      required. Based on this, buffers are allocated, and data copied into them*/
2194   ierr = PetscMalloc4(size,&w1,size,&w2,size,&w3,size,&w4);CHKERRQ(ierr);   /* mesg size */
2195   ierr = PetscMemzero(w1,size*sizeof(PetscMPIInt));CHKERRQ(ierr);   /* initialize work vector*/
2196   ierr = PetscMemzero(w2,size*sizeof(PetscMPIInt));CHKERRQ(ierr);   /* initialize work vector*/
2197   ierr = PetscMemzero(w3,size*sizeof(PetscMPIInt));CHKERRQ(ierr);   /* initialize work vector*/
2198 
2199   for (i=0; i<ismax; i++) {
2200     ierr   = PetscMemzero(w4,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialize work vector*/
2201     jmax   = nrow[i];
2202     irow_i = irow[i];
2203 
2204     if (scall == MAT_INITIAL_MATRIX) {
2205       ierr   = PetscMalloc1(jmax,&row2proc_i);CHKERRQ(ierr);
2206       row2proc[i] = row2proc_i;
2207     } else {
2208       row2proc_i = row2proc[i];
2209     }
2210 
2211     if (issorted[i]) proc = 0;
2212     for (j=0; j<jmax; j++) {
2213       if (!issorted[i]) proc = 0;
2214       row = irow_i[j];
2215       while (row >= C->rmap->range[proc+1]) proc++;
2216       w4[proc]++;
2217       row2proc_i[j] = proc; /* map row index to proc */
2218     }
2219     for (j=0; j<size; j++) {
2220       if (w4[j]) { w1[j] += w4[j];  w3[j]++;}
2221     }
2222   }
2223 
2224   nrqs     = 0;              /* no of outgoing messages */
2225   msz      = 0;              /* total mesg length (for all procs) */
2226   w1[rank] = 0;              /* no mesg sent to self */
2227   w3[rank] = 0;
2228   for (i=0; i<size; i++) {
2229     if (w1[i])  { w2[i] = 1; nrqs++;} /* there exists a message to proc i */
2230   }
2231   ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr); /*(proc -array)*/
2232   for (i=0,j=0; i<size; i++) {
2233     if (w1[i]) { pa[j] = i; j++; }
2234   }
2235 
2236   /* Each message would have a header = 1 + 2*(no of IS) + data */
2237   for (i=0; i<nrqs; i++) {
2238     j      = pa[i];
2239     w1[j] += w2[j] + 2* w3[j];
2240     msz   += w1[j];
2241   }
2242   ierr = PetscInfo2(0,"Number of outgoing messages %D Total message length %D\n",nrqs,msz);CHKERRQ(ierr);
2243 
2244   /* Determine the number of messages to expect, their lengths, from from-ids */
2245   ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
2246   ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
2247 
2248   /* Now post the Irecvs corresponding to these messages */
2249   ierr = PetscPostIrecvInt(comm,tag0,nrqr,onodes1,olengths1,&rbuf1,&r_waits1);CHKERRQ(ierr);
2250 
2251   ierr = PetscFree(onodes1);CHKERRQ(ierr);
2252   ierr = PetscFree(olengths1);CHKERRQ(ierr);
2253 
2254   /* Allocate Memory for outgoing messages */
2255   ierr = PetscMalloc4(size,&sbuf1,size,&ptr,2*msz,&tmp,size,&ctr);CHKERRQ(ierr);
2256   ierr = PetscMemzero(sbuf1,size*sizeof(PetscInt*));CHKERRQ(ierr);
2257   ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
2258 
2259   {
2260     PetscInt *iptr = tmp;
2261     k    = 0;
2262     for (i=0; i<nrqs; i++) {
2263       j        = pa[i];
2264       iptr    += k;
2265       sbuf1[j] = iptr;
2266       k        = w1[j];
2267     }
2268   }
2269 
2270   /* Form the outgoing messages */
2271   /* Initialize the header space */
2272   for (i=0; i<nrqs; i++) {
2273     j           = pa[i];
2274     sbuf1[j][0] = 0;
2275     ierr        = PetscMemzero(sbuf1[j]+1,2*w3[j]*sizeof(PetscInt));CHKERRQ(ierr);
2276     ptr[j]      = sbuf1[j] + 2*w3[j] + 1;
2277   }
2278 
2279   /* Parse the isrow and copy data into outbuf */
2280   for (i=0; i<ismax; i++) {
2281     row2proc_i = row2proc[i];
2282     ierr   = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
2283     irow_i = irow[i];
2284     jmax   = nrow[i];
2285     for (j=0; j<jmax; j++) {  /* parse the indices of each IS */
2286       proc = row2proc_i[j];
2287       if (proc != rank) { /* copy to the outgoing buf*/
2288         ctr[proc]++;
2289         *ptr[proc] = irow_i[j];
2290         ptr[proc]++;
2291       }
2292     }
2293     /* Update the headers for the current IS */
2294     for (j=0; j<size; j++) { /* Can Optimise this loop too */
2295       if ((ctr_j = ctr[j])) {
2296         sbuf1_j        = sbuf1[j];
2297         k              = ++sbuf1_j[0];
2298         sbuf1_j[2*k]   = ctr_j;
2299         sbuf1_j[2*k-1] = i;
2300       }
2301     }
2302   }
2303 
2304   /*  Now  post the sends */
2305   ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
2306   for (i=0; i<nrqs; ++i) {
2307     j    = pa[i];
2308     ierr = MPI_Isend(sbuf1[j],w1[j],MPIU_INT,j,tag0,comm,s_waits1+i);CHKERRQ(ierr);
2309   }
2310 
2311   /* Post Receives to capture the buffer size */
2312   ierr     = PetscMalloc1(nrqs+1,&r_waits2);CHKERRQ(ierr);
2313   ierr     = PetscMalloc1(nrqs+1,&rbuf2);CHKERRQ(ierr);
2314   rbuf2[0] = tmp + msz;
2315   for (i=1; i<nrqs; ++i) {
2316     rbuf2[i] = rbuf2[i-1]+w1[pa[i-1]];
2317   }
2318   for (i=0; i<nrqs; ++i) {
2319     j    = pa[i];
2320     ierr = MPI_Irecv(rbuf2[i],w1[j],MPIU_INT,j,tag1,comm,r_waits2+i);CHKERRQ(ierr);
2321   }
2322 
2323   /* Send to other procs the buf size they should allocate */
2324 
2325 
2326   /* Receive messages*/
2327   ierr = PetscMalloc1(nrqr+1,&s_waits2);CHKERRQ(ierr);
2328   ierr = PetscMalloc1(nrqr+1,&r_status1);CHKERRQ(ierr);
2329   ierr = PetscMalloc3(nrqr,&sbuf2,nrqr,&req_size,nrqr,&req_source);CHKERRQ(ierr);
2330   {
2331     PetscInt   *sAi = a->i,*sBi = b->i,id,rstart = C->rmap->rstart;
2332     PetscInt   *sbuf2_i;
2333 
2334     for (i=0; i<nrqr; ++i) {
2335       ierr = MPI_Waitany(nrqr,r_waits1,&idex,r_status1+i);CHKERRQ(ierr);
2336 
2337       req_size[idex] = 0;
2338       rbuf1_i        = rbuf1[idex];
2339       start          = 2*rbuf1_i[0] + 1;
2340       ierr           = MPI_Get_count(r_status1+i,MPIU_INT,&end);CHKERRQ(ierr);
2341       ierr           = PetscMalloc1(end+1,&sbuf2[idex]);CHKERRQ(ierr);
2342       sbuf2_i        = sbuf2[idex];
2343       for (j=start; j<end; j++) {
2344         id              = rbuf1_i[j] - rstart;
2345         ncols           = sAi[id+1] - sAi[id] + sBi[id+1] - sBi[id];
2346         sbuf2_i[j]      = ncols;
2347         req_size[idex] += ncols;
2348       }
2349       req_source[idex] = r_status1[i].MPI_SOURCE;
2350       /* form the header */
2351       sbuf2_i[0] = req_size[idex];
2352       for (j=1; j<start; j++) sbuf2_i[j] = rbuf1_i[j];
2353 
2354       ierr = MPI_Isend(sbuf2_i,end,MPIU_INT,req_source[idex],tag1,comm,s_waits2+i);CHKERRQ(ierr);
2355     }
2356   }
2357   ierr = PetscFree(r_status1);CHKERRQ(ierr);
2358   ierr = PetscFree(r_waits1);CHKERRQ(ierr);
2359 
2360   /*  recv buffer sizes */
2361   /* Receive messages*/
2362 
2363   ierr = PetscMalloc1(nrqs+1,&rbuf3);CHKERRQ(ierr);
2364   ierr = PetscMalloc1(nrqs+1,&rbuf4);CHKERRQ(ierr);
2365   ierr = PetscMalloc1(nrqs+1,&r_waits3);CHKERRQ(ierr);
2366   ierr = PetscMalloc1(nrqs+1,&r_waits4);CHKERRQ(ierr);
2367   ierr = PetscMalloc1(nrqs+1,&r_status2);CHKERRQ(ierr);
2368 
2369   for (i=0; i<nrqs; ++i) {
2370     ierr = MPI_Waitany(nrqs,r_waits2,&idex,r_status2+i);CHKERRQ(ierr);
2371     ierr = PetscMalloc1(rbuf2[idex][0]+1,&rbuf3[idex]);CHKERRQ(ierr);
2372     ierr = PetscMalloc1(rbuf2[idex][0]+1,&rbuf4[idex]);CHKERRQ(ierr);
2373     ierr = MPI_Irecv(rbuf3[idex],rbuf2[idex][0],MPIU_INT,r_status2[i].MPI_SOURCE,tag2,comm,r_waits3+idex);CHKERRQ(ierr);
2374     ierr = MPI_Irecv(rbuf4[idex],rbuf2[idex][0],MPIU_SCALAR,r_status2[i].MPI_SOURCE,tag3,comm,r_waits4+idex);CHKERRQ(ierr);
2375   }
2376   ierr = PetscFree(r_status2);CHKERRQ(ierr);
2377   ierr = PetscFree(r_waits2);CHKERRQ(ierr);
2378 
2379   /* Wait on sends1 and sends2 */
2380   ierr = PetscMalloc1(nrqs+1,&s_status1);CHKERRQ(ierr);
2381   ierr = PetscMalloc1(nrqr+1,&s_status2);CHKERRQ(ierr);
2382 
2383   if (nrqs) {ierr = MPI_Waitall(nrqs,s_waits1,s_status1);CHKERRQ(ierr);}
2384   if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits2,s_status2);CHKERRQ(ierr);}
2385   ierr = PetscFree(s_status1);CHKERRQ(ierr);
2386   ierr = PetscFree(s_status2);CHKERRQ(ierr);
2387   ierr = PetscFree(s_waits1);CHKERRQ(ierr);
2388   ierr = PetscFree(s_waits2);CHKERRQ(ierr);
2389 
2390   /* Now allocate buffers for a->j, and send them off */
2391   ierr = PetscMalloc1(nrqr+1,&sbuf_aj);CHKERRQ(ierr);
2392   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
2393   ierr = PetscMalloc1(j+1,&sbuf_aj[0]);CHKERRQ(ierr);
2394   for (i=1; i<nrqr; i++) sbuf_aj[i] = sbuf_aj[i-1] + req_size[i-1];
2395 
2396   ierr = PetscMalloc1(nrqr+1,&s_waits3);CHKERRQ(ierr);
2397   {
2398     PetscInt nzA,nzB,*a_i = a->i,*b_i = b->i,lwrite;
2399     PetscInt *cworkA,*cworkB,cstart = C->cmap->rstart,rstart = C->rmap->rstart,*bmap = c->garray;
2400     PetscInt cend = C->cmap->rend;
2401     PetscInt *a_j = a->j,*b_j = b->j,ctmp;
2402 
2403     for (i=0; i<nrqr; i++) {
2404       rbuf1_i   = rbuf1[i];
2405       sbuf_aj_i = sbuf_aj[i];
2406       ct1       = 2*rbuf1_i[0] + 1;
2407       ct2       = 0;
2408       for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
2409         kmax = rbuf1[i][2*j];
2410         for (k=0; k<kmax; k++,ct1++) {
2411           row    = rbuf1_i[ct1] - rstart;
2412           nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
2413           ncols  = nzA + nzB;
2414           cworkA = a_j + a_i[row]; cworkB = b_j + b_i[row];
2415 
2416           /* load the column indices for this row into cols*/
2417           cols = sbuf_aj_i + ct2;
2418 
2419           lwrite = 0;
2420           for (l=0; l<nzB; l++) {
2421             if ((ctmp = bmap[cworkB[l]]) < cstart) cols[lwrite++] = ctmp;
2422           }
2423           for (l=0; l<nzA; l++) cols[lwrite++] = cstart + cworkA[l];
2424           for (l=0; l<nzB; l++) {
2425             if ((ctmp = bmap[cworkB[l]]) >= cend) cols[lwrite++] = ctmp;
2426           }
2427 
2428           ct2 += ncols;
2429         }
2430       }
2431       ierr = MPI_Isend(sbuf_aj_i,req_size[i],MPIU_INT,req_source[i],tag2,comm,s_waits3+i);CHKERRQ(ierr);
2432     }
2433   }
2434   ierr = PetscMalloc1(nrqs+1,&r_status3);CHKERRQ(ierr);
2435   ierr = PetscMalloc1(nrqr+1,&s_status3);CHKERRQ(ierr);
2436 
2437   ierr = PetscMalloc1(nrqs+1,&r_status4);CHKERRQ(ierr);
2438   ierr = PetscMalloc1(nrqr+1,&s_status4);CHKERRQ(ierr);
2439 
2440   /* Form the matrix */
2441   /* create col map: global col of C -> local col of submatrices */
2442   {
2443     const PetscInt *icol_i;
2444 #if defined(PETSC_USE_CTABLE)
2445     ierr = PetscMalloc1(1+ismax,&cmap);CHKERRQ(ierr);
2446     for (i=0; i<ismax; i++) {
2447       if (!allcolumns[i]) {
2448         ierr = PetscTableCreate(ncol[i]+1,C->cmap->N+1,&cmap[i]);CHKERRQ(ierr);
2449 
2450         jmax   = ncol[i];
2451         icol_i = icol[i];
2452         cmap_i = cmap[i];
2453         for (j=0; j<jmax; j++) {
2454           ierr = PetscTableAdd(cmap[i],icol_i[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
2455         }
2456       } else {
2457         cmap[i] = NULL;
2458       }
2459     }
2460 #else
2461     ierr = PetscMalloc1(ismax,&cmap);CHKERRQ(ierr);
2462     for (i=0; i<ismax; i++) {
2463       if (!allcolumns[i]) {
2464         ierr   = PetscMalloc1(C->cmap->N,&cmap[i]);CHKERRQ(ierr);
2465         ierr   = PetscMemzero(cmap[i],C->cmap->N*sizeof(PetscInt));CHKERRQ(ierr);
2466         jmax   = ncol[i];
2467         icol_i = icol[i];
2468         cmap_i = cmap[i];
2469         for (j=0; j<jmax; j++) {
2470           cmap_i[icol_i[j]] = j+1;
2471         }
2472       } else {
2473         cmap[i] = NULL;
2474       }
2475     }
2476 #endif
2477   }
2478 
2479   /* Create lens which is required for MatCreate... */
2480   for (i=0,j=0; i<ismax; i++) j += nrow[i];
2481   ierr = PetscMalloc1(ismax,&lens);CHKERRQ(ierr);
2482   if (ismax) {
2483     ierr = PetscMalloc1(j,&lens[0]);CHKERRQ(ierr);
2484     ierr = PetscMemzero(lens[0],j*sizeof(PetscInt));CHKERRQ(ierr);
2485   }
2486   for (i=1; i<ismax; i++) lens[i] = lens[i-1] + nrow[i-1];
2487 
2488   /* Update lens from local data */
2489   for (i=0; i<ismax; i++) {
2490     row2proc_i = row2proc[i];
2491     jmax = nrow[i];
2492     if (!allcolumns[i]) cmap_i = cmap[i];
2493     irow_i = irow[i];
2494     lens_i = lens[i];
2495     for (j=0; j<jmax; j++) {
2496       row = irow_i[j];
2497       proc = row2proc_i[j];
2498       if (proc == rank) {
2499         ierr = MatGetRow_MPIAIJ(C,row,&ncols,&cols,0);CHKERRQ(ierr);
2500         if (!allcolumns[i]) {
2501           for (k=0; k<ncols; k++) {
2502 #if defined(PETSC_USE_CTABLE)
2503             ierr = PetscTableFind(cmap_i,cols[k]+1,&tcol);CHKERRQ(ierr);
2504 #else
2505             tcol = cmap_i[cols[k]];
2506 #endif
2507             if (tcol) lens_i[j]++;
2508           }
2509         } else { /* allcolumns */
2510           lens_i[j] = ncols;
2511         }
2512         ierr = MatRestoreRow_MPIAIJ(C,row,&ncols,&cols,0);CHKERRQ(ierr);
2513       }
2514     }
2515   }
2516 
2517   /* Create row map: global row of C -> local row of submatrices */
2518 #if defined(PETSC_USE_CTABLE)
2519   ierr = PetscMalloc1(1+ismax,&rmap);CHKERRQ(ierr);
2520   for (i=0; i<ismax; i++) {
2521     ierr   = PetscTableCreate(nrow[i]+1,C->rmap->N+1,&rmap[i]);CHKERRQ(ierr);
2522     irow_i = irow[i];
2523     jmax   = nrow[i];
2524     for (j=0; j<jmax; j++) {
2525       ierr = PetscTableAdd(rmap[i],irow_i[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
2526     }
2527   }
2528 #else
2529   ierr = PetscMalloc1(ismax,&rmap);CHKERRQ(ierr);
2530   if (ismax) {
2531     ierr = PetscMalloc1(ismax*C->rmap->N,&rmap[0]);CHKERRQ(ierr);
2532     ierr = PetscMemzero(rmap[0],ismax*C->rmap->N*sizeof(PetscInt));CHKERRQ(ierr);
2533   }
2534   for (i=1; i<ismax; i++) rmap[i] = rmap[i-1] + C->rmap->N;
2535   for (i=0; i<ismax; i++) {
2536     rmap_i = rmap[i];
2537     irow_i = irow[i];
2538     jmax   = nrow[i];
2539     for (j=0; j<jmax; j++) {
2540       rmap_i[irow_i[j]] = j;
2541     }
2542   }
2543 #endif
2544 
2545   /* Update lens from offproc data */
2546   {
2547     PetscInt *rbuf2_i,*rbuf3_i,*sbuf1_i;
2548 
2549     for (tmp2=0; tmp2<nrqs; tmp2++) {
2550       ierr    = MPI_Waitany(nrqs,r_waits3,&idex2,r_status3+tmp2);CHKERRQ(ierr);
2551       idex    = pa[idex2];
2552       sbuf1_i = sbuf1[idex];
2553       jmax    = sbuf1_i[0];
2554       ct1     = 2*jmax+1;
2555       ct2     = 0;
2556       rbuf2_i = rbuf2[idex2];
2557       rbuf3_i = rbuf3[idex2];
2558       for (j=1; j<=jmax; j++) {
2559         is_no  = sbuf1_i[2*j-1];
2560         max1   = sbuf1_i[2*j];
2561         lens_i = lens[is_no];
2562         if (!allcolumns[is_no]) cmap_i = cmap[is_no];
2563         rmap_i = rmap[is_no];
2564         for (k=0; k<max1; k++,ct1++) {
2565 #if defined(PETSC_USE_CTABLE)
2566           ierr = PetscTableFind(rmap_i,sbuf1_i[ct1]+1,&row);CHKERRQ(ierr);
2567           row--;
2568           if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"row not found in table");
2569 #else
2570           row = rmap_i[sbuf1_i[ct1]]; /* the val in the new matrix to be */
2571 #endif
2572           max2 = rbuf2_i[ct1];
2573           for (l=0; l<max2; l++,ct2++) {
2574             if (!allcolumns[is_no]) {
2575 #if defined(PETSC_USE_CTABLE)
2576               ierr = PetscTableFind(cmap_i,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
2577 #else
2578               tcol = cmap_i[rbuf3_i[ct2]];
2579 #endif
2580               if (tcol) lens_i[row]++;
2581             } else { /* allcolumns */
2582               lens_i[row]++; /* lens_i[row] += max2 ? */
2583             }
2584           }
2585         }
2586       }
2587     }
2588   }
2589   ierr = PetscFree(r_status3);CHKERRQ(ierr);
2590   ierr = PetscFree(r_waits3);CHKERRQ(ierr);
2591   if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits3,s_status3);CHKERRQ(ierr);}
2592   ierr = PetscFree(s_status3);CHKERRQ(ierr);
2593   ierr = PetscFree(s_waits3);CHKERRQ(ierr);
2594 
2595   /* Create the submatrices */
2596   if (scall == MAT_INITIAL_MATRIX) {
2597     for (i=0; i<ismax; i++) {
2598       PetscInt    rbs,cbs;
2599       Mat_SeqAIJ* subc;
2600 
2601       ierr = ISGetBlockSize(isrow[i],&rbs);CHKERRQ(ierr);
2602       ierr = ISGetBlockSize(iscol[i],&cbs);CHKERRQ(ierr);
2603 
2604       ierr = MatCreate(PETSC_COMM_SELF,submats+i);CHKERRQ(ierr);
2605       ierr = MatSetSizes(submats[i],nrow[i],ncol[i],PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2606 
2607       ierr = MatSetBlockSizes(submats[i],rbs,cbs);CHKERRQ(ierr);
2608       ierr = MatSetType(submats[i],((PetscObject)A)->type_name);CHKERRQ(ierr);
2609       ierr = MatSeqAIJSetPreallocation(submats[i],0,lens[i]);CHKERRQ(ierr);
2610 
2611       /* create struct Mat_SubMat and attached it to submat */
2612       ierr = PetscNew(&smat_i);CHKERRQ(ierr);
2613       subc = (Mat_SeqAIJ*)submats[i]->data;
2614       subc->submatis1 = smat_i;
2615       smats[i]        = smat_i;
2616 
2617       smat_i->destroy          = submats[i]->ops->destroy;
2618       submats[i]->ops->destroy = MatDestroy_MPIAIJ_MatGetSubmatrices;
2619       submats[i]->factortype   = C->factortype;
2620 
2621       smat_i->nrqs        = 0;//nrqs;
2622       smat_i->nrqr        = 0;//nrqr;
2623       smat_i->rbuf1       = NULL;//rbuf1;
2624       smat_i->rbuf2       = NULL;//rbuf2;
2625       smat_i->rbuf3       = NULL;//rbuf3;
2626       smat_i->sbuf2       = NULL;//sbuf2;
2627       smat_i->req_source2 = NULL;//req_source2;
2628 
2629       smat_i->sbuf1       = NULL;//sbuf1;
2630       smat_i->ptr         = NULL;//ptr;
2631       smat_i->tmp         = NULL;//tmp;
2632       smat_i->ctr         = NULL;//ctr;
2633 
2634       smat_i->pa           = NULL;//pa;
2635       smat_i->req_size     = NULL;//req_size;
2636       smat_i->req_source1  = NULL;//req_source1;
2637 
2638       smat_i->allcolumns  = allcolumns[i];
2639       smat_i->row2proc    = row2proc[i];
2640       smat_i->rmap        = NULL;//rmap;
2641       smat_i->cmap        = NULL;//cmap;
2642 #if defined(PETSC_USE_CTABLE)
2643       smat_i->rmap_loc    = NULL;//rmap_loc;
2644       smat_i->cmap_loc    = NULL;//cmap_loc;
2645 #endif
2646 
2647     }
2648   }
2649 
2650     /* Allocate buffers for a->a, and send them off */
2651   ierr = PetscMalloc1(nrqr+1,&sbuf_aa);CHKERRQ(ierr);
2652   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
2653   ierr = PetscMalloc1(j+1,&sbuf_aa[0]);CHKERRQ(ierr);
2654   for (i=1; i<nrqr; i++) sbuf_aa[i] = sbuf_aa[i-1] + req_size[i-1];
2655 
2656   ierr = PetscMalloc1(nrqr+1,&s_waits4);CHKERRQ(ierr);
2657   {
2658     PetscInt    nzA,nzB,*a_i = a->i,*b_i = b->i, *cworkB,lwrite;
2659     PetscInt    cstart = C->cmap->rstart,rstart = C->rmap->rstart,*bmap = c->garray;
2660     PetscInt    cend   = C->cmap->rend;
2661     PetscInt    *b_j   = b->j;
2662     PetscScalar *vworkA,*vworkB,*a_a = a->a,*b_a = b->a;
2663 
2664     for (i=0; i<nrqr; i++) {
2665       rbuf1_i   = rbuf1[i];
2666       sbuf_aa_i = sbuf_aa[i];
2667       ct1       = 2*rbuf1_i[0]+1;
2668       ct2       = 0;
2669       for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
2670         kmax = rbuf1_i[2*j];
2671         for (k=0; k<kmax; k++,ct1++) {
2672           row    = rbuf1_i[ct1] - rstart;
2673           nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
2674           ncols  = nzA + nzB;
2675           cworkB = b_j + b_i[row];
2676           vworkA = a_a + a_i[row];
2677           vworkB = b_a + b_i[row];
2678 
2679           /* load the column values for this row into vals*/
2680           vals = sbuf_aa_i+ct2;
2681 
2682           lwrite = 0;
2683           for (l=0; l<nzB; l++) {
2684             if ((bmap[cworkB[l]]) < cstart) vals[lwrite++] = vworkB[l];
2685           }
2686           for (l=0; l<nzA; l++) vals[lwrite++] = vworkA[l];
2687           for (l=0; l<nzB; l++) {
2688             if ((bmap[cworkB[l]]) >= cend) vals[lwrite++] = vworkB[l];
2689           }
2690 
2691           ct2 += ncols;
2692         }
2693       }
2694       ierr = MPI_Isend(sbuf_aa_i,req_size[i],MPIU_SCALAR,req_source[i],tag3,comm,s_waits4+i);CHKERRQ(ierr);
2695     }
2696   }
2697   ierr = PetscFree(rbuf1[0]);CHKERRQ(ierr);
2698   ierr = PetscFree(rbuf1);CHKERRQ(ierr);
2699 
2700 
2701   /* Assemble the matrices */
2702   /* First assemble the local rows */
2703   {
2704     PetscInt    ilen_row,*imat_ilen,*imat_j,*imat_i,old_row;
2705     PetscScalar *imat_a;
2706 
2707     for (i=0; i<ismax; i++) {
2708       row2proc_i = row2proc[i];
2709       mat       = (Mat_SeqAIJ*)submats[i]->data;
2710       imat_ilen = mat->ilen;
2711       imat_j    = mat->j;
2712       imat_i    = mat->i;
2713       imat_a    = mat->a;
2714 
2715       if (!allcolumns[i]) cmap_i = cmap[i];
2716       rmap_i = rmap[i];
2717       irow_i = irow[i];
2718       jmax   = nrow[i];
2719       for (j=0; j<jmax; j++) {
2720         row  = irow_i[j];
2721         proc = row2proc_i[j];
2722         if (proc == rank) {
2723           old_row = row;
2724 #if defined(PETSC_USE_CTABLE)
2725           ierr = PetscTableFind(rmap_i,row+1,&row);CHKERRQ(ierr);
2726           row--;
2727 #else
2728           row = rmap_i[row];
2729 #endif
2730           ilen_row = imat_ilen[row];
2731           ierr     = MatGetRow_MPIAIJ(C,old_row,&ncols,&cols,&vals);CHKERRQ(ierr);
2732           mat_i    = imat_i[row];
2733           mat_a    = imat_a + mat_i;
2734           mat_j    = imat_j + mat_i;
2735           if (!allcolumns[i]) {
2736             for (k=0; k<ncols; k++) {
2737 #if defined(PETSC_USE_CTABLE)
2738               ierr = PetscTableFind(cmap_i,cols[k]+1,&tcol);CHKERRQ(ierr);
2739 #else
2740               tcol = cmap_i[cols[k]];
2741 #endif
2742               if (tcol) {
2743                 *mat_j++ = tcol - 1;
2744                 *mat_a++ = vals[k];
2745                 ilen_row++;
2746               }
2747             }
2748           } else { /* allcolumns */
2749             for (k=0; k<ncols; k++) {
2750               *mat_j++ = cols[k];  /* global col index! */
2751               *mat_a++ = vals[k];
2752               ilen_row++;
2753             }
2754           }
2755           ierr = MatRestoreRow_MPIAIJ(C,old_row,&ncols,&cols,&vals);CHKERRQ(ierr);
2756 
2757           imat_ilen[row] = ilen_row;
2758         }
2759       }
2760     }
2761   }
2762 
2763   /*   Now assemble the off proc rows*/
2764   {
2765     PetscInt    *sbuf1_i,*rbuf2_i,*rbuf3_i,*imat_ilen,ilen;
2766     PetscInt    *imat_j,*imat_i;
2767     PetscScalar *imat_a,*rbuf4_i;
2768 
2769     for (tmp2=0; tmp2<nrqs; tmp2++) {
2770       ierr    = MPI_Waitany(nrqs,r_waits4,&idex2,r_status4+tmp2);CHKERRQ(ierr);
2771       idex    = pa[idex2];
2772       sbuf1_i = sbuf1[idex];
2773       jmax    = sbuf1_i[0];
2774       ct1     = 2*jmax + 1;
2775       ct2     = 0;
2776       rbuf2_i = rbuf2[idex2];
2777       rbuf3_i = rbuf3[idex2];
2778       rbuf4_i = rbuf4[idex2];
2779       for (j=1; j<=jmax; j++) {
2780         is_no     = sbuf1_i[2*j-1];
2781         rmap_i    = rmap[is_no];
2782         if (!allcolumns[is_no]) cmap_i = cmap[is_no];
2783         mat       = (Mat_SeqAIJ*)submats[is_no]->data;
2784         imat_ilen = mat->ilen;
2785         imat_j    = mat->j;
2786         imat_i    = mat->i;
2787         imat_a    = mat->a;
2788         max1      = sbuf1_i[2*j];
2789         for (k=0; k<max1; k++,ct1++) {
2790           row = sbuf1_i[ct1];
2791 #if defined(PETSC_USE_CTABLE)
2792           ierr = PetscTableFind(rmap_i,row+1,&row);CHKERRQ(ierr);
2793           row--;
2794 #else
2795           row = rmap_i[row];
2796 #endif
2797           ilen  = imat_ilen[row];
2798           mat_i = imat_i[row];
2799           mat_a = imat_a + mat_i;
2800           mat_j = imat_j + mat_i;
2801           max2  = rbuf2_i[ct1];
2802           if (!allcolumns[is_no]) {
2803             for (l=0; l<max2; l++,ct2++) {
2804 
2805 #if defined(PETSC_USE_CTABLE)
2806               ierr = PetscTableFind(cmap_i,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
2807 #else
2808               tcol = cmap_i[rbuf3_i[ct2]];
2809 #endif
2810               if (tcol) {
2811                 *mat_j++ = tcol - 1;
2812                 *mat_a++ = rbuf4_i[ct2];
2813                 ilen++;
2814               }
2815             }
2816           } else { /* allcolumns */
2817             for (l=0; l<max2; l++,ct2++) {
2818               *mat_j++ = rbuf3_i[ct2]; /* same global column index of C */
2819               *mat_a++ = rbuf4_i[ct2];
2820               ilen++;
2821             }
2822           }
2823           imat_ilen[row] = ilen;
2824         }
2825       }
2826     }
2827   }
2828 
2829   /* sort the rows */
2830   {
2831     PetscInt    *imat_ilen,*imat_j,*imat_i;
2832     PetscScalar *imat_a;
2833 
2834     for (i=0; i<ismax; i++) {
2835       mat       = (Mat_SeqAIJ*)submats[i]->data;
2836       imat_j    = mat->j;
2837       imat_i    = mat->i;
2838       imat_a    = mat->a;
2839       imat_ilen = mat->ilen;
2840 
2841       if (allcolumns[i]) continue;
2842       jmax = nrow[i];
2843       for (j=0; j<jmax; j++) {
2844         PetscInt ilen;
2845 
2846         mat_i = imat_i[j];
2847         mat_a = imat_a + mat_i;
2848         mat_j = imat_j + mat_i;
2849         ilen  = imat_ilen[j];
2850         ierr  = PetscSortIntWithScalarArray(ilen,mat_j,mat_a);CHKERRQ(ierr);
2851       }
2852     }
2853   }
2854 
2855   ierr = PetscFree(r_status4);CHKERRQ(ierr);
2856   ierr = PetscFree(r_waits4);CHKERRQ(ierr);
2857   if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits4,s_status4);CHKERRQ(ierr);}
2858   ierr = PetscFree(s_waits4);CHKERRQ(ierr);
2859   ierr = PetscFree(s_status4);CHKERRQ(ierr);
2860 
2861   /* Restore the indices */
2862   for (i=0; i<ismax; i++) {
2863     ierr = ISRestoreIndices(isrow[i],irow+i);CHKERRQ(ierr);
2864     if (!allcolumns[i]) {
2865       ierr = ISRestoreIndices(iscol[i],icol+i);CHKERRQ(ierr);
2866     }
2867   }
2868 
2869   /* Destroy allocated memory */
2870   ierr = PetscFree4(irow,icol,nrow,ncol);CHKERRQ(ierr);
2871   ierr = PetscFree4(w1,w2,w3,w4);CHKERRQ(ierr);
2872   ierr = PetscFree(pa);CHKERRQ(ierr);
2873 
2874   ierr = PetscFree4(sbuf1,ptr,tmp,ctr);CHKERRQ(ierr);
2875   ierr = PetscFree(rbuf2);CHKERRQ(ierr);
2876   for (i=0; i<nrqr; ++i) {
2877     ierr = PetscFree(sbuf2[i]);CHKERRQ(ierr);
2878   }
2879   for (i=0; i<nrqs; ++i) {
2880     ierr = PetscFree(rbuf3[i]);CHKERRQ(ierr);
2881     ierr = PetscFree(rbuf4[i]);CHKERRQ(ierr);
2882   }
2883 
2884   ierr = PetscFree3(sbuf2,req_size,req_source);CHKERRQ(ierr);
2885   ierr = PetscFree(rbuf3);CHKERRQ(ierr);
2886   ierr = PetscFree(rbuf4);CHKERRQ(ierr);
2887   ierr = PetscFree(sbuf_aj[0]);CHKERRQ(ierr);
2888   ierr = PetscFree(sbuf_aj);CHKERRQ(ierr);
2889   ierr = PetscFree(sbuf_aa[0]);CHKERRQ(ierr);
2890   ierr = PetscFree(sbuf_aa);CHKERRQ(ierr);
2891 
2892 #if defined(PETSC_USE_CTABLE)
2893   for (i=0; i<ismax; i++) {ierr = PetscTableDestroy((PetscTable*)&rmap[i]);CHKERRQ(ierr);}
2894 #else
2895   if (ismax) {ierr = PetscFree(rmap[0]);CHKERRQ(ierr);}
2896 #endif
2897   ierr = PetscFree(rmap);CHKERRQ(ierr);
2898 
2899   for (i=0; i<ismax; i++) {
2900     if (!allcolumns[i]) {
2901 #if defined(PETSC_USE_CTABLE)
2902       ierr = PetscTableDestroy((PetscTable*)&cmap[i]);CHKERRQ(ierr);
2903 #else
2904       ierr = PetscFree(cmap[i]);CHKERRQ(ierr);
2905 #endif
2906     }
2907   }
2908   ierr = PetscFree(cmap);CHKERRQ(ierr);
2909   if (ismax) {ierr = PetscFree(lens[0]);CHKERRQ(ierr);}
2910   ierr = PetscFree(lens);CHKERRQ(ierr);
2911 
2912   for (i=0; i<ismax; i++) {
2913     ierr = MatAssemblyBegin(submats[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2914     ierr = MatAssemblyEnd(submats[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2915   }
2916 
2917   ierr = PetscFree(issorted);CHKERRQ(ierr);
2918   ierr = PetscFree(row2proc);CHKERRQ(ierr);
2919   ierr = PetscFree(smats);CHKERRQ(ierr);
2920   PetscFunctionReturn(0);
2921 }
2922 
2923 /*
2924  Permute A & B into C's *local* index space using rowemb,dcolemb for A and rowemb,ocolemb for B.
2925  Embeddings are supposed to be injections and the above implies that the range of rowemb is a subset
2926  of [0,m), dcolemb is in [0,n) and ocolemb is in [N-n).
2927  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A&B.
2928  After that B's columns are mapped into C's global column space, so that C is in the "disassembled"
2929  state, and needs to be "assembled" later by compressing B's column space.
2930 
2931  This function may be called in lieu of preallocation, so C should not be expected to be preallocated.
2932  Following this call, C->A & C->B have been created, even if empty.
2933  */
2934 PetscErrorCode MatSetSeqMats_MPIAIJ(Mat C,IS rowemb,IS dcolemb,IS ocolemb,MatStructure pattern,Mat A,Mat B)
2935 {
2936   /* If making this function public, change the error returned in this function away from _PLIB. */
2937   PetscErrorCode ierr;
2938   Mat_MPIAIJ     *aij;
2939   Mat_SeqAIJ     *Baij;
2940   PetscBool      seqaij,Bdisassembled;
2941   PetscInt       m,n,*nz,i,j,ngcol,col,rstart,rend,shift,count;
2942   PetscScalar    v;
2943   const PetscInt *rowindices,*colindices;
2944 
2945   PetscFunctionBegin;
2946   /* Check to make sure the component matrices (and embeddings) are compatible with C. */
2947   if (A) {
2948     ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
2949     if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diagonal matrix is of wrong type");
2950     if (rowemb) {
2951       ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
2952       if (m != A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Row IS of size %D is incompatible with diag matrix row size %D",m,A->rmap->n);
2953     } else {
2954       if (C->rmap->n != A->rmap->n) {
2955 	SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag seq matrix is row-incompatible with the MPIAIJ matrix");
2956       }
2957     }
2958     if (dcolemb) {
2959       ierr = ISGetLocalSize(dcolemb,&n);CHKERRQ(ierr);
2960       if (n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag col IS of size %D is incompatible with diag matrix col size %D",n,A->cmap->n);
2961     } else {
2962       if (C->cmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag seq matrix is col-incompatible with the MPIAIJ matrix");
2963     }
2964   }
2965   if (B) {
2966     ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
2967     if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diagonal matrix is of wrong type");
2968     if (rowemb) {
2969       ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
2970       if (m != B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Row IS of size %D is incompatible with off-diag matrix row size %D",m,A->rmap->n);
2971     } else {
2972       if (C->rmap->n != B->rmap->n) {
2973 	SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diag seq matrix is row-incompatible with the MPIAIJ matrix");
2974       }
2975     }
2976     if (ocolemb) {
2977       ierr = ISGetLocalSize(ocolemb,&n);CHKERRQ(ierr);
2978       if (n != B->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diag col IS of size %D is incompatible with off-diag matrix col size %D",n,B->cmap->n);
2979     } else {
2980       if (C->cmap->N - C->cmap->n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diag seq matrix is col-incompatible with the MPIAIJ matrix");
2981     }
2982   }
2983 
2984   aij    = (Mat_MPIAIJ*)(C->data);
2985   if (!aij->A) {
2986     /* Mimic parts of MatMPIAIJSetPreallocation() */
2987     ierr   = MatCreate(PETSC_COMM_SELF,&aij->A);CHKERRQ(ierr);
2988     ierr   = MatSetSizes(aij->A,C->rmap->n,C->cmap->n,C->rmap->n,C->cmap->n);CHKERRQ(ierr);
2989     ierr   = MatSetBlockSizesFromMats(aij->A,C,C);CHKERRQ(ierr);
2990     ierr   = MatSetType(aij->A,MATSEQAIJ);CHKERRQ(ierr);
2991     ierr   = PetscLogObjectParent((PetscObject)C,(PetscObject)aij->A);CHKERRQ(ierr);
2992   }
2993   if (A) {
2994     ierr   = MatSetSeqMat_SeqAIJ(aij->A,rowemb,dcolemb,pattern,A);CHKERRQ(ierr);
2995   } else {
2996     ierr = MatSetUp(aij->A);CHKERRQ(ierr);
2997   }
2998   if (B) { /* Destroy the old matrix or the column map, depending on the sparsity pattern. */
2999     /*
3000       If pattern == DIFFERENT_NONZERO_PATTERN, we reallocate B and
3001       need to "disassemble" B -- convert it to using C's global indices.
3002       To insert the values we take the safer, albeit more expensive, route of MatSetValues().
3003 
3004       If pattern == SUBSET_NONZERO_PATTERN, we do not "disassemble" B and do not reallocate;
3005       we MatZeroValues(B) first, so there may be a bunch of zeros that, perhaps, could be compacted out.
3006 
3007       TODO: Put B's values into aij->B's aij structure in place using the embedding ISs?
3008       At least avoid calling MatSetValues() and the implied searches?
3009     */
3010 
3011     if (B && pattern == DIFFERENT_NONZERO_PATTERN) {
3012 #if defined(PETSC_USE_CTABLE)
3013       ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
3014 #else
3015       ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
3016       /* A bit of a HACK: ideally we should deal with case aij->B all in one code block below. */
3017       if (aij->B) {
3018         ierr = PetscLogObjectMemory((PetscObject)C,-aij->B->cmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3019       }
3020 #endif
3021       ngcol = 0;
3022       if (aij->lvec) {
3023 	ierr = VecGetSize(aij->lvec,&ngcol);CHKERRQ(ierr);
3024       }
3025       if (aij->garray) {
3026 	ierr = PetscFree(aij->garray);CHKERRQ(ierr);
3027 	ierr = PetscLogObjectMemory((PetscObject)C,-ngcol*sizeof(PetscInt));CHKERRQ(ierr);
3028       }
3029       ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
3030       ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
3031     }
3032     if (aij->B && B && pattern == DIFFERENT_NONZERO_PATTERN) {
3033       ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
3034     }
3035     if (aij->B && B && pattern == SUBSET_NONZERO_PATTERN) {
3036       ierr = MatZeroEntries(aij->B);CHKERRQ(ierr);
3037     }
3038   }
3039   Bdisassembled = PETSC_FALSE;
3040   if (!aij->B) {
3041     ierr = MatCreate(PETSC_COMM_SELF,&aij->B);CHKERRQ(ierr);
3042     ierr = PetscLogObjectParent((PetscObject)C,(PetscObject)aij->B);CHKERRQ(ierr);
3043     ierr = MatSetSizes(aij->B,C->rmap->n,C->cmap->N,C->rmap->n,C->cmap->N);CHKERRQ(ierr);
3044     ierr = MatSetBlockSizesFromMats(aij->B,B,B);CHKERRQ(ierr);
3045     ierr = MatSetType(aij->B,MATSEQAIJ);CHKERRQ(ierr);
3046     Bdisassembled = PETSC_TRUE;
3047   }
3048   if (B) {
3049     Baij = (Mat_SeqAIJ*)(B->data);
3050     if (pattern == DIFFERENT_NONZERO_PATTERN) {
3051       ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
3052       for (i=0; i<B->rmap->n; i++) {
3053 	nz[i] = Baij->i[i+1] - Baij->i[i];
3054       }
3055       ierr = MatSeqAIJSetPreallocation(aij->B,0,nz);CHKERRQ(ierr);
3056       ierr = PetscFree(nz);CHKERRQ(ierr);
3057     }
3058 
3059     ierr  = PetscLayoutGetRange(C->rmap,&rstart,&rend);CHKERRQ(ierr);
3060     shift = rend-rstart;
3061     count = 0;
3062     rowindices = NULL;
3063     colindices = NULL;
3064     if (rowemb) {
3065       ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
3066     }
3067     if (ocolemb) {
3068       ierr = ISGetIndices(ocolemb,&colindices);CHKERRQ(ierr);
3069     }
3070     for (i=0; i<B->rmap->n; i++) {
3071       PetscInt row;
3072       row = i;
3073       if (rowindices) row = rowindices[i];
3074       for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
3075 	col  = Baij->j[count];
3076 	if (colindices) col = colindices[col];
3077 	if (Bdisassembled && col>=rstart) col += shift;
3078 	v    = Baij->a[count];
3079 	ierr = MatSetValues(aij->B,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
3080 	++count;
3081       }
3082     }
3083     /* No assembly for aij->B is necessary. */
3084     /* FIXME: set aij->B's nonzerostate correctly. */
3085   } else {
3086     ierr = MatSetUp(aij->B);CHKERRQ(ierr);
3087   }
3088   C->preallocated  = PETSC_TRUE;
3089   C->was_assembled = PETSC_FALSE;
3090   C->assembled     = PETSC_FALSE;
3091    /*
3092       C will need to be assembled so that aij->B can be compressed into local form in MatSetUpMultiply_MPIAIJ().
3093       Furthermore, its nonzerostate will need to be based on that of aij->A's and aij->B's.
3094    */
3095   PetscFunctionReturn(0);
3096 }
3097 
3098 /*
3099   B uses local indices with column indices ranging between 0 and N-n; they  must be interpreted using garray.
3100  */
3101 PetscErrorCode MatGetSeqMats_MPIAIJ(Mat C,Mat *A,Mat *B)
3102 {
3103   Mat_MPIAIJ *aij = (Mat_MPIAIJ*) (C->data);
3104 
3105   PetscFunctionBegin;
3106   PetscValidPointer(A,2);
3107   PetscValidPointer(B,3);
3108   /* FIXME: make sure C is assembled */
3109   *A = aij->A;
3110   *B = aij->B;
3111   /* Note that we don't incref *A and *B, so be careful! */
3112   PetscFunctionReturn(0);
3113 }
3114 
3115 /*
3116   Extract MPI submatrices encoded by pairs of IS that may live on subcomms of C.
3117   NOT SCALABLE due to the use of ISGetNonlocalIS() (see below).
3118 */
3119 PetscErrorCode MatGetSubMatricesMPI_MPIXAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[],
3120                                                  PetscErrorCode(*getsubmats_seq)(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat**),
3121 					         PetscErrorCode(*getlocalmats)(Mat,Mat*,Mat*),
3122 					         PetscErrorCode(*setseqmat)(Mat,IS,IS,MatStructure,Mat),
3123 					         PetscErrorCode(*setseqmats)(Mat,IS,IS,IS,MatStructure,Mat,Mat))
3124 {
3125   PetscErrorCode ierr;
3126   PetscMPIInt    isize,flag;
3127   PetscInt       i,ii,cismax,ispar;
3128   Mat            *A,*B;
3129   IS             *isrow_p,*iscol_p,*cisrow,*ciscol,*ciscol_p;
3130 
3131   PetscFunctionBegin;
3132   if (!ismax) PetscFunctionReturn(0);
3133 
3134   for (i = 0, cismax = 0; i < ismax; ++i) {
3135     PetscMPIInt isize;
3136     ierr = MPI_Comm_compare(((PetscObject)isrow[i])->comm,((PetscObject)iscol[i])->comm,&flag);CHKERRQ(ierr);
3137     if (flag != MPI_IDENT) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Row and column index sets must have the same communicator");
3138     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm, &isize);CHKERRQ(ierr);
3139     if (isize > 1) ++cismax;
3140   }
3141 
3142   /*
3143      If cismax is zero on all C's ranks, then and only then can we use purely sequential matrix extraction.
3144      ispar counts the number of parallel ISs across C's comm.
3145   */
3146   ierr = MPIU_Allreduce(&cismax,&ispar,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
3147   if (!ispar) { /* Sequential ISs only across C's comm, so can call the sequential matrix extraction subroutine. */
3148     ierr = (*getsubmats_seq)(C,ismax,isrow,iscol,scall,submat);CHKERRQ(ierr);
3149     PetscFunctionReturn(0);
3150   }
3151 
3152   /* if (ispar) */
3153   /*
3154     Construct the "complements" -- the off-processor indices -- of the iscol ISs for parallel ISs only.
3155     These are used to extract the off-diag portion of the resulting parallel matrix.
3156     The row IS for the off-diag portion is the same as for the diag portion,
3157     so we merely alias (without increfing) the row IS, while skipping those that are sequential.
3158   */
3159   ierr = PetscMalloc2(cismax,&cisrow,cismax,&ciscol);CHKERRQ(ierr);
3160   ierr = PetscMalloc1(cismax,&ciscol_p);CHKERRQ(ierr);
3161   for (i = 0, ii = 0; i < ismax; ++i) {
3162     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3163     if (isize > 1) {
3164       /*
3165 	 TODO: This is the part that's ***NOT SCALABLE***.
3166 	 To fix this we need to extract just the indices of C's nonzero columns
3167 	 that lie on the intersection of isrow[i] and ciscol[ii] -- the nonlocal
3168 	 part of iscol[i] -- without actually computing ciscol[ii]. This also has
3169 	 to be done without serializing on the IS list, so, most likely, it is best
3170 	 done by rewriting MatGetSubMatrices_MPIAIJ() directly.
3171       */
3172       ierr = ISGetNonlocalIS(iscol[i],&(ciscol[ii]));CHKERRQ(ierr);
3173       /* Now we have to
3174 	 (a) make sure ciscol[ii] is sorted, since, even if the off-proc indices
3175 	     were sorted on each rank, concatenated they might no longer be sorted;
3176 	 (b) Use ISSortPermutation() to construct ciscol_p, the mapping from the
3177 	     indices in the nondecreasing order to the original index positions.
3178 	 If ciscol[ii] is strictly increasing, the permutation IS is NULL.
3179       */
3180       ierr = ISSortPermutation(ciscol[ii],PETSC_FALSE,ciscol_p+ii);CHKERRQ(ierr);
3181       ierr = ISSort(ciscol[ii]);CHKERRQ(ierr);
3182       ++ii;
3183     }
3184   }
3185   ierr = PetscMalloc2(ismax,&isrow_p,ismax,&iscol_p);CHKERRQ(ierr);
3186   for (i = 0, ii = 0; i < ismax; ++i) {
3187     PetscInt       j,issize;
3188     const PetscInt *indices;
3189 
3190     /*
3191        Permute the indices into a nondecreasing order. Reject row and col indices with duplicates.
3192      */
3193     ierr = ISSortPermutation(isrow[i],PETSC_FALSE,isrow_p+i);CHKERRQ(ierr);
3194     ierr = ISSort(isrow[i]);CHKERRQ(ierr);
3195     ierr = ISGetLocalSize(isrow[i],&issize);CHKERRQ(ierr);
3196     ierr = ISGetIndices(isrow[i],&indices);CHKERRQ(ierr);
3197     for (j = 1; j < issize; ++j) {
3198       if (indices[j] == indices[j-1]) {
3199 	SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Repeated indices in row IS %D: indices at %D and %D are both %D",i,j-1,j,indices[j]);
3200       }
3201     }
3202     ierr = ISRestoreIndices(isrow[i],&indices);CHKERRQ(ierr);
3203 
3204 
3205     ierr = ISSortPermutation(iscol[i],PETSC_FALSE,iscol_p+i);CHKERRQ(ierr);
3206     ierr = ISSort(iscol[i]);CHKERRQ(ierr);
3207     ierr = ISGetLocalSize(iscol[i],&issize);CHKERRQ(ierr);
3208     ierr = ISGetIndices(iscol[i],&indices);CHKERRQ(ierr);
3209     for (j = 1; j < issize; ++j) {
3210       if (indices[j-1] == indices[j]) {
3211 	SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Repeated indices in col IS %D: indices at %D and %D are both %D",i,j-1,j,indices[j]);
3212       }
3213     }
3214     ierr = ISRestoreIndices(iscol[i],&indices);CHKERRQ(ierr);
3215     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3216     if (isize > 1) {
3217       cisrow[ii] = isrow[i];
3218       ++ii;
3219     }
3220   }
3221   /*
3222     Allocate the necessary arrays to hold the resulting parallel matrices as well as the intermediate
3223     array of sequential matrices underlying the resulting parallel matrices.
3224     Which arrays to allocate is based on the value of MatReuse scall and whether ISs are sorted and/or
3225     contain duplicates.
3226 
3227     There are as many diag matrices as there are original index sets. There are only as many parallel
3228     and off-diag matrices, as there are parallel (comm size > 1) index sets.
3229 
3230     ARRAYS that can hold Seq matrices get allocated in any event -- either here or by getsubmats_seq():
3231     - If the array of MPI matrices already exists and is being reused, we need to allocate the array
3232       and extract the underlying seq matrices into it to serve as placeholders, into which getsubmats_seq
3233       will deposite the extracted diag and off-diag parts. Thus, we allocate the A&B arrays and fill them
3234       with A[i] and B[ii] extracted from the corresponding MPI submat.
3235     - However, if the rows, A's column indices or B's column indices are not sorted, the extracted A[i] & B[ii]
3236       will have a different order from what getsubmats_seq expects.  To handle this case -- indicated
3237       by a nonzero isrow_p[i], iscol_p[i], or ciscol_p[ii] -- we duplicate A[i] --> AA[i], B[ii] --> BB[ii]
3238       (retrieve composed AA[i] or BB[ii]) and reuse them here. AA[i] and BB[ii] are then used to permute its
3239       values into A[i] and B[ii] sitting inside the corresponding submat.
3240     - If no reuse is taking place then getsubmats_seq will allocate the A&B arrays and create the corresponding
3241       A[i], B[ii], AA[i] or BB[ii] matrices.
3242   */
3243   /* Parallel matrix array is allocated here only if no reuse is taking place. If reused, it is passed in by the caller. */
3244   if (scall == MAT_INITIAL_MATRIX) {
3245     ierr = PetscMalloc1(ismax,submat);CHKERRQ(ierr);
3246   }
3247 
3248   /* Now obtain the sequential A and B submatrices separately. */
3249   /* scall=MAT_REUSE_MATRIX is not handled yet, because getsubmats_seq() requires reuse of A and B */
3250   ierr = (*getsubmats_seq)(C,ismax,isrow,iscol,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
3251   ierr = (*getsubmats_seq)(C,cismax,cisrow,ciscol,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
3252 
3253   /*
3254     If scall == MAT_REUSE_MATRIX AND the permutations are NULL, we are done, since the sequential
3255     matrices A & B have been extracted directly into the parallel matrices containing them, or
3256     simply into the sequential matrix identical with the corresponding A (if isize == 1).
3257     Note that in that case colmap doesn't need to be rebuilt, since the matrices are expected
3258     to have the same sparsity pattern.
3259     Otherwise, A and/or B have to be properly embedded into C's index spaces and the correct colmap
3260     must be constructed for C. This is done by setseqmat(s).
3261   */
3262   for (i = 0, ii = 0; i < ismax; ++i) {
3263     /*
3264        TODO: cache ciscol, permutation ISs and maybe cisrow? What about isrow & iscol?
3265        That way we can avoid sorting and computing permutations when reusing.
3266        To this end:
3267         - remove the old cache, if it exists, when extracting submatrices with MAT_INITIAL_MATRIX
3268 	- if caching arrays to hold the ISs, make and compose a container for them so that it can
3269 	  be destroyed upon destruction of C (use PetscContainerUserDestroy() to clear out the contents).
3270     */
3271     MatStructure pattern;
3272     pattern = DIFFERENT_NONZERO_PATTERN;
3273 
3274     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3275     /* Construct submat[i] from the Seq pieces A (and B, if necessary). */
3276     if (isize > 1) {
3277       if (scall == MAT_INITIAL_MATRIX) {
3278 	ierr = MatCreate(((PetscObject)isrow[i])->comm,(*submat)+i);CHKERRQ(ierr);
3279 	ierr = MatSetSizes((*submat)[i],A[i]->rmap->n,A[i]->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3280 	ierr = MatSetType((*submat)[i],MATMPIAIJ);CHKERRQ(ierr);
3281 	ierr = PetscLayoutSetUp((*submat)[i]->rmap);CHKERRQ(ierr);
3282 	ierr = PetscLayoutSetUp((*submat)[i]->cmap);CHKERRQ(ierr);
3283       }
3284       /*
3285 	For each parallel isrow[i], insert the extracted sequential matrices into the parallel matrix.
3286       */
3287       {
3288 	Mat AA,BB;
3289         AA = A[i];
3290         BB = B[ii];
3291 	if (AA || BB) {
3292 	  ierr = setseqmats((*submat)[i],isrow_p[i],iscol_p[i],ciscol_p[ii],pattern,AA,BB);CHKERRQ(ierr);
3293 	  ierr = MatAssemblyBegin((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3294 	  ierr = MatAssemblyEnd((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3295 	}
3296 
3297         ierr = MatDestroy(&AA);CHKERRQ(ierr);
3298         ierr = MatDestroy(&BB);CHKERRQ(ierr);
3299       }
3300       ierr = ISDestroy(ciscol+ii);CHKERRQ(ierr);
3301       ierr = ISDestroy(ciscol_p+ii);CHKERRQ(ierr);
3302       ++ii;
3303     } else { /* if (isize == 1) */
3304       if (scall == MAT_REUSE_MATRIX) {
3305         ierr = MatDestroy(&(*submat)[i]);CHKERRQ(ierr);
3306       }
3307       if (isrow_p[i] || iscol_p[i]) {
3308         ierr = MatDuplicate(A[i],MAT_DO_NOT_COPY_VALUES,(*submat)+i);CHKERRQ(ierr);
3309         ierr = setseqmat((*submat)[i],isrow_p[i],iscol_p[i],pattern,A[i]);CHKERRQ(ierr);
3310 	/* Otherwise A is extracted straight into (*submats)[i]. */
3311 	/* TODO: Compose A[i] on (*submat([i] for future use, if ((isrow_p[i] || iscol_p[i]) && MAT_INITIAL_MATRIX). */
3312 	ierr = MatDestroy(A+i);CHKERRQ(ierr);
3313       } else (*submat)[i] = A[i];
3314     }
3315     ierr = ISDestroy(&isrow_p[i]);CHKERRQ(ierr);
3316     ierr = ISDestroy(&iscol_p[i]);CHKERRQ(ierr);
3317   }
3318   ierr = PetscFree2(cisrow,ciscol);CHKERRQ(ierr);
3319   ierr = PetscFree2(isrow_p,iscol_p);CHKERRQ(ierr);
3320   ierr = PetscFree(ciscol_p);CHKERRQ(ierr);
3321   ierr = PetscFree(A);CHKERRQ(ierr);
3322   ierr = PetscFree(B);CHKERRQ(ierr);
3323   PetscFunctionReturn(0);
3324 }
3325 
3326 PetscErrorCode MatGetSubMatricesMPI_MPIAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
3327 {
3328   PetscErrorCode ierr;
3329 
3330   PetscFunctionBegin;
3331   ierr = MatGetSubMatricesMPI_MPIXAIJ(C,ismax,isrow,iscol,scall,submat,MatGetSubMatrices_MPIAIJ,MatGetSeqMats_MPIAIJ,MatSetSeqMat_SeqAIJ,MatSetSeqMats_MPIAIJ);CHKERRQ(ierr);
3332   PetscFunctionReturn(0);
3333 }
3334