xref: /petsc/src/mat/impls/aij/mpi/mpiov.c (revision 30a70a9a1e7e01515cfe7cbbe08231a7725b4889)
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,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 
1224 PetscErrorCode MatDestroy_Dummy_MatGetSubmatrices(Mat C)
1225 {
1226   PetscErrorCode ierr;
1227   Mat_SubMat     *submatj = (Mat_SubMat*)C->data;
1228   PetscInt       i;
1229 
1230   PetscFunctionBegin;
1231   printf("MatDestroy_Dummy_MatGetSubmatrices...\n");
1232 
1233   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
1234     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
1235 
1236     for (i=0; i<submatj->nrqr; ++i) {
1237       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
1238     }
1239     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
1240 
1241     if (submatj->rbuf1) {
1242       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
1243       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
1244     }
1245 
1246     for (i=0; i<submatj->nrqs; ++i) {
1247       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
1248     }
1249     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
1250     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
1251   }
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   ierr = submatj->destroy(C);CHKERRQ(ierr);
1269   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
1270 
1271   ierr = PetscFree(submatj);CHKERRQ(ierr);
1272   PetscFunctionReturn(0);
1273 }
1274 
1275 PetscErrorCode MatDestroy_MPIAIJ_MatGetSubmatrices(Mat C)
1276 {
1277   PetscErrorCode ierr;
1278   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
1279   Mat_SubMat     *submatj = c->submatis1;
1280   PetscInt       i;
1281 
1282   PetscFunctionBegin;
1283   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
1284     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
1285 
1286     for (i=0; i<submatj->nrqr; ++i) {
1287       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
1288     }
1289     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
1290 
1291     if (submatj->rbuf1) {
1292       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
1293       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
1294     }
1295 
1296     for (i=0; i<submatj->nrqs; ++i) {
1297       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
1298     }
1299     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
1300     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
1301   }
1302 
1303 #if defined(PETSC_USE_CTABLE)
1304   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
1305   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
1306   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
1307 #else
1308   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
1309 #endif
1310 
1311   if (!submatj->allcolumns) {
1312 #if defined(PETSC_USE_CTABLE)
1313     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
1314 #else
1315     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
1316 #endif
1317   }
1318   ierr = submatj->destroy(C);CHKERRQ(ierr);
1319   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
1320 
1321   ierr = PetscFree(submatj);CHKERRQ(ierr);
1322   PetscFunctionReturn(0);
1323 }
1324 
1325 PetscErrorCode MatGetSubMatrices_MPIAIJ_SingleIS_Local(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,PetscBool allcolumns,Mat *submats)
1326 {
1327   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
1328   Mat            submat,A = c->A,B = c->B;
1329   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data,*subc;
1330   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,nzA,nzB;
1331   PetscInt       cstart = C->cmap->rstart,cend = C->cmap->rend,rstart = C->rmap->rstart,*bmap = c->garray;
1332   const PetscInt *icol,*irow;
1333   PetscInt       nrow,ncol,start;
1334   PetscErrorCode ierr;
1335   PetscMPIInt    rank,size,tag1,tag2,tag3,tag4,*w1,*w2,nrqr;
1336   PetscInt       **sbuf1,**sbuf2,i,j,k,l,ct1,ct2,ct3,**rbuf1,row,proc;
1337   PetscInt       nrqs=0,msz,**ptr,*req_size,*ctr,*pa,*tmp,tcol,*iptr;
1338   PetscInt       **rbuf3,*req_source1,*req_source2,**sbuf_aj,**rbuf2,max1,nnz;
1339   PetscInt       *lens,rmax,ncols,*cols,Crow;
1340 #if defined(PETSC_USE_CTABLE)
1341   PetscTable     cmap,rmap;
1342   PetscInt       *cmap_loc,*rmap_loc;
1343 #else
1344   PetscInt       *cmap,*rmap;
1345 #endif
1346   PetscInt       ctr_j,*sbuf1_j,*sbuf_aj_i,*rbuf1_i,kmax,*sbuf1_i,*rbuf2_i,*rbuf3_i;
1347   PetscInt       *cworkB,lwrite,*subcols,*row2proc;
1348   PetscScalar    *vworkA,*vworkB,*a_a = a->a,*b_a = b->a,*subvals=NULL;
1349   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2,*r_waits3;
1350   MPI_Request    *r_waits4,*s_waits3 = NULL,*s_waits4;
1351   MPI_Status     *r_status1,*r_status2,*s_status1,*s_status3 = NULL,*s_status2;
1352   MPI_Status     *r_status3 = NULL,*r_status4,*s_status4;
1353   MPI_Comm       comm;
1354   PetscScalar    **rbuf4,**sbuf_aa,*vals,*sbuf_aa_i,*rbuf4_i;
1355   PetscMPIInt    *onodes1,*olengths1,idex,end;
1356   Mat_SubMat     *smatis1;
1357   PetscBool      isrowsorted;
1358 
1359   PetscFunctionBegin;
1360   if (ismax != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This routine only works when all processes have ismax=1");
1361 
1362   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1363   size = c->size;
1364   rank = c->rank;
1365 
1366   ierr = ISSorted(isrow[0],&isrowsorted);CHKERRQ(ierr);
1367   if (!isrowsorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow[0] must be sorted");
1368 
1369   ierr = ISGetIndices(isrow[0],&irow);CHKERRQ(ierr);
1370   ierr = ISGetLocalSize(isrow[0],&nrow);CHKERRQ(ierr);
1371   if (allcolumns) {
1372     icol = NULL;
1373     ncol = C->cmap->N;
1374   } else {
1375     ierr = ISGetIndices(iscol[0],&icol);CHKERRQ(ierr);
1376     ierr = ISGetLocalSize(iscol[0],&ncol);CHKERRQ(ierr);
1377   }
1378 
1379   if (scall == MAT_INITIAL_MATRIX) {
1380     PetscInt *sbuf2_i,*cworkA,lwrite,ctmp;
1381 
1382     /* Get some new tags to keep the communication clean */
1383     tag1 = ((PetscObject)C)->tag;
1384     ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
1385     ierr = PetscObjectGetNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
1386 
1387     /* evaluate communication - mesg to who, length of mesg, and buffer space
1388      required. Based on this, buffers are allocated, and data copied into them */
1389     ierr = PetscCalloc2(size,&w1,size,&w2);CHKERRQ(ierr);
1390     ierr = PetscMalloc1(nrow,&row2proc);CHKERRQ(ierr);
1391 
1392     /* w1[proc] = num of rows owned by proc -- to be requested */
1393     proc = 0;
1394     nrqs = 0; /* num of outgoing messages */
1395     for (j=0; j<nrow; j++) {
1396       row  = irow[j]; /* sorted! */
1397       while (row >= C->rmap->range[proc+1]) proc++;
1398       w1[proc]++;
1399       row2proc[j] = proc; /* map row index to proc */
1400 
1401       if (proc != rank && !w2[proc]) {
1402         w2[proc] = 1; nrqs++;
1403       }
1404     }
1405     w1[rank] = 0;  /* rows owned by self will not be requested */
1406 
1407     ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr); /*(proc -array)*/
1408     for (proc=0,j=0; proc<size; proc++) {
1409       if (w1[proc]) { pa[j++] = proc;}
1410     }
1411 
1412     /* Each message would have a header = 1 + 2*(num of IS) + data (here,num of IS = 1) */
1413     msz = 0;              /* total mesg length (for all procs) */
1414     for (i=0; i<nrqs; i++) {
1415       proc      = pa[i];
1416       w1[proc] += 3;
1417       msz      += w1[proc];
1418     }
1419     ierr = PetscInfo2(0,"Number of outgoing messages %D Total message length %D\n",nrqs,msz);CHKERRQ(ierr);
1420 
1421     /* Determine nrqr, the number of messages to expect, their lengths, from from-ids */
1422     /* if w2[proc]=1, a message of length w1[proc] will be sent to proc; */
1423     ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
1424 
1425     /* Input: nrqs: nsend; nrqr: nrecv; w1: msg length to be sent;
1426        Output: onodes1: recv node-ids; olengths1: corresponding recv message length */
1427     ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
1428 
1429     /* Now post the Irecvs corresponding to these messages */
1430     ierr = PetscPostIrecvInt(comm,tag1,nrqr,onodes1,olengths1,&rbuf1,&r_waits1);CHKERRQ(ierr);
1431 
1432     ierr = PetscFree(onodes1);CHKERRQ(ierr);
1433     ierr = PetscFree(olengths1);CHKERRQ(ierr);
1434 
1435     /* Allocate Memory for outgoing messages */
1436     ierr = PetscMalloc4(size,&sbuf1,size,&ptr,2*msz,&tmp,size,&ctr);CHKERRQ(ierr);
1437     ierr = PetscMemzero(sbuf1,size*sizeof(PetscInt*));CHKERRQ(ierr);
1438     ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
1439 
1440     /* subf1[pa[0]] = tmp, subf1[pa[i]] = subf1[pa[i-1]] + w1[pa[i-1]] */
1441     iptr = tmp;
1442     for (i=0; i<nrqs; i++) {
1443       proc        = pa[i];
1444       sbuf1[proc] = iptr;
1445       iptr       += w1[proc];
1446     }
1447 
1448     /* Form the outgoing messages */
1449     /* Initialize the header space */
1450     for (i=0; i<nrqs; i++) {
1451       proc      = pa[i];
1452       ierr      = PetscMemzero(sbuf1[proc],3*sizeof(PetscInt));CHKERRQ(ierr);
1453       ptr[proc] = sbuf1[proc] + 3;
1454     }
1455 
1456     /* Parse the isrow and copy data into outbuf */
1457     ierr = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
1458     for (j=0; j<nrow; j++) {  /* parse the indices of each IS */
1459       proc = row2proc[j];
1460       if (proc != rank) { /* copy to the outgoing buf*/
1461         *ptr[proc] = irow[j];
1462         ctr[proc]++; ptr[proc]++;
1463       }
1464     }
1465 
1466     /* Update the headers for the current IS */
1467     for (j=0; j<size; j++) { /* Can Optimise this loop too */
1468       if ((ctr_j = ctr[j])) {
1469         sbuf1_j        = sbuf1[j];
1470         k              = ++sbuf1_j[0];
1471         sbuf1_j[2*k]   = ctr_j;
1472         sbuf1_j[2*k-1] = 0;
1473       }
1474     }
1475 
1476     /* Now post the sends */
1477     ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
1478     for (i=0; i<nrqs; ++i) {
1479       proc = pa[i];
1480       ierr = MPI_Isend(sbuf1[proc],w1[proc],MPIU_INT,proc,tag1,comm,s_waits1+i);CHKERRQ(ierr);
1481     }
1482 
1483     /* Post Receives to capture the buffer size */
1484     ierr = PetscMalloc4(nrqs+1,&r_status2,nrqr+1,&s_waits2,nrqs+1,&r_waits2,nrqr+1,&s_status2);CHKERRQ(ierr);
1485     ierr = PetscMalloc3(nrqs+1,&req_source2,nrqs+1,&rbuf2,nrqs+1,&rbuf3);CHKERRQ(ierr);
1486 
1487     rbuf2[0] = tmp + msz;
1488     for (i=1; i<nrqs; ++i) rbuf2[i] = rbuf2[i-1] + w1[pa[i-1]];
1489 
1490     for (i=0; i<nrqs; ++i) {
1491       proc = pa[i];
1492       ierr = MPI_Irecv(rbuf2[i],w1[proc],MPIU_INT,proc,tag2,comm,r_waits2+i);CHKERRQ(ierr);
1493     }
1494 
1495     ierr = PetscFree2(w1,w2);CHKERRQ(ierr);
1496 
1497     /* Send to other procs the buf size they should allocate */
1498     /* Receive messages*/
1499     ierr = PetscMalloc1(nrqr+1,&r_status1);CHKERRQ(ierr);
1500     ierr = PetscMalloc3(nrqr,&sbuf2,nrqr,&req_size,nrqr,&req_source1);CHKERRQ(ierr);
1501 
1502     ierr = MPI_Waitall(nrqr,r_waits1,r_status1);CHKERRQ(ierr);
1503     for (i=0; i<nrqr; ++i) {
1504       req_size[i] = 0;
1505       rbuf1_i        = rbuf1[i];
1506       start          = 2*rbuf1_i[0] + 1;
1507       ierr           = MPI_Get_count(r_status1+i,MPIU_INT,&end);CHKERRQ(ierr);
1508       ierr           = PetscMalloc1(end+1,&sbuf2[i]);CHKERRQ(ierr);
1509       sbuf2_i        = sbuf2[i];
1510       for (j=start; j<end; j++) {
1511         k            = rbuf1_i[j] - rstart;
1512         ncols        = ai[k+1] - ai[k] + bi[k+1] - bi[k];
1513         sbuf2_i[j]   = ncols;
1514         req_size[i] += ncols;
1515       }
1516       req_source1[i] = r_status1[i].MPI_SOURCE;
1517 
1518       /* form the header */
1519       sbuf2_i[0] = req_size[i];
1520       for (j=1; j<start; j++) sbuf2_i[j] = rbuf1_i[j];
1521 
1522       ierr = MPI_Isend(sbuf2_i,end,MPIU_INT,req_source1[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
1523     }
1524 
1525     ierr = PetscFree(r_status1);CHKERRQ(ierr);
1526     ierr = PetscFree(r_waits1);CHKERRQ(ierr);
1527 
1528     /* rbuf2 is received, Post recv column indices a->j */
1529     ierr = MPI_Waitall(nrqs,r_waits2,r_status2);CHKERRQ(ierr);
1530 
1531     ierr = PetscMalloc4(nrqs+1,&r_waits3,nrqr+1,&s_waits3,nrqs+1,&r_status3,nrqr+1,&s_status3);CHKERRQ(ierr);
1532     for (i=0; i<nrqs; ++i) {
1533       ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf3[i]);CHKERRQ(ierr);
1534       req_source2[i] = r_status2[i].MPI_SOURCE;
1535       ierr = MPI_Irecv(rbuf3[i],rbuf2[i][0],MPIU_INT,req_source2[i],tag3,comm,r_waits3+i);CHKERRQ(ierr);
1536     }
1537 
1538     /* Wait on sends1 and sends2 */
1539     ierr = PetscMalloc1(nrqs+1,&s_status1);CHKERRQ(ierr);
1540     ierr = MPI_Waitall(nrqs,s_waits1,s_status1);CHKERRQ(ierr);
1541     ierr = PetscFree(s_waits1);CHKERRQ(ierr);
1542     ierr = PetscFree(s_status1);CHKERRQ(ierr);
1543 
1544     ierr = MPI_Waitall(nrqr,s_waits2,s_status2);CHKERRQ(ierr);
1545     ierr = PetscFree4(r_status2,s_waits2,r_waits2,s_status2);CHKERRQ(ierr);
1546 
1547     /* Now allocate sending buffers for a->j, and send them off */
1548     ierr = PetscMalloc1(nrqr+1,&sbuf_aj);CHKERRQ(ierr);
1549     for (i=0,j=0; i<nrqr; i++) j += req_size[i];
1550     ierr = PetscMalloc1(j+1,&sbuf_aj[0]);CHKERRQ(ierr);
1551     for (i=1; i<nrqr; i++) sbuf_aj[i] = sbuf_aj[i-1] + req_size[i-1];
1552 
1553     for (i=0; i<nrqr; i++) { /* for each requested message */
1554       rbuf1_i   = rbuf1[i];
1555       sbuf_aj_i = sbuf_aj[i];
1556       ct1       = 2*rbuf1_i[0] + 1;
1557       ct2       = 0;
1558       /* max1=rbuf1_i[0]; if (max1 != 1) SETERRQ1(PETSC_COMM_SELF,0,"max1 %d != 1",max1); */
1559 
1560       kmax = rbuf1[i][2];
1561       for (k=0; k<kmax; k++,ct1++) { /* for each row */
1562         row    = rbuf1_i[ct1] - rstart;
1563         nzA    = ai[row+1] - ai[row];
1564         nzB    = bi[row+1] - bi[row];
1565         ncols  = nzA + nzB;
1566         cworkA = aj + ai[row]; cworkB = bj + bi[row];
1567 
1568         /* load the column indices for this row into cols*/
1569         cols = sbuf_aj_i + ct2;
1570 
1571         lwrite = 0;
1572         for (l=0; l<nzB; l++) {
1573           if ((ctmp = bmap[cworkB[l]]) < cstart) cols[lwrite++] = ctmp;
1574         }
1575         for (l=0; l<nzA; l++) cols[lwrite++] = cstart + cworkA[l];
1576         for (l=0; l<nzB; l++) {
1577           if ((ctmp = bmap[cworkB[l]]) >= cend) cols[lwrite++] = ctmp;
1578         }
1579 
1580         ct2 += ncols;
1581       }
1582       ierr = MPI_Isend(sbuf_aj_i,req_size[i],MPIU_INT,req_source1[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
1583     }
1584 
1585     /* create column map (cmap): global col of C -> local col of submat */
1586 #if defined(PETSC_USE_CTABLE)
1587     if (!allcolumns) {
1588       ierr = PetscTableCreate(ncol+1,C->cmap->N+1,&cmap);CHKERRQ(ierr);
1589       ierr = PetscCalloc1(C->cmap->n,&cmap_loc);CHKERRQ(ierr);
1590       for (j=0; j<ncol; j++) { /* use array cmap_loc[] for local col indices */
1591         if (icol[j] >= cstart && icol[j] <cend) {
1592           cmap_loc[icol[j] - cstart] = j+1;
1593         } else { /* use PetscTable for non-local col indices */
1594           ierr = PetscTableAdd(cmap,icol[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
1595         }
1596       }
1597     } else {
1598       cmap     = NULL;
1599       cmap_loc = NULL;
1600     }
1601     ierr = PetscCalloc1(C->rmap->n,&rmap_loc);CHKERRQ(ierr);
1602 #else
1603     if (!allcolumns) {
1604       ierr   = PetscCalloc1(C->cmap->N,&cmap);CHKERRQ(ierr);
1605       for (j=0; j<ncol; j++) cmap[icol[j]] = j+1;
1606     } else {
1607       cmap = NULL;
1608     }
1609 #endif
1610 
1611     /* Create lens for MatSeqAIJSetPreallocation() */
1612     ierr = PetscCalloc1(nrow,&lens);CHKERRQ(ierr);
1613 
1614     /* Compute lens from local part of C */
1615     for (j=0; j<nrow; j++) {
1616       row  = irow[j];
1617       proc = row2proc[j];
1618       if (proc == rank) {
1619         /* diagonal part A = c->A */
1620         ncols = ai[row-rstart+1] - ai[row-rstart];
1621         cols  = aj + ai[row-rstart];
1622         if (!allcolumns) {
1623           for (k=0; k<ncols; k++) {
1624 #if defined(PETSC_USE_CTABLE)
1625             tcol = cmap_loc[cols[k]];
1626 #else
1627             tcol = cmap[cols[k]+cstart];
1628 #endif
1629             if (tcol) lens[j]++;
1630           }
1631         } else { /* allcolumns */
1632           lens[j] = ncols;
1633         }
1634 
1635         /* off-diagonal part B = c->B */
1636         ncols = bi[row-rstart+1] - bi[row-rstart];
1637         cols  = bj + bi[row-rstart];
1638         if (!allcolumns) {
1639           for (k=0; k<ncols; k++) {
1640 #if defined(PETSC_USE_CTABLE)
1641             ierr = PetscTableFind(cmap,bmap[cols[k]]+1,&tcol);CHKERRQ(ierr);
1642 #else
1643             tcol = cmap[bmap[cols[k]]];
1644 #endif
1645             if (tcol) lens[j]++;
1646           }
1647         } else { /* allcolumns */
1648           lens[j] += ncols;
1649         }
1650       }
1651     }
1652 
1653     /* Create row map (rmap): global row of C -> local row of submat */
1654 #if defined(PETSC_USE_CTABLE)
1655     ierr = PetscTableCreate(nrow+1,C->rmap->N+1,&rmap);CHKERRQ(ierr);
1656     for (j=0; j<nrow; j++) {
1657       row  = irow[j];
1658       proc = row2proc[j];
1659       if (proc == rank) { /* a local row */
1660         rmap_loc[row - rstart] = j;
1661       } else {
1662         ierr = PetscTableAdd(rmap,irow[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
1663       }
1664     }
1665 #else
1666     ierr = PetscCalloc1(C->rmap->N,&rmap);CHKERRQ(ierr);
1667     for (j=0; j<nrow; j++) {
1668       rmap[irow[j]] = j;
1669     }
1670 #endif
1671 
1672     /* Update lens from offproc data */
1673     /* recv a->j is done */
1674     ierr    = MPI_Waitall(nrqs,r_waits3,r_status3);CHKERRQ(ierr);
1675     for (i=0; i<nrqs; i++) {
1676       proc    = pa[i];
1677       sbuf1_i = sbuf1[proc];
1678       /* jmax    = sbuf1_i[0]; if (jmax != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"jmax !=1"); */
1679       ct1     = 2 + 1;
1680       ct2     = 0;
1681       rbuf2_i = rbuf2[i]; /* received length of C->j */
1682       rbuf3_i = rbuf3[i]; /* received C->j */
1683 
1684       /* is_no  = sbuf1_i[2*j-1]; if (is_no != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_no !=0"); */
1685       max1   = sbuf1_i[2];
1686       for (k=0; k<max1; k++,ct1++) {
1687 #if defined(PETSC_USE_CTABLE)
1688         ierr = PetscTableFind(rmap,sbuf1_i[ct1]+1,&row);CHKERRQ(ierr);
1689         row--;
1690         if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"row not found in table");
1691 #else
1692         row = rmap[sbuf1_i[ct1]]; /* the row index in submat */
1693 #endif
1694         /* Now, store row index of submat in sbuf1_i[ct1] */
1695         sbuf1_i[ct1] = row;
1696 
1697         nnz = rbuf2_i[ct1];
1698         if (!allcolumns) {
1699           for (l=0; l<nnz; l++,ct2++) {
1700 #if defined(PETSC_USE_CTABLE)
1701             if (rbuf3_i[ct2] >= cstart && rbuf3_i[ct2] <cend) {
1702               tcol = cmap_loc[rbuf3_i[ct2] - cstart];
1703             } else {
1704               ierr = PetscTableFind(cmap,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
1705             }
1706 #else
1707             tcol = cmap[rbuf3_i[ct2]]; /* column index in submat */
1708 #endif
1709             if (tcol) lens[row]++;
1710           }
1711         } else { /* allcolumns */
1712           lens[row] += nnz;
1713         }
1714       }
1715     }
1716     ierr = MPI_Waitall(nrqr,s_waits3,s_status3);CHKERRQ(ierr);
1717     ierr = PetscFree4(r_waits3,s_waits3,r_status3,s_status3);CHKERRQ(ierr);
1718 
1719     /* Create the submatrices */
1720     ierr = MatCreate(PETSC_COMM_SELF,&submat);CHKERRQ(ierr);
1721     ierr = MatSetSizes(submat,nrow,ncol,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1722 
1723     ierr = ISGetBlockSize(isrow[0],&i);CHKERRQ(ierr);
1724     ierr = ISGetBlockSize(iscol[0],&j);CHKERRQ(ierr);
1725     ierr = MatSetBlockSizes(submat,i,j);CHKERRQ(ierr);
1726     ierr = MatSetType(submat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1727     ierr = MatSeqAIJSetPreallocation(submat,0,lens);CHKERRQ(ierr);
1728 
1729     /* create struct Mat_SubMat and attached it to submat */
1730     ierr = PetscNew(&smatis1);CHKERRQ(ierr);
1731     subc = (Mat_SeqAIJ*)submat->data;
1732     subc->submatis1 = smatis1;
1733 
1734     smatis1->id          = 0;
1735     smatis1->nrqs        = nrqs;
1736     smatis1->nrqr        = nrqr;
1737     smatis1->rbuf1       = rbuf1;
1738     smatis1->rbuf2       = rbuf2;
1739     smatis1->rbuf3       = rbuf3;
1740     smatis1->sbuf2       = sbuf2;
1741     smatis1->req_source2 = req_source2;
1742 
1743     smatis1->sbuf1       = sbuf1;
1744     smatis1->ptr         = ptr;
1745     smatis1->tmp         = tmp;
1746     smatis1->ctr         = ctr;
1747 
1748     smatis1->pa           = pa;
1749     smatis1->req_size     = req_size;
1750     smatis1->req_source1  = req_source1;
1751 
1752     smatis1->allcolumns  = allcolumns;
1753     smatis1->singleis    = PETSC_TRUE;
1754     smatis1->row2proc    = row2proc;
1755     smatis1->rmap        = rmap;
1756     smatis1->cmap        = cmap;
1757 #if defined(PETSC_USE_CTABLE)
1758     smatis1->rmap_loc    = rmap_loc;
1759     smatis1->cmap_loc    = cmap_loc;
1760 #endif
1761 
1762     smatis1->destroy     = submat->ops->destroy;
1763     submat->ops->destroy = MatDestroy_MPIAIJ_MatGetSubmatrices;
1764     submat->factortype   = C->factortype;
1765 
1766     /* compute rmax */
1767     rmax = 0;
1768     for (i=0; i<nrow; i++) rmax = PetscMax(rmax,lens[i]);
1769 
1770   } else { /* scall == MAT_REUSE_MATRIX */
1771     submat = submats[0];
1772     if (submat->rmap->n != nrow || submat->cmap->n != ncol) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
1773 
1774     subc    = (Mat_SeqAIJ*)submat->data;
1775     rmax    = subc->rmax;
1776     smatis1 = subc->submatis1;
1777     nrqs        = smatis1->nrqs;
1778     nrqr        = smatis1->nrqr;
1779     rbuf1       = smatis1->rbuf1;
1780     rbuf2       = smatis1->rbuf2;
1781     rbuf3       = smatis1->rbuf3;
1782     req_source2 = smatis1->req_source2;
1783 
1784     sbuf1     = smatis1->sbuf1;
1785     sbuf2     = smatis1->sbuf2;
1786     ptr       = smatis1->ptr;
1787     tmp       = smatis1->tmp;
1788     ctr       = smatis1->ctr;
1789 
1790     pa         = smatis1->pa;
1791     req_size   = smatis1->req_size;
1792     req_source1 = smatis1->req_source1;
1793 
1794     allcolumns = smatis1->allcolumns;
1795     row2proc   = smatis1->row2proc;
1796     rmap       = smatis1->rmap;
1797     cmap       = smatis1->cmap;
1798 #if defined(PETSC_USE_CTABLE)
1799     rmap_loc   = smatis1->rmap_loc;
1800     cmap_loc   = smatis1->cmap_loc;
1801 #endif
1802   }
1803 
1804   /* Post recv matrix values */
1805   ierr = PetscMalloc3(nrqs+1,&rbuf4, rmax,&subcols, rmax,&subvals);CHKERRQ(ierr);
1806   ierr = PetscMalloc4(nrqs+1,&r_waits4,nrqr+1,&s_waits4,nrqs+1,&r_status4,nrqr+1,&s_status4);CHKERRQ(ierr);
1807   ierr = PetscObjectGetNewTag((PetscObject)C,&tag4);CHKERRQ(ierr);
1808   for (i=0; i<nrqs; ++i) {
1809     ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf4[i]);CHKERRQ(ierr);
1810     ierr = MPI_Irecv(rbuf4[i],rbuf2[i][0],MPIU_SCALAR,req_source2[i],tag4,comm,r_waits4+i);CHKERRQ(ierr);
1811   }
1812 
1813   /* Allocate sending buffers for a->a, and send them off */
1814   ierr = PetscMalloc1(nrqr+1,&sbuf_aa);CHKERRQ(ierr);
1815   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
1816   ierr = PetscMalloc1(j+1,&sbuf_aa[0]);CHKERRQ(ierr);
1817   for (i=1; i<nrqr; i++) sbuf_aa[i] = sbuf_aa[i-1] + req_size[i-1];
1818 
1819   for (i=0; i<nrqr; i++) {
1820     rbuf1_i   = rbuf1[i];
1821     sbuf_aa_i = sbuf_aa[i];
1822     ct1       = 2*rbuf1_i[0]+1;
1823     ct2       = 0;
1824     /* max1=rbuf1_i[0]; if (max1 != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"max1 !=1"); */
1825 
1826     kmax = rbuf1_i[2];
1827     for (k=0; k<kmax; k++,ct1++) {
1828       row = rbuf1_i[ct1] - rstart;
1829       nzA = ai[row+1] - ai[row];
1830       nzB = bi[row+1] - bi[row];
1831       ncols  = nzA + nzB;
1832       cworkB = bj + bi[row];
1833       vworkA = a_a + ai[row];
1834       vworkB = b_a + bi[row];
1835 
1836       /* load the column values for this row into vals*/
1837       vals = sbuf_aa_i + ct2;
1838 
1839       lwrite = 0;
1840       for (l=0; l<nzB; l++) {
1841         if ((bmap[cworkB[l]]) < cstart) vals[lwrite++] = vworkB[l];
1842       }
1843       for (l=0; l<nzA; l++) vals[lwrite++] = vworkA[l];
1844       for (l=0; l<nzB; l++) {
1845         if ((bmap[cworkB[l]]) >= cend) vals[lwrite++] = vworkB[l];
1846       }
1847 
1848       ct2 += ncols;
1849     }
1850     ierr = MPI_Isend(sbuf_aa_i,req_size[i],MPIU_SCALAR,req_source1[i],tag4,comm,s_waits4+i);CHKERRQ(ierr);
1851   }
1852 
1853   /* Assemble submat */
1854   /* First assemble the local rows */
1855   for (j=0; j<nrow; j++) {
1856     row  = irow[j];
1857     proc = row2proc[j];
1858     if (proc == rank) {
1859       Crow = row - rstart;  /* local row index of C */
1860 #if defined(PETSC_USE_CTABLE)
1861       row = rmap_loc[Crow]; /* row index of submat */
1862 #else
1863       row = rmap[row];
1864 #endif
1865 
1866       if (allcolumns) {
1867         /* diagonal part A = c->A */
1868         ncols = ai[Crow+1] - ai[Crow];
1869         cols  = aj + ai[Crow];
1870         vals  = a->a + ai[Crow];
1871         i     = 0;
1872         for (k=0; k<ncols; k++) {
1873           subcols[i]   = cols[k] + cstart;
1874           subvals[i++] = vals[k];
1875         }
1876 
1877         /* off-diagonal part B = c->B */
1878         ncols = bi[Crow+1] - bi[Crow];
1879         cols  = bj + bi[Crow];
1880         vals  = b->a + bi[Crow];
1881         for (k=0; k<ncols; k++) {
1882           subcols[i]   = bmap[cols[k]];
1883           subvals[i++] = vals[k];
1884         }
1885 
1886         ierr = MatSetValues_SeqAIJ(submat,1,&row,i,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1887 
1888       } else { /* !allcolumns */
1889 #if defined(PETSC_USE_CTABLE)
1890         /* diagonal part A = c->A */
1891         ncols = ai[Crow+1] - ai[Crow];
1892         cols  = aj + ai[Crow];
1893         vals  = a->a + ai[Crow];
1894         i     = 0;
1895         for (k=0; k<ncols; k++) {
1896           tcol = cmap_loc[cols[k]];
1897           if (tcol) {
1898             subcols[i]   = --tcol;
1899             subvals[i++] = vals[k];
1900           }
1901         }
1902 
1903         /* off-diagonal part B = c->B */
1904         ncols = bi[Crow+1] - bi[Crow];
1905         cols  = bj + bi[Crow];
1906         vals  = b->a + bi[Crow];
1907         for (k=0; k<ncols; k++) {
1908           ierr = PetscTableFind(cmap,bmap[cols[k]]+1,&tcol);CHKERRQ(ierr);
1909           if (tcol) {
1910             subcols[i]   = --tcol;
1911             subvals[i++] = vals[k];
1912           }
1913         }
1914 #else
1915         /* diagonal part A = c->A */
1916         ncols = ai[Crow+1] - ai[Crow];
1917         cols  = aj + ai[Crow];
1918         vals  = a->a + ai[Crow];
1919         i     = 0;
1920         for (k=0; k<ncols; k++) {
1921           tcol = cmap[cols[k]+cstart];
1922           if (tcol) {
1923             subcols[i]   = --tcol;
1924             subvals[i++] = vals[k];
1925           }
1926         }
1927 
1928         /* off-diagonal part B = c->B */
1929         ncols = bi[Crow+1] - bi[Crow];
1930         cols  = bj + bi[Crow];
1931         vals  = b->a + bi[Crow];
1932         for (k=0; k<ncols; k++) {
1933           tcol = cmap[bmap[cols[k]]];
1934           if (tcol) {
1935             subcols[i]   = --tcol;
1936             subvals[i++] = vals[k];
1937           }
1938         }
1939 #endif
1940         ierr = MatSetValues_SeqAIJ(submat,1,&row,i,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1941       }
1942     }
1943   }
1944 
1945   /* Now assemble the off-proc rows */
1946   for (i=0; i<nrqs; i++) { /* for each requested message */
1947     /* recv values from other processes */
1948     ierr    = MPI_Waitany(nrqs,r_waits4,&idex,r_status4+i);CHKERRQ(ierr);
1949     proc    = pa[idex];
1950     sbuf1_i = sbuf1[proc];
1951     /* jmax    = sbuf1_i[0]; if (jmax != 1)SETERRQ1(PETSC_COMM_SELF,0,"jmax %d != 1",jmax); */
1952     ct1     = 2 + 1;
1953     ct2     = 0; /* count of received C->j */
1954     ct3     = 0; /* count of received C->j that will be inserted into submat */
1955     rbuf2_i = rbuf2[idex]; /* int** received length of C->j from other processes */
1956     rbuf3_i = rbuf3[idex]; /* int** received C->j from other processes */
1957     rbuf4_i = rbuf4[idex]; /* scalar** received C->a from other processes */
1958 
1959     /* is_no = sbuf1_i[2*j-1]; if (is_no != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_no !=0"); */
1960     max1 = sbuf1_i[2];             /* num of rows */
1961     for (k=0; k<max1; k++,ct1++) { /* for each recved row */
1962       row = sbuf1_i[ct1]; /* row index of submat */
1963       if (!allcolumns) {
1964         idex = 0;
1965         if (scall == MAT_INITIAL_MATRIX) {
1966           nnz  = rbuf2_i[ct1]; /* num of C entries in this row */
1967           for (l=0; l<nnz; l++,ct2++) { /* for each recved column */
1968 #if defined(PETSC_USE_CTABLE)
1969             if (rbuf3_i[ct2] >= cstart && rbuf3_i[ct2] <cend) {
1970               tcol = cmap_loc[rbuf3_i[ct2] - cstart];
1971             } else {
1972               ierr = PetscTableFind(cmap,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
1973             }
1974 #else
1975             tcol = cmap[rbuf3_i[ct2]];
1976 #endif
1977             if (tcol) {
1978               subcols[idex]   = --tcol;
1979               subvals[idex++] = rbuf4_i[ct2];
1980 
1981               /* We receive an entire column of C, but a subset of it needs to be inserted into submat.
1982                For reuse, we replace received C->j with index that should be inserted to submat */
1983               rbuf3_i[ct3++] = ct2;
1984             }
1985           }
1986           ierr = MatSetValues_SeqAIJ(submat,1,&row,idex,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1987 
1988         } else { /* scall == MAT_REUSE_MATRIX */
1989           submat = submats[0];
1990           subc   = (Mat_SeqAIJ*)submat->data;
1991 
1992           nnz = subc->i[row+1] - subc->i[row]; /* num of submat entries in this row */
1993           for (l=0; l<nnz; l++) {
1994             ct2 = rbuf3_i[ct3++]; /* index of rbuf4_i[] which needs to be inserted into submat */
1995             subvals[idex++] = rbuf4_i[ct2];
1996           }
1997 
1998           bj = subc->j + subc->i[row];
1999           ierr = MatSetValues_SeqAIJ(submat,1,&row,nnz,bj,subvals,INSERT_VALUES);CHKERRQ(ierr);
2000         }
2001       } else { /* allcolumns */
2002         nnz  = rbuf2_i[ct1]; /* num of C entries in this row */
2003         ierr = MatSetValues_SeqAIJ(submat,1,&row,nnz,rbuf3_i+ct2,rbuf4_i+ct2,INSERT_VALUES);CHKERRQ(ierr);
2004         ct2 += nnz;
2005       }
2006     }
2007   }
2008 
2009   /* sending a->a are done */
2010   ierr = MPI_Waitall(nrqr,s_waits4,s_status4);CHKERRQ(ierr);
2011   ierr = PetscFree4(r_waits4,s_waits4,r_status4,s_status4);CHKERRQ(ierr);
2012 
2013   ierr = MatAssemblyBegin(submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2014   ierr = MatAssemblyEnd(submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2015   submats[0] = submat;
2016 
2017   /* Restore the indices */
2018   ierr = ISRestoreIndices(isrow[0],&irow);CHKERRQ(ierr);
2019   if (!allcolumns) {
2020     ierr = ISRestoreIndices(iscol[0],&icol);CHKERRQ(ierr);
2021   }
2022 
2023   /* Destroy allocated memory */
2024   for (i=0; i<nrqs; ++i) {
2025     ierr = PetscFree3(rbuf4[i],subcols,subvals);CHKERRQ(ierr);
2026   }
2027   ierr = PetscFree3(rbuf4,subcols,subvals);CHKERRQ(ierr);
2028   ierr = PetscFree(sbuf_aa[0]);CHKERRQ(ierr);
2029   ierr = PetscFree(sbuf_aa);CHKERRQ(ierr);
2030 
2031   if (scall == MAT_INITIAL_MATRIX) {
2032     ierr = PetscFree(lens);CHKERRQ(ierr);
2033     ierr = PetscFree(sbuf_aj[0]);CHKERRQ(ierr);
2034     ierr = PetscFree(sbuf_aj);CHKERRQ(ierr);
2035   }
2036   PetscFunctionReturn(0);
2037 }
2038 
2039 PetscErrorCode MatGetSubMatrices_MPIAIJ_SingleIS(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
2040 {
2041   PetscErrorCode ierr;
2042   PetscInt       ncol;
2043   PetscBool      colflag,allcolumns=PETSC_FALSE;
2044 
2045   PetscFunctionBegin;
2046   /* Allocate memory to hold all the submatrices */
2047   if (scall == MAT_INITIAL_MATRIX) {
2048     ierr = PetscMalloc1(1,submat);CHKERRQ(ierr);
2049   }
2050 
2051   /* Check for special case: each processor gets entire matrix columns */
2052   ierr = ISIdentity(iscol[0],&colflag);CHKERRQ(ierr);
2053   ierr = ISGetLocalSize(iscol[0],&ncol);CHKERRQ(ierr);
2054   if (colflag && ncol == C->cmap->N) allcolumns = PETSC_TRUE;
2055 
2056   ierr = MatGetSubMatrices_MPIAIJ_SingleIS_Local(C,ismax,isrow,iscol,scall,allcolumns,*submat);CHKERRQ(ierr);
2057   PetscFunctionReturn(0);
2058 }
2059 
2060 PetscErrorCode MatGetSubMatrices_MPIAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
2061 {
2062   PetscErrorCode ierr;
2063   PetscInt       nmax,nstages,i,pos,max_no,nrow,ncol,in[2],out[2];
2064   PetscBool      rowflag,colflag,wantallmatrix=PETSC_FALSE;
2065   Mat_SeqAIJ     *subc;
2066   Mat_SubMat     *smat;
2067 
2068   PetscFunctionBegin;
2069   /* Check for special case: each processor has a single IS */
2070   if (C->submat_singleis) { /* flag is set in PCSetUp_ASM() to skip MPIU_Allreduce() */
2071     ierr = MatGetSubMatrices_MPIAIJ_SingleIS(C,ismax,isrow,iscol,scall,submat);CHKERRQ(ierr);
2072     C->submat_singleis = PETSC_FALSE; /* resume its default value in case C will be used for non-singlis */
2073     PetscFunctionReturn(0);
2074   }
2075 
2076   /* Collect global wantallmatrix and nstages */
2077   if (!C->cmap->N) nmax=20*1000000/sizeof(PetscInt);
2078   else nmax = 20*1000000 / (C->cmap->N * sizeof(PetscInt));
2079   if (!nmax) nmax = 1;
2080 
2081   if (scall == MAT_INITIAL_MATRIX) {
2082     /* Collect global wantallmatrix and nstages */
2083     if (ismax == 1 && C->rmap->N == C->cmap->N) {
2084       ierr = ISIdentity(*isrow,&rowflag);CHKERRQ(ierr);
2085       ierr = ISIdentity(*iscol,&colflag);CHKERRQ(ierr);
2086       ierr = ISGetLocalSize(*isrow,&nrow);CHKERRQ(ierr);
2087       ierr = ISGetLocalSize(*iscol,&ncol);CHKERRQ(ierr);
2088       if (rowflag && colflag && nrow == C->rmap->N && ncol == C->cmap->N) {
2089         wantallmatrix = PETSC_TRUE;
2090 
2091         ierr = PetscOptionsGetBool(((PetscObject)C)->options,((PetscObject)C)->prefix,"-use_fast_submatrix",&wantallmatrix,NULL);CHKERRQ(ierr);
2092       }
2093     }
2094 
2095     /* Determine the number of stages through which submatrices are done
2096        Each stage will extract nmax submatrices.
2097        nmax is determined by the matrix column dimension.
2098        If the original matrix has 20M columns, only one submatrix per stage is allowed, etc.
2099     */
2100     nstages = ismax/nmax + ((ismax % nmax) ? 1 : 0); /* local nstages */
2101 
2102     in[0] = -1*(PetscInt)wantallmatrix;
2103     in[1] = nstages;
2104     ierr = MPIU_Allreduce(in,out,2,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
2105     wantallmatrix = (PetscBool)(-out[0]);
2106     nstages       = out[1]; /* Make sure every processor loops through the global nstages */
2107 
2108   } else { /* MAT_REUSE_MATRIX */
2109     if (ismax) {
2110       subc = (Mat_SeqAIJ*)(*submat)[0]->data;
2111       smat = subc->submatis1;
2112     } else { /* (*submat)[0] is a dummy matrix */
2113       smat = (Mat_SubMat*)(*submat)[0]->data;
2114     }
2115     if (!smat) {
2116       /* smat is not generated by MatGetSubMatrix_MPIAIJ_All(...,MAT_INITIAL_MATRIX,...) */
2117       wantallmatrix = PETSC_TRUE;
2118     } else if (smat->singleis) {
2119       ierr = MatGetSubMatrices_MPIAIJ_SingleIS(C,ismax,isrow,iscol,scall,submat);CHKERRQ(ierr);
2120       PetscFunctionReturn(0);
2121     } else {
2122       nstages = smat->nstages;
2123     }
2124   }
2125 
2126   if (wantallmatrix) {
2127     ierr = MatGetSubMatrix_MPIAIJ_All(C,MAT_GET_VALUES,scall,submat);CHKERRQ(ierr);
2128     PetscFunctionReturn(0);
2129   }
2130 
2131   /* Allocate memory to hold all the submatrices and dummy submatrices */
2132   if (scall == MAT_INITIAL_MATRIX) {
2133     ierr = PetscCalloc1(ismax+nstages,submat);CHKERRQ(ierr);
2134   }
2135 
2136 #if 0
2137   PetscMPIInt rank;
2138   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)C),&rank);CHKERRQ(ierr);
2139   printf("[%d] reuse %d, ismax %d, CN %d, nstages %d, nmax %d\n",rank,scall,ismax,C->cmap->N,nstages,nmax);
2140 #endif
2141   for (i=0,pos=0; i<nstages; i++) {
2142     if (pos+nmax <= ismax) max_no = nmax;
2143     else if (pos == ismax) max_no = 0;
2144     else                   max_no = ismax-pos;
2145     /* if (!max_no) printf("[%d] max_no=0, %d-stage\n",rank,i); */
2146     ierr = MatGetSubMatrices_MPIAIJ_Local(C,max_no,isrow+pos,iscol+pos,scall,*submat+pos);CHKERRQ(ierr);
2147     if (!max_no && scall == MAT_INITIAL_MATRIX) { /* submat[pos] is a dummy matrix */
2148       smat = (Mat_SubMat*)(*submat)[pos]->data;
2149       smat->nstages = nstages;
2150     }
2151     pos += max_no;
2152   }
2153 
2154   if (ismax && scall == MAT_INITIAL_MATRIX) {
2155     /* save nstages for reuse */
2156     subc = (Mat_SeqAIJ*)(*submat)[0]->data;
2157     smat = subc->submatis1;
2158     smat->nstages = nstages;
2159   }
2160   PetscFunctionReturn(0);
2161 }
2162 
2163 /* -------------------------------------------------------------------------*/
2164 PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submats)
2165 {
2166   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
2167   Mat            A  = c->A;
2168   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)c->B->data,*subc;
2169   const PetscInt **icol,**irow;
2170   PetscInt       *nrow,*ncol,start;
2171   PetscErrorCode ierr;
2172   PetscMPIInt    rank,size,tag0,tag2,tag3,tag4,*w1,*w2,*w3,*w4,nrqr;
2173   PetscInt       **sbuf1,**sbuf2,i,j,k,l,ct1,ct2,**rbuf1,row,proc=-1;
2174   PetscInt       nrqs=0,msz,**ptr=NULL,*req_size=NULL,*ctr=NULL,*pa,*tmp=NULL,tcol;
2175   PetscInt       **rbuf3=NULL,*req_source1=NULL,*req_source2,**sbuf_aj,**rbuf2=NULL,max1,max2;
2176   PetscInt       **lens,is_no,ncols,*cols,mat_i,*mat_j,tmp2,jmax;
2177 #if defined(PETSC_USE_CTABLE)
2178   PetscTable     *cmap,cmap_i=NULL,*rmap,rmap_i;
2179 #else
2180   PetscInt       **cmap,*cmap_i=NULL,**rmap,*rmap_i;
2181 #endif
2182   const PetscInt *irow_i;
2183   PetscInt       ctr_j,*sbuf1_j,*sbuf_aj_i,*rbuf1_i,kmax,*lens_i;
2184   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2,*r_waits3;
2185   MPI_Request    *r_waits4,*s_waits3,*s_waits4;
2186   MPI_Status     *r_status1,*r_status2,*s_status1,*s_status3,*s_status2;
2187   MPI_Status     *r_status3,*r_status4,*s_status4;
2188   MPI_Comm       comm;
2189   PetscScalar    **rbuf4,*rbuf4_i,**sbuf_aa,*vals,*mat_a,*imat_a,*sbuf_aa_i;
2190   PetscMPIInt    *onodes1,*olengths1,end;
2191   PetscInt       **row2proc,*row2proc_i,ilen_row,*imat_ilen,*imat_j,*imat_i,old_row;
2192   Mat_SubMat     *smat_i;
2193   PetscBool      *issorted,*allcolumns,colflag,iscsorted=PETSC_TRUE;
2194   PetscInt       *sbuf1_i,*rbuf2_i,*rbuf3_i,ilen;
2195 
2196   PetscFunctionBegin;
2197   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2198   size = c->size;
2199   rank = c->rank;
2200 
2201   ierr = PetscMalloc4(ismax,&row2proc,ismax,&cmap,ismax,&rmap,ismax+1,&allcolumns);CHKERRQ(ierr);
2202   ierr = PetscMalloc5(ismax,&irow,ismax,&icol,ismax,&nrow,ismax,&ncol,ismax,&issorted);CHKERRQ(ierr);
2203 
2204   for (i=0; i<ismax; i++) {
2205     ierr = ISSorted(iscol[i],&issorted[i]);CHKERRQ(ierr);
2206     if (!issorted[i]) iscsorted = issorted[i];
2207 
2208     ierr = ISSorted(isrow[i],&issorted[i]);CHKERRQ(ierr);
2209 
2210     ierr = ISGetIndices(isrow[i],&irow[i]);CHKERRQ(ierr);
2211     ierr = ISGetLocalSize(isrow[i],&nrow[i]);CHKERRQ(ierr);
2212 
2213     /* Check for special case: allcolumn */
2214     ierr = ISIdentity(iscol[i],&colflag);CHKERRQ(ierr);
2215     ierr = ISGetLocalSize(iscol[i],&ncol[i]);CHKERRQ(ierr);
2216     if (colflag && ncol[i] == C->cmap->N) {
2217       allcolumns[i] = PETSC_TRUE;
2218       icol[i] = NULL;
2219     } else {
2220       allcolumns[i] = PETSC_FALSE;
2221       ierr = ISGetIndices(iscol[i],&icol[i]);CHKERRQ(ierr);
2222     }
2223   }
2224 
2225   if (scall == MAT_REUSE_MATRIX) {
2226     /* Assumes new rows are same length as the old rows */
2227     for (i=0; i<ismax; i++) {
2228       if (!submats[i]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"submats[%D] is null, cannot reuse",i);
2229       subc = (Mat_SeqAIJ*)submats[i]->data;
2230       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");
2231 
2232       /* Initial matrix as if empty */
2233       ierr = PetscMemzero(subc->ilen,submats[i]->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2234 
2235       smat_i   = subc->submatis1;
2236 
2237       nrqs        = smat_i->nrqs;
2238       nrqr        = smat_i->nrqr;
2239       rbuf1       = smat_i->rbuf1;
2240       rbuf2       = smat_i->rbuf2;
2241       rbuf3       = smat_i->rbuf3;
2242       req_source2 = smat_i->req_source2;
2243 
2244       sbuf1     = smat_i->sbuf1;
2245       sbuf2     = smat_i->sbuf2;
2246       ptr       = smat_i->ptr;
2247       tmp       = smat_i->tmp;
2248       ctr       = smat_i->ctr;
2249 
2250       pa          = smat_i->pa;
2251       req_size    = smat_i->req_size;
2252       req_source1 = smat_i->req_source1;
2253 
2254       allcolumns[i] = smat_i->allcolumns;
2255       row2proc[i]   = smat_i->row2proc;
2256       rmap[i]       = smat_i->rmap;
2257       cmap[i]       = smat_i->cmap;
2258     }
2259 
2260     if (!ismax){ /* Get dummy submatrices and retrieve struct submatis1 */
2261       if (!submats[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"submats are null, cannot reuse");
2262       smat_i = (Mat_SubMat*)submats[0]->data;
2263 
2264       nrqs        = smat_i->nrqs;
2265       nrqr        = smat_i->nrqr;
2266       rbuf1       = smat_i->rbuf1;
2267       rbuf2       = smat_i->rbuf2;
2268       rbuf3       = smat_i->rbuf3;
2269       req_source2 = smat_i->req_source2;
2270 
2271       sbuf1       = smat_i->sbuf1;
2272       sbuf2       = smat_i->sbuf2;
2273       ptr         = smat_i->ptr;
2274       tmp         = smat_i->tmp;
2275       ctr         = smat_i->ctr;
2276 
2277       pa          = smat_i->pa;
2278       req_size    = smat_i->req_size;
2279       req_source1 = smat_i->req_source1;
2280 
2281       allcolumns[0] = PETSC_TRUE;
2282     }
2283   } else { /* scall == MAT_INITIAL_MATRIX */
2284     /* Get some new tags to keep the communication clean */
2285     ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
2286     ierr = PetscObjectGetNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
2287 
2288     /* evaluate communication - mesg to who, length of mesg, and buffer space
2289      required. Based on this, buffers are allocated, and data copied into them*/
2290     ierr = PetscCalloc4(size,&w1,size,&w2,size,&w3,size,&w4);CHKERRQ(ierr);   /* mesg size, initialize work vectors */
2291 
2292     for (i=0; i<ismax; i++) {
2293       jmax   = nrow[i];
2294       irow_i = irow[i];
2295 
2296       ierr   = PetscMalloc1(jmax,&row2proc_i);CHKERRQ(ierr);
2297       row2proc[i] = row2proc_i;
2298 
2299       if (issorted[i]) proc = 0;
2300       for (j=0; j<jmax; j++) {
2301         if (!issorted[i]) proc = 0;
2302         row = irow_i[j];
2303         while (row >= C->rmap->range[proc+1]) proc++;
2304         w4[proc]++;
2305         row2proc_i[j] = proc; /* map row index to proc */
2306       }
2307       for (j=0; j<size; j++) {
2308         if (w4[j]) { w1[j] += w4[j];  w3[j]++; w4[j] = 0;}
2309       }
2310     }
2311 
2312     nrqs     = 0;              /* no of outgoing messages */
2313     msz      = 0;              /* total mesg length (for all procs) */
2314     w1[rank] = 0;              /* no mesg sent to self */
2315     w3[rank] = 0;
2316     for (i=0; i<size; i++) {
2317       if (w1[i])  { w2[i] = 1; nrqs++;} /* there exists a message to proc i */
2318     }
2319     ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr); /*(proc -array)*/
2320     for (i=0,j=0; i<size; i++) {
2321       if (w1[i]) { pa[j] = i; j++; }
2322     }
2323 
2324     /* Each message would have a header = 1 + 2*(no of IS) + data */
2325     for (i=0; i<nrqs; i++) {
2326       j      = pa[i];
2327       w1[j] += w2[j] + 2* w3[j];
2328       msz   += w1[j];
2329     }
2330     ierr = PetscInfo2(0,"Number of outgoing messages %D Total message length %D\n",nrqs,msz);CHKERRQ(ierr);
2331 
2332     /* Determine the number of messages to expect, their lengths, from from-ids */
2333     ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
2334     ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
2335 
2336     /* Now post the Irecvs corresponding to these messages */
2337     tag0 = ((PetscObject)C)->tag;
2338     ierr = PetscPostIrecvInt(comm,tag0,nrqr,onodes1,olengths1,&rbuf1,&r_waits1);CHKERRQ(ierr);
2339 
2340     ierr = PetscFree(onodes1);CHKERRQ(ierr);
2341     ierr = PetscFree(olengths1);CHKERRQ(ierr);
2342 
2343     /* Allocate Memory for outgoing messages */
2344     ierr = PetscMalloc4(size,&sbuf1,size,&ptr,2*msz,&tmp,size,&ctr);CHKERRQ(ierr);
2345     ierr = PetscMemzero(sbuf1,size*sizeof(PetscInt*));CHKERRQ(ierr);
2346     ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
2347 
2348     {
2349       PetscInt *iptr = tmp;
2350       k    = 0;
2351       for (i=0; i<nrqs; i++) {
2352         j        = pa[i];
2353         iptr    += k;
2354         sbuf1[j] = iptr;
2355         k        = w1[j];
2356       }
2357     }
2358 
2359     /* Form the outgoing messages. Initialize the header space */
2360     for (i=0; i<nrqs; i++) {
2361       j           = pa[i];
2362       sbuf1[j][0] = 0;
2363       ierr        = PetscMemzero(sbuf1[j]+1,2*w3[j]*sizeof(PetscInt));CHKERRQ(ierr);
2364       ptr[j]      = sbuf1[j] + 2*w3[j] + 1;
2365     }
2366 
2367     /* Parse the isrow and copy data into outbuf */
2368     for (i=0; i<ismax; i++) {
2369       row2proc_i = row2proc[i];
2370       ierr   = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
2371       irow_i = irow[i];
2372       jmax   = nrow[i];
2373       for (j=0; j<jmax; j++) {  /* parse the indices of each IS */
2374         proc = row2proc_i[j];
2375         if (proc != rank) { /* copy to the outgoing buf*/
2376           ctr[proc]++;
2377           *ptr[proc] = irow_i[j];
2378           ptr[proc]++;
2379         }
2380       }
2381       /* Update the headers for the current IS */
2382       for (j=0; j<size; j++) { /* Can Optimise this loop too */
2383         if ((ctr_j = ctr[j])) {
2384           sbuf1_j        = sbuf1[j];
2385           k              = ++sbuf1_j[0];
2386           sbuf1_j[2*k]   = ctr_j;
2387           sbuf1_j[2*k-1] = i;
2388         }
2389       }
2390     }
2391 
2392     /*  Now  post the sends */
2393     ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
2394     for (i=0; i<nrqs; ++i) {
2395       j    = pa[i];
2396       ierr = MPI_Isend(sbuf1[j],w1[j],MPIU_INT,j,tag0,comm,s_waits1+i);CHKERRQ(ierr);
2397     }
2398 
2399     /* Post Receives to capture the buffer size */
2400     ierr = PetscMalloc1(nrqs+1,&r_waits2);CHKERRQ(ierr);
2401     ierr = PetscMalloc3(nrqs+1,&req_source2,nrqs+1,&rbuf2,nrqs+1,&rbuf3);CHKERRQ(ierr);
2402     rbuf2[0] = tmp + msz;
2403     for (i=1; i<nrqs; ++i) {
2404       rbuf2[i] = rbuf2[i-1]+w1[pa[i-1]];
2405     }
2406     for (i=0; i<nrqs; ++i) {
2407       j    = pa[i];
2408       ierr = MPI_Irecv(rbuf2[i],w1[j],MPIU_INT,j,tag2,comm,r_waits2+i);CHKERRQ(ierr);
2409     }
2410 
2411     /* Send to other procs the buf size they should allocate */
2412     /* Receive messages*/
2413     ierr = PetscMalloc1(nrqr+1,&s_waits2);CHKERRQ(ierr);
2414     ierr = PetscMalloc1(nrqr+1,&r_status1);CHKERRQ(ierr);
2415     ierr = PetscMalloc3(nrqr,&sbuf2,nrqr,&req_size,nrqr,&req_source1);CHKERRQ(ierr);
2416     {
2417       PetscInt   *sAi = a->i,*sBi = b->i,id,rstart = C->rmap->rstart;
2418       PetscInt   *sbuf2_i;
2419 
2420       ierr = MPI_Waitall(nrqr,r_waits1,r_status1);CHKERRQ(ierr);
2421       for (i=0; i<nrqr; ++i) {
2422         req_size[i] = 0;
2423         rbuf1_i        = rbuf1[i];
2424         start          = 2*rbuf1_i[0] + 1;
2425         ierr           = MPI_Get_count(r_status1+i,MPIU_INT,&end);CHKERRQ(ierr);
2426         ierr           = PetscMalloc1(end+1,&sbuf2[i]);CHKERRQ(ierr);
2427         sbuf2_i        = sbuf2[i];
2428         for (j=start; j<end; j++) {
2429           id              = rbuf1_i[j] - rstart;
2430           ncols           = sAi[id+1] - sAi[id] + sBi[id+1] - sBi[id];
2431           sbuf2_i[j]      = ncols;
2432           req_size[i] += ncols;
2433         }
2434         req_source1[i] = r_status1[i].MPI_SOURCE;
2435         /* form the header */
2436         sbuf2_i[0] = req_size[i];
2437         for (j=1; j<start; j++) sbuf2_i[j] = rbuf1_i[j];
2438 
2439         ierr = MPI_Isend(sbuf2_i,end,MPIU_INT,req_source1[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
2440       }
2441     }
2442     ierr = PetscFree(r_status1);CHKERRQ(ierr);
2443     ierr = PetscFree(r_waits1);CHKERRQ(ierr);
2444     ierr = PetscFree4(w1,w2,w3,w4);CHKERRQ(ierr);
2445 
2446     /* Receive messages*/
2447     ierr = PetscMalloc1(nrqs+1,&r_waits3);CHKERRQ(ierr);
2448     ierr = PetscMalloc1(nrqs+1,&r_status2);CHKERRQ(ierr);
2449 
2450     ierr = MPI_Waitall(nrqs,r_waits2,r_status2);CHKERRQ(ierr);
2451     for (i=0; i<nrqs; ++i) {
2452       ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf3[i]);CHKERRQ(ierr);
2453       req_source2[i] = r_status2[i].MPI_SOURCE;
2454       ierr = MPI_Irecv(rbuf3[i],rbuf2[i][0],MPIU_INT,req_source2[i],tag3,comm,r_waits3+i);CHKERRQ(ierr);
2455     }
2456     ierr = PetscFree(r_status2);CHKERRQ(ierr);
2457     ierr = PetscFree(r_waits2);CHKERRQ(ierr);
2458 
2459     /* Wait on sends1 and sends2 */
2460     ierr = PetscMalloc1(nrqs+1,&s_status1);CHKERRQ(ierr);
2461     ierr = PetscMalloc1(nrqr+1,&s_status2);CHKERRQ(ierr);
2462 
2463     if (nrqs) {ierr = MPI_Waitall(nrqs,s_waits1,s_status1);CHKERRQ(ierr);}
2464     if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits2,s_status2);CHKERRQ(ierr);}
2465     ierr = PetscFree(s_status1);CHKERRQ(ierr);
2466     ierr = PetscFree(s_status2);CHKERRQ(ierr);
2467     ierr = PetscFree(s_waits1);CHKERRQ(ierr);
2468     ierr = PetscFree(s_waits2);CHKERRQ(ierr);
2469 
2470     /* Now allocate sending buffers for a->j, and send them off */
2471     ierr = PetscMalloc1(nrqr+1,&sbuf_aj);CHKERRQ(ierr);
2472     for (i=0,j=0; i<nrqr; i++) j += req_size[i];
2473     ierr = PetscMalloc1(j+1,&sbuf_aj[0]);CHKERRQ(ierr);
2474     for (i=1; i<nrqr; i++) sbuf_aj[i] = sbuf_aj[i-1] + req_size[i-1];
2475 
2476     ierr = PetscMalloc1(nrqr+1,&s_waits3);CHKERRQ(ierr);
2477     {
2478       PetscInt nzA,nzB,*a_i = a->i,*b_i = b->i,lwrite;
2479       PetscInt *cworkA,*cworkB,cstart = C->cmap->rstart,rstart = C->rmap->rstart,*bmap = c->garray;
2480       PetscInt cend = C->cmap->rend;
2481       PetscInt *a_j = a->j,*b_j = b->j,ctmp;
2482 
2483       for (i=0; i<nrqr; i++) {
2484         rbuf1_i   = rbuf1[i];
2485         sbuf_aj_i = sbuf_aj[i];
2486         ct1       = 2*rbuf1_i[0] + 1;
2487         ct2       = 0;
2488         for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
2489           kmax = rbuf1[i][2*j];
2490           for (k=0; k<kmax; k++,ct1++) {
2491             row    = rbuf1_i[ct1] - rstart;
2492             nzA    = a_i[row+1] - a_i[row]; nzB = b_i[row+1] - b_i[row];
2493             ncols  = nzA + nzB;
2494             cworkA = a_j + a_i[row]; cworkB = b_j + b_i[row];
2495 
2496             /* load the column indices for this row into cols */
2497             cols = sbuf_aj_i + ct2;
2498 
2499             lwrite = 0;
2500             for (l=0; l<nzB; l++) {
2501               if ((ctmp = bmap[cworkB[l]]) < cstart) cols[lwrite++] = ctmp;
2502             }
2503             for (l=0; l<nzA; l++) cols[lwrite++] = cstart + cworkA[l];
2504             for (l=0; l<nzB; l++) {
2505               if ((ctmp = bmap[cworkB[l]]) >= cend) cols[lwrite++] = ctmp;
2506             }
2507 
2508             ct2 += ncols;
2509           }
2510         }
2511         ierr = MPI_Isend(sbuf_aj_i,req_size[i],MPIU_INT,req_source1[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
2512       }
2513     }
2514     ierr = PetscMalloc2(nrqs+1,&r_status3,nrqr+1,&s_status3);CHKERRQ(ierr);
2515 
2516     /* create col map: global col of C -> local col of submatrices */
2517     {
2518       const PetscInt *icol_i;
2519 #if defined(PETSC_USE_CTABLE)
2520       for (i=0; i<ismax; i++) {
2521         if (!allcolumns[i]) {
2522           ierr = PetscTableCreate(ncol[i]+1,C->cmap->N+1,&cmap[i]);CHKERRQ(ierr);
2523 
2524           jmax   = ncol[i];
2525           icol_i = icol[i];
2526           cmap_i = cmap[i];
2527           for (j=0; j<jmax; j++) {
2528             ierr = PetscTableAdd(cmap[i],icol_i[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
2529           }
2530         } else cmap[i] = NULL;
2531       }
2532 #else
2533       for (i=0; i<ismax; i++) {
2534         if (!allcolumns[i]) {
2535           ierr   = PetscCalloc1(C->cmap->N,&cmap[i]);CHKERRQ(ierr);
2536           jmax   = ncol[i];
2537           icol_i = icol[i];
2538           cmap_i = cmap[i];
2539           for (j=0; j<jmax; j++) {
2540             cmap_i[icol_i[j]] = j+1;
2541           }
2542         } else cmap[i] = NULL;
2543       }
2544 #endif
2545     }
2546 
2547     /* Create lens which is required for MatCreate... */
2548     for (i=0,j=0; i<ismax; i++) j += nrow[i];
2549     ierr = PetscMalloc1(ismax,&lens);CHKERRQ(ierr);
2550 
2551     if (ismax) {
2552       ierr = PetscCalloc1(j,&lens[0]);CHKERRQ(ierr);
2553     }
2554     for (i=1; i<ismax; i++) lens[i] = lens[i-1] + nrow[i-1];
2555 
2556     /* Update lens from local data */
2557     for (i=0; i<ismax; i++) {
2558       row2proc_i = row2proc[i];
2559       jmax = nrow[i];
2560       if (!allcolumns[i]) cmap_i = cmap[i];
2561       irow_i = irow[i];
2562       lens_i = lens[i];
2563       for (j=0; j<jmax; j++) {
2564         row = irow_i[j];
2565         proc = row2proc_i[j];
2566         if (proc == rank) {
2567           ierr = MatGetRow_MPIAIJ(C,row,&ncols,&cols,0);CHKERRQ(ierr);
2568           if (!allcolumns[i]) {
2569             for (k=0; k<ncols; k++) {
2570 #if defined(PETSC_USE_CTABLE)
2571               ierr = PetscTableFind(cmap_i,cols[k]+1,&tcol);CHKERRQ(ierr);
2572 #else
2573               tcol = cmap_i[cols[k]];
2574 #endif
2575               if (tcol) lens_i[j]++;
2576             }
2577           } else { /* allcolumns */
2578             lens_i[j] = ncols;
2579           }
2580           ierr = MatRestoreRow_MPIAIJ(C,row,&ncols,&cols,0);CHKERRQ(ierr);
2581         }
2582       }
2583     }
2584 
2585     /* Create row map: global row of C -> local row of submatrices */
2586 #if defined(PETSC_USE_CTABLE)
2587     for (i=0; i<ismax; i++) {
2588       ierr   = PetscTableCreate(nrow[i]+1,C->rmap->N+1,&rmap[i]);CHKERRQ(ierr);
2589       irow_i = irow[i];
2590       jmax   = nrow[i];
2591       for (j=0; j<jmax; j++) {
2592       ierr = PetscTableAdd(rmap[i],irow_i[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
2593       }
2594     }
2595 #else
2596     for (i=0; i<ismax; i++) {
2597       ierr   = PetscCalloc1(C->rmap->N,&rmap[i]);CHKERRQ(ierr);
2598       rmap_i = rmap[i];
2599       irow_i = irow[i];
2600       jmax   = nrow[i];
2601       for (j=0; j<jmax; j++) {
2602         rmap_i[irow_i[j]] = j;
2603       }
2604     }
2605 #endif
2606 
2607     /* Update lens from offproc data */
2608     {
2609       PetscInt *rbuf2_i,*rbuf3_i,*sbuf1_i;
2610 
2611       ierr    = MPI_Waitall(nrqs,r_waits3,r_status3);CHKERRQ(ierr);
2612       for (tmp2=0; tmp2<nrqs; tmp2++) {
2613         sbuf1_i = sbuf1[pa[tmp2]];
2614         jmax    = sbuf1_i[0];
2615         ct1     = 2*jmax+1;
2616         ct2     = 0;
2617         rbuf2_i = rbuf2[tmp2];
2618         rbuf3_i = rbuf3[tmp2];
2619         for (j=1; j<=jmax; j++) {
2620           is_no  = sbuf1_i[2*j-1];
2621           max1   = sbuf1_i[2*j];
2622           lens_i = lens[is_no];
2623           if (!allcolumns[is_no]) cmap_i = cmap[is_no];
2624           rmap_i = rmap[is_no];
2625           for (k=0; k<max1; k++,ct1++) {
2626 #if defined(PETSC_USE_CTABLE)
2627             ierr = PetscTableFind(rmap_i,sbuf1_i[ct1]+1,&row);CHKERRQ(ierr);
2628             row--;
2629             if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"row not found in table");
2630 #else
2631             row = rmap_i[sbuf1_i[ct1]]; /* the val in the new matrix to be */
2632 #endif
2633             max2 = rbuf2_i[ct1];
2634             for (l=0; l<max2; l++,ct2++) {
2635               if (!allcolumns[is_no]) {
2636 #if defined(PETSC_USE_CTABLE)
2637                 ierr = PetscTableFind(cmap_i,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
2638 #else
2639                 tcol = cmap_i[rbuf3_i[ct2]];
2640 #endif
2641                 if (tcol) lens_i[row]++;
2642               } else { /* allcolumns */
2643                 lens_i[row]++; /* lens_i[row] += max2 ? */
2644               }
2645             }
2646           }
2647         }
2648       }
2649     }
2650     ierr = PetscFree(r_waits3);CHKERRQ(ierr);
2651     if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits3,s_status3);CHKERRQ(ierr);}
2652     ierr = PetscFree2(r_status3,s_status3);CHKERRQ(ierr);
2653     ierr = PetscFree(s_waits3);CHKERRQ(ierr);
2654 
2655     /* Create the submatrices */
2656     for (i=0; i<ismax; i++) {
2657       PetscInt    rbs,cbs;
2658 
2659       ierr = ISGetBlockSize(isrow[i],&rbs);CHKERRQ(ierr);
2660       ierr = ISGetBlockSize(iscol[i],&cbs);CHKERRQ(ierr);
2661 
2662       ierr = MatCreate(PETSC_COMM_SELF,submats+i);CHKERRQ(ierr);
2663       ierr = MatSetSizes(submats[i],nrow[i],ncol[i],PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2664 
2665       ierr = MatSetBlockSizes(submats[i],rbs,cbs);CHKERRQ(ierr);
2666       ierr = MatSetType(submats[i],((PetscObject)A)->type_name);CHKERRQ(ierr);
2667       ierr = MatSeqAIJSetPreallocation(submats[i],0,lens[i]);CHKERRQ(ierr);
2668 
2669       /* create struct Mat_SubMat and attached it to submat */
2670       ierr = PetscNew(&smat_i);CHKERRQ(ierr);
2671       subc = (Mat_SeqAIJ*)submats[i]->data;
2672       subc->submatis1 = smat_i;
2673 
2674       smat_i->destroy          = submats[i]->ops->destroy;
2675       submats[i]->ops->destroy = MatDestroy_MPIAIJ_MatGetSubmatrices;
2676       submats[i]->factortype   = C->factortype;
2677 
2678       smat_i->id          = i;
2679       smat_i->nrqs        = nrqs;
2680       smat_i->nrqr        = nrqr;
2681       smat_i->rbuf1       = rbuf1;
2682       smat_i->rbuf2       = rbuf2;
2683       smat_i->rbuf3       = rbuf3;
2684       smat_i->sbuf2       = sbuf2;
2685       smat_i->req_source2 = req_source2;
2686 
2687       smat_i->sbuf1       = sbuf1;
2688       smat_i->ptr         = ptr;
2689       smat_i->tmp         = tmp;
2690       smat_i->ctr         = ctr;
2691 
2692       smat_i->pa           = pa;
2693       smat_i->req_size     = req_size;
2694       smat_i->req_source1  = req_source1;
2695 
2696       smat_i->allcolumns  = allcolumns[i];
2697       smat_i->singleis    = PETSC_FALSE;
2698       smat_i->row2proc    = row2proc[i];
2699       smat_i->rmap        = rmap[i];
2700       smat_i->cmap        = cmap[i];
2701     }
2702 
2703     if (!ismax) { /* Create dummy submats[0] for reuse struct subc */
2704       ierr = MatCreate(PETSC_COMM_SELF,&submats[0]);CHKERRQ(ierr);
2705       ierr = MatSetSizes(submats[0],0,0,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2706       ierr = MatSetType(submats[0],MATDUMMY);CHKERRQ(ierr);
2707 
2708       /* create struct Mat_SubMat and attached it to submat */
2709       ierr = PetscNewLog(submats[0],&smat_i);CHKERRQ(ierr);
2710       submats[0]->data = (void*)smat_i;
2711 
2712       smat_i->destroy          = submats[0]->ops->destroy;
2713       submats[0]->ops->destroy = MatDestroy_Dummy_MatGetSubmatrices;
2714       submats[0]->factortype   = C->factortype;
2715 
2716       smat_i->id          = i;
2717       smat_i->nrqs        = nrqs;
2718       smat_i->nrqr        = nrqr;
2719       smat_i->rbuf1       = rbuf1;
2720       smat_i->rbuf2       = rbuf2;
2721       smat_i->rbuf3       = rbuf3;
2722       smat_i->sbuf2       = sbuf2;
2723       smat_i->req_source2 = req_source2;
2724 
2725       smat_i->sbuf1       = sbuf1;
2726       smat_i->ptr         = ptr;
2727       smat_i->tmp         = tmp;
2728       smat_i->ctr         = ctr;
2729 
2730       smat_i->pa           = pa;
2731       smat_i->req_size     = req_size;
2732       smat_i->req_source1  = req_source1;
2733 
2734       smat_i->allcolumns  = PETSC_TRUE;
2735       smat_i->singleis    = PETSC_FALSE;
2736       smat_i->row2proc    = NULL;
2737       smat_i->rmap        = NULL;
2738       smat_i->cmap        = NULL;
2739     }
2740 
2741     if (ismax) {ierr = PetscFree(lens[0]);CHKERRQ(ierr);}
2742     ierr = PetscFree(lens);CHKERRQ(ierr);
2743     ierr = PetscFree(sbuf_aj[0]);CHKERRQ(ierr);
2744     ierr = PetscFree(sbuf_aj);CHKERRQ(ierr);
2745 
2746   } /* endof scall == MAT_INITIAL_MATRIX */
2747 
2748   /* Post recv matrix values */
2749   ierr = PetscObjectGetNewTag((PetscObject)C,&tag4);CHKERRQ(ierr);
2750   ierr = PetscMalloc1(nrqs+1,&rbuf4);CHKERRQ(ierr);
2751   ierr = PetscMalloc1(nrqs+1,&r_waits4);CHKERRQ(ierr);
2752   ierr = PetscMalloc1(nrqs+1,&r_status4);CHKERRQ(ierr);
2753   ierr = PetscMalloc1(nrqr+1,&s_status4);CHKERRQ(ierr);
2754   for (i=0; i<nrqs; ++i) {
2755     ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf4[i]);CHKERRQ(ierr);
2756     ierr = MPI_Irecv(rbuf4[i],rbuf2[i][0],MPIU_SCALAR,req_source2[i],tag4,comm,r_waits4+i);CHKERRQ(ierr);
2757   }
2758 
2759   /* Allocate sending buffers for a->a, and send them off */
2760   ierr = PetscMalloc1(nrqr+1,&sbuf_aa);CHKERRQ(ierr);
2761   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
2762   ierr = PetscMalloc1(j+1,&sbuf_aa[0]);CHKERRQ(ierr);
2763   for (i=1; i<nrqr; i++) sbuf_aa[i] = sbuf_aa[i-1] + req_size[i-1];
2764 
2765   ierr = PetscMalloc1(nrqr+1,&s_waits4);CHKERRQ(ierr);
2766   {
2767     PetscInt    nzA,nzB,*a_i = a->i,*b_i = b->i, *cworkB,lwrite;
2768     PetscInt    cstart = C->cmap->rstart,rstart = C->rmap->rstart,*bmap = c->garray;
2769     PetscInt    cend   = C->cmap->rend;
2770     PetscInt    *b_j   = b->j;
2771     PetscScalar *vworkA,*vworkB,*a_a = a->a,*b_a = b->a;
2772 
2773     for (i=0; i<nrqr; i++) {
2774       rbuf1_i   = rbuf1[i];
2775       sbuf_aa_i = sbuf_aa[i];
2776       ct1       = 2*rbuf1_i[0]+1;
2777       ct2       = 0;
2778       for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
2779         kmax = rbuf1_i[2*j];
2780         for (k=0; k<kmax; k++,ct1++) {
2781           row    = rbuf1_i[ct1] - rstart;
2782           nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
2783           ncols  = nzA + nzB;
2784           cworkB = b_j + b_i[row];
2785           vworkA = a_a + a_i[row];
2786           vworkB = b_a + b_i[row];
2787 
2788           /* load the column values for this row into vals*/
2789           vals = sbuf_aa_i+ct2;
2790 
2791           lwrite = 0;
2792           for (l=0; l<nzB; l++) {
2793             if ((bmap[cworkB[l]]) < cstart) vals[lwrite++] = vworkB[l];
2794           }
2795           for (l=0; l<nzA; l++) vals[lwrite++] = vworkA[l];
2796           for (l=0; l<nzB; l++) {
2797             if ((bmap[cworkB[l]]) >= cend) vals[lwrite++] = vworkB[l];
2798           }
2799 
2800           ct2 += ncols;
2801         }
2802       }
2803       ierr = MPI_Isend(sbuf_aa_i,req_size[i],MPIU_SCALAR,req_source1[i],tag4,comm,s_waits4+i);CHKERRQ(ierr);
2804     }
2805   }
2806 
2807   /* Assemble the matrices */
2808   /* First assemble the local rows */
2809   for (i=0; i<ismax; i++) {
2810     row2proc_i = row2proc[i];
2811     subc      = (Mat_SeqAIJ*)submats[i]->data;
2812     imat_ilen = subc->ilen;
2813     imat_j    = subc->j;
2814     imat_i    = subc->i;
2815     imat_a    = subc->a;
2816 
2817     if (!allcolumns[i]) cmap_i = cmap[i];
2818     rmap_i = rmap[i];
2819     irow_i = irow[i];
2820     jmax   = nrow[i];
2821     for (j=0; j<jmax; j++) {
2822       row  = irow_i[j];
2823       proc = row2proc_i[j];
2824       if (proc == rank) {
2825         old_row = row;
2826 #if defined(PETSC_USE_CTABLE)
2827         ierr = PetscTableFind(rmap_i,row+1,&row);CHKERRQ(ierr);
2828         row--;
2829 #else
2830         row = rmap_i[row];
2831 #endif
2832         ilen_row = imat_ilen[row];
2833         ierr     = MatGetRow_MPIAIJ(C,old_row,&ncols,&cols,&vals);CHKERRQ(ierr);
2834         mat_i    = imat_i[row];
2835         mat_a    = imat_a + mat_i;
2836         mat_j    = imat_j + mat_i;
2837         if (!allcolumns[i]) {
2838           for (k=0; k<ncols; k++) {
2839 #if defined(PETSC_USE_CTABLE)
2840             ierr = PetscTableFind(cmap_i,cols[k]+1,&tcol);CHKERRQ(ierr);
2841 #else
2842             tcol = cmap_i[cols[k]];
2843 #endif
2844             if (tcol) {
2845               *mat_j++ = tcol - 1;
2846               *mat_a++ = vals[k];
2847               ilen_row++;
2848             }
2849           }
2850         } else { /* allcolumns */
2851           for (k=0; k<ncols; k++) {
2852             *mat_j++ = cols[k];  /* global col index! */
2853             *mat_a++ = vals[k];
2854             ilen_row++;
2855           }
2856         }
2857         ierr = MatRestoreRow_MPIAIJ(C,old_row,&ncols,&cols,&vals);CHKERRQ(ierr);
2858 
2859         imat_ilen[row] = ilen_row;
2860       }
2861     }
2862   }
2863 
2864   /* Now assemble the off proc rows */
2865   ierr    = MPI_Waitall(nrqs,r_waits4,r_status4);CHKERRQ(ierr);
2866   for (tmp2=0; tmp2<nrqs; tmp2++) {
2867     sbuf1_i = sbuf1[pa[tmp2]];
2868     jmax    = sbuf1_i[0];
2869     ct1     = 2*jmax + 1;
2870     ct2     = 0;
2871     rbuf2_i = rbuf2[tmp2];
2872     rbuf3_i = rbuf3[tmp2];
2873     rbuf4_i = rbuf4[tmp2];
2874     for (j=1; j<=jmax; j++) {
2875       is_no     = sbuf1_i[2*j-1];
2876       rmap_i    = rmap[is_no];
2877       if (!allcolumns[is_no]) cmap_i = cmap[is_no];
2878       subc      = (Mat_SeqAIJ*)submats[is_no]->data;
2879       imat_ilen = subc->ilen;
2880       imat_j    = subc->j;
2881       imat_i    = subc->i;
2882       imat_a    = subc->a;
2883       max1      = sbuf1_i[2*j];
2884       for (k=0; k<max1; k++,ct1++) {
2885         row = sbuf1_i[ct1];
2886 #if defined(PETSC_USE_CTABLE)
2887         ierr = PetscTableFind(rmap_i,row+1,&row);CHKERRQ(ierr);
2888         row--;
2889 #else
2890         row = rmap_i[row];
2891 #endif
2892         ilen  = imat_ilen[row];
2893         mat_i = imat_i[row];
2894         mat_a = imat_a + mat_i;
2895         mat_j = imat_j + mat_i;
2896         max2  = rbuf2_i[ct1];
2897         if (!allcolumns[is_no]) {
2898           for (l=0; l<max2; l++,ct2++) {
2899 #if defined(PETSC_USE_CTABLE)
2900             ierr = PetscTableFind(cmap_i,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
2901 #else
2902             tcol = cmap_i[rbuf3_i[ct2]];
2903 #endif
2904             if (tcol) {
2905               *mat_j++ = tcol - 1;
2906               *mat_a++ = rbuf4_i[ct2];
2907               ilen++;
2908             }
2909           }
2910         } else { /* allcolumns */
2911           for (l=0; l<max2; l++,ct2++) {
2912             *mat_j++ = rbuf3_i[ct2]; /* same global column index of C */
2913             *mat_a++ = rbuf4_i[ct2];
2914             ilen++;
2915           }
2916         }
2917         imat_ilen[row] = ilen;
2918       }
2919     }
2920   }
2921 
2922   if (!iscsorted) { /* sort column indices of the rows */
2923     for (i=0; i<ismax; i++) {
2924       subc      = (Mat_SeqAIJ*)submats[i]->data;
2925       imat_j    = subc->j;
2926       imat_i    = subc->i;
2927       imat_a    = subc->a;
2928       imat_ilen = subc->ilen;
2929 
2930       if (allcolumns[i]) continue;
2931       jmax = nrow[i];
2932       for (j=0; j<jmax; j++) {
2933         mat_i = imat_i[j];
2934         mat_a = imat_a + mat_i;
2935         mat_j = imat_j + mat_i;
2936         ierr  = PetscSortIntWithScalarArray(imat_ilen[j],mat_j,mat_a);CHKERRQ(ierr);
2937       }
2938     }
2939   }
2940 
2941   ierr = PetscFree(r_status4);CHKERRQ(ierr);
2942   ierr = PetscFree(r_waits4);CHKERRQ(ierr);
2943   if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits4,s_status4);CHKERRQ(ierr);}
2944   ierr = PetscFree(s_waits4);CHKERRQ(ierr);
2945   ierr = PetscFree(s_status4);CHKERRQ(ierr);
2946 
2947   /* Restore the indices */
2948   for (i=0; i<ismax; i++) {
2949     ierr = ISRestoreIndices(isrow[i],irow+i);CHKERRQ(ierr);
2950     if (!allcolumns[i]) {
2951       ierr = ISRestoreIndices(iscol[i],icol+i);CHKERRQ(ierr);
2952     }
2953   }
2954 
2955   for (i=0; i<ismax; i++) {
2956     ierr = MatAssemblyBegin(submats[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2957     ierr = MatAssemblyEnd(submats[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2958   }
2959   if (!ismax) { /* a dummy matrix */
2960     //ierr = MatAssemblyBegin(submats[0],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2961     //ierr = MatAssemblyEnd(submats[0],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2962   }
2963 
2964   /* Destroy allocated memory */
2965   ierr = PetscFree(sbuf_aa[0]);CHKERRQ(ierr);
2966   ierr = PetscFree(sbuf_aa);CHKERRQ(ierr);
2967   ierr = PetscFree5(irow,icol,nrow,ncol,issorted);CHKERRQ(ierr);
2968 
2969   for (i=0; i<nrqs; ++i) {
2970     ierr = PetscFree(rbuf4[i]);CHKERRQ(ierr);
2971   }
2972   ierr = PetscFree(rbuf4);CHKERRQ(ierr);
2973 
2974   ierr = PetscFree4(row2proc,cmap,rmap,allcolumns);CHKERRQ(ierr);
2975   PetscFunctionReturn(0);
2976 }
2977 
2978 /*
2979  Permute A & B into C's *local* index space using rowemb,dcolemb for A and rowemb,ocolemb for B.
2980  Embeddings are supposed to be injections and the above implies that the range of rowemb is a subset
2981  of [0,m), dcolemb is in [0,n) and ocolemb is in [N-n).
2982  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A&B.
2983  After that B's columns are mapped into C's global column space, so that C is in the "disassembled"
2984  state, and needs to be "assembled" later by compressing B's column space.
2985 
2986  This function may be called in lieu of preallocation, so C should not be expected to be preallocated.
2987  Following this call, C->A & C->B have been created, even if empty.
2988  */
2989 PetscErrorCode MatSetSeqMats_MPIAIJ(Mat C,IS rowemb,IS dcolemb,IS ocolemb,MatStructure pattern,Mat A,Mat B)
2990 {
2991   /* If making this function public, change the error returned in this function away from _PLIB. */
2992   PetscErrorCode ierr;
2993   Mat_MPIAIJ     *aij;
2994   Mat_SeqAIJ     *Baij;
2995   PetscBool      seqaij,Bdisassembled;
2996   PetscInt       m,n,*nz,i,j,ngcol,col,rstart,rend,shift,count;
2997   PetscScalar    v;
2998   const PetscInt *rowindices,*colindices;
2999 
3000   PetscFunctionBegin;
3001   /* Check to make sure the component matrices (and embeddings) are compatible with C. */
3002   if (A) {
3003     ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
3004     if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diagonal matrix is of wrong type");
3005     if (rowemb) {
3006       ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
3007       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);
3008     } else {
3009       if (C->rmap->n != A->rmap->n) {
3010 	SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag seq matrix is row-incompatible with the MPIAIJ matrix");
3011       }
3012     }
3013     if (dcolemb) {
3014       ierr = ISGetLocalSize(dcolemb,&n);CHKERRQ(ierr);
3015       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);
3016     } else {
3017       if (C->cmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag seq matrix is col-incompatible with the MPIAIJ matrix");
3018     }
3019   }
3020   if (B) {
3021     ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
3022     if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diagonal matrix is of wrong type");
3023     if (rowemb) {
3024       ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
3025       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);
3026     } else {
3027       if (C->rmap->n != B->rmap->n) {
3028 	SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diag seq matrix is row-incompatible with the MPIAIJ matrix");
3029       }
3030     }
3031     if (ocolemb) {
3032       ierr = ISGetLocalSize(ocolemb,&n);CHKERRQ(ierr);
3033       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);
3034     } else {
3035       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");
3036     }
3037   }
3038 
3039   aij = (Mat_MPIAIJ*)C->data;
3040   if (!aij->A) {
3041     /* Mimic parts of MatMPIAIJSetPreallocation() */
3042     ierr   = MatCreate(PETSC_COMM_SELF,&aij->A);CHKERRQ(ierr);
3043     ierr   = MatSetSizes(aij->A,C->rmap->n,C->cmap->n,C->rmap->n,C->cmap->n);CHKERRQ(ierr);
3044     ierr   = MatSetBlockSizesFromMats(aij->A,C,C);CHKERRQ(ierr);
3045     ierr   = MatSetType(aij->A,MATSEQAIJ);CHKERRQ(ierr);
3046     ierr   = PetscLogObjectParent((PetscObject)C,(PetscObject)aij->A);CHKERRQ(ierr);
3047   }
3048   if (A) {
3049     ierr   = MatSetSeqMat_SeqAIJ(aij->A,rowemb,dcolemb,pattern,A);CHKERRQ(ierr);
3050   } else {
3051     ierr = MatSetUp(aij->A);CHKERRQ(ierr);
3052   }
3053   if (B) { /* Destroy the old matrix or the column map, depending on the sparsity pattern. */
3054     /*
3055       If pattern == DIFFERENT_NONZERO_PATTERN, we reallocate B and
3056       need to "disassemble" B -- convert it to using C's global indices.
3057       To insert the values we take the safer, albeit more expensive, route of MatSetValues().
3058 
3059       If pattern == SUBSET_NONZERO_PATTERN, we do not "disassemble" B and do not reallocate;
3060       we MatZeroValues(B) first, so there may be a bunch of zeros that, perhaps, could be compacted out.
3061 
3062       TODO: Put B's values into aij->B's aij structure in place using the embedding ISs?
3063       At least avoid calling MatSetValues() and the implied searches?
3064     */
3065 
3066     if (B && pattern == DIFFERENT_NONZERO_PATTERN) {
3067 #if defined(PETSC_USE_CTABLE)
3068       ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
3069 #else
3070       ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
3071       /* A bit of a HACK: ideally we should deal with case aij->B all in one code block below. */
3072       if (aij->B) {
3073         ierr = PetscLogObjectMemory((PetscObject)C,-aij->B->cmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3074       }
3075 #endif
3076       ngcol = 0;
3077       if (aij->lvec) {
3078 	ierr = VecGetSize(aij->lvec,&ngcol);CHKERRQ(ierr);
3079       }
3080       if (aij->garray) {
3081 	ierr = PetscFree(aij->garray);CHKERRQ(ierr);
3082 	ierr = PetscLogObjectMemory((PetscObject)C,-ngcol*sizeof(PetscInt));CHKERRQ(ierr);
3083       }
3084       ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
3085       ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
3086     }
3087     if (aij->B && B && pattern == DIFFERENT_NONZERO_PATTERN) {
3088       ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
3089     }
3090     if (aij->B && B && pattern == SUBSET_NONZERO_PATTERN) {
3091       ierr = MatZeroEntries(aij->B);CHKERRQ(ierr);
3092     }
3093   }
3094   Bdisassembled = PETSC_FALSE;
3095   if (!aij->B) {
3096     ierr = MatCreate(PETSC_COMM_SELF,&aij->B);CHKERRQ(ierr);
3097     ierr = PetscLogObjectParent((PetscObject)C,(PetscObject)aij->B);CHKERRQ(ierr);
3098     ierr = MatSetSizes(aij->B,C->rmap->n,C->cmap->N,C->rmap->n,C->cmap->N);CHKERRQ(ierr);
3099     ierr = MatSetBlockSizesFromMats(aij->B,B,B);CHKERRQ(ierr);
3100     ierr = MatSetType(aij->B,MATSEQAIJ);CHKERRQ(ierr);
3101     Bdisassembled = PETSC_TRUE;
3102   }
3103   if (B) {
3104     Baij = (Mat_SeqAIJ*)B->data;
3105     if (pattern == DIFFERENT_NONZERO_PATTERN) {
3106       ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
3107       for (i=0; i<B->rmap->n; i++) {
3108 	nz[i] = Baij->i[i+1] - Baij->i[i];
3109       }
3110       ierr = MatSeqAIJSetPreallocation(aij->B,0,nz);CHKERRQ(ierr);
3111       ierr = PetscFree(nz);CHKERRQ(ierr);
3112     }
3113 
3114     ierr  = PetscLayoutGetRange(C->rmap,&rstart,&rend);CHKERRQ(ierr);
3115     shift = rend-rstart;
3116     count = 0;
3117     rowindices = NULL;
3118     colindices = NULL;
3119     if (rowemb) {
3120       ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
3121     }
3122     if (ocolemb) {
3123       ierr = ISGetIndices(ocolemb,&colindices);CHKERRQ(ierr);
3124     }
3125     for (i=0; i<B->rmap->n; i++) {
3126       PetscInt row;
3127       row = i;
3128       if (rowindices) row = rowindices[i];
3129       for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
3130 	col  = Baij->j[count];
3131 	if (colindices) col = colindices[col];
3132 	if (Bdisassembled && col>=rstart) col += shift;
3133 	v    = Baij->a[count];
3134 	ierr = MatSetValues(aij->B,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
3135 	++count;
3136       }
3137     }
3138     /* No assembly for aij->B is necessary. */
3139     /* FIXME: set aij->B's nonzerostate correctly. */
3140   } else {
3141     ierr = MatSetUp(aij->B);CHKERRQ(ierr);
3142   }
3143   C->preallocated  = PETSC_TRUE;
3144   C->was_assembled = PETSC_FALSE;
3145   C->assembled     = PETSC_FALSE;
3146    /*
3147       C will need to be assembled so that aij->B can be compressed into local form in MatSetUpMultiply_MPIAIJ().
3148       Furthermore, its nonzerostate will need to be based on that of aij->A's and aij->B's.
3149    */
3150   PetscFunctionReturn(0);
3151 }
3152 
3153 /*
3154   B uses local indices with column indices ranging between 0 and N-n; they  must be interpreted using garray.
3155  */
3156 PetscErrorCode MatGetSeqMats_MPIAIJ(Mat C,Mat *A,Mat *B)
3157 {
3158   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)C->data;
3159 
3160   PetscFunctionBegin;
3161   PetscValidPointer(A,2);
3162   PetscValidPointer(B,3);
3163   /* FIXME: make sure C is assembled */
3164   *A = aij->A;
3165   *B = aij->B;
3166   /* Note that we don't incref *A and *B, so be careful! */
3167   PetscFunctionReturn(0);
3168 }
3169 
3170 /*
3171   Extract MPI submatrices encoded by pairs of IS that may live on subcomms of C.
3172   NOT SCALABLE due to the use of ISGetNonlocalIS() (see below).
3173 */
3174 PetscErrorCode MatGetSubMatricesMPI_MPIXAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[],
3175                                                  PetscErrorCode(*getsubmats_seq)(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat**),
3176 					         PetscErrorCode(*getlocalmats)(Mat,Mat*,Mat*),
3177 					         PetscErrorCode(*setseqmat)(Mat,IS,IS,MatStructure,Mat),
3178 					         PetscErrorCode(*setseqmats)(Mat,IS,IS,IS,MatStructure,Mat,Mat))
3179 {
3180   PetscErrorCode ierr;
3181   PetscMPIInt    isize,flag;
3182   PetscInt       i,ii,cismax,ispar;
3183   Mat            *A,*B;
3184   IS             *isrow_p,*iscol_p,*cisrow,*ciscol,*ciscol_p;
3185 
3186   PetscFunctionBegin;
3187   if (!ismax) PetscFunctionReturn(0);
3188 
3189   for (i = 0, cismax = 0; i < ismax; ++i) {
3190     PetscMPIInt isize;
3191     ierr = MPI_Comm_compare(((PetscObject)isrow[i])->comm,((PetscObject)iscol[i])->comm,&flag);CHKERRQ(ierr);
3192     if (flag != MPI_IDENT) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Row and column index sets must have the same communicator");
3193     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm, &isize);CHKERRQ(ierr);
3194     if (isize > 1) ++cismax;
3195   }
3196 
3197   /*
3198      If cismax is zero on all C's ranks, then and only then can we use purely sequential matrix extraction.
3199      ispar counts the number of parallel ISs across C's comm.
3200   */
3201   ierr = MPIU_Allreduce(&cismax,&ispar,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
3202   if (!ispar) { /* Sequential ISs only across C's comm, so can call the sequential matrix extraction subroutine. */
3203     ierr = (*getsubmats_seq)(C,ismax,isrow,iscol,scall,submat);CHKERRQ(ierr);
3204     PetscFunctionReturn(0);
3205   }
3206 
3207   /* if (ispar) */
3208   /*
3209     Construct the "complements" -- the off-processor indices -- of the iscol ISs for parallel ISs only.
3210     These are used to extract the off-diag portion of the resulting parallel matrix.
3211     The row IS for the off-diag portion is the same as for the diag portion,
3212     so we merely alias (without increfing) the row IS, while skipping those that are sequential.
3213   */
3214   ierr = PetscMalloc2(cismax,&cisrow,cismax,&ciscol);CHKERRQ(ierr);
3215   ierr = PetscMalloc1(cismax,&ciscol_p);CHKERRQ(ierr);
3216   for (i = 0, ii = 0; i < ismax; ++i) {
3217     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3218     if (isize > 1) {
3219       /*
3220 	 TODO: This is the part that's ***NOT SCALABLE***.
3221 	 To fix this we need to extract just the indices of C's nonzero columns
3222 	 that lie on the intersection of isrow[i] and ciscol[ii] -- the nonlocal
3223 	 part of iscol[i] -- without actually computing ciscol[ii]. This also has
3224 	 to be done without serializing on the IS list, so, most likely, it is best
3225 	 done by rewriting MatGetSubMatrices_MPIAIJ() directly.
3226       */
3227       ierr = ISGetNonlocalIS(iscol[i],&(ciscol[ii]));CHKERRQ(ierr);
3228       /* Now we have to
3229 	 (a) make sure ciscol[ii] is sorted, since, even if the off-proc indices
3230 	     were sorted on each rank, concatenated they might no longer be sorted;
3231 	 (b) Use ISSortPermutation() to construct ciscol_p, the mapping from the
3232 	     indices in the nondecreasing order to the original index positions.
3233 	 If ciscol[ii] is strictly increasing, the permutation IS is NULL.
3234       */
3235       ierr = ISSortPermutation(ciscol[ii],PETSC_FALSE,ciscol_p+ii);CHKERRQ(ierr);
3236       ierr = ISSort(ciscol[ii]);CHKERRQ(ierr);
3237       ++ii;
3238     }
3239   }
3240   ierr = PetscMalloc2(ismax,&isrow_p,ismax,&iscol_p);CHKERRQ(ierr);
3241   for (i = 0, ii = 0; i < ismax; ++i) {
3242     PetscInt       j,issize;
3243     const PetscInt *indices;
3244 
3245     /*
3246        Permute the indices into a nondecreasing order. Reject row and col indices with duplicates.
3247      */
3248     ierr = ISSortPermutation(isrow[i],PETSC_FALSE,isrow_p+i);CHKERRQ(ierr);
3249     ierr = ISSort(isrow[i]);CHKERRQ(ierr);
3250     ierr = ISGetLocalSize(isrow[i],&issize);CHKERRQ(ierr);
3251     ierr = ISGetIndices(isrow[i],&indices);CHKERRQ(ierr);
3252     for (j = 1; j < issize; ++j) {
3253       if (indices[j] == indices[j-1]) {
3254 	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]);
3255       }
3256     }
3257     ierr = ISRestoreIndices(isrow[i],&indices);CHKERRQ(ierr);
3258 
3259 
3260     ierr = ISSortPermutation(iscol[i],PETSC_FALSE,iscol_p+i);CHKERRQ(ierr);
3261     ierr = ISSort(iscol[i]);CHKERRQ(ierr);
3262     ierr = ISGetLocalSize(iscol[i],&issize);CHKERRQ(ierr);
3263     ierr = ISGetIndices(iscol[i],&indices);CHKERRQ(ierr);
3264     for (j = 1; j < issize; ++j) {
3265       if (indices[j-1] == indices[j]) {
3266 	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]);
3267       }
3268     }
3269     ierr = ISRestoreIndices(iscol[i],&indices);CHKERRQ(ierr);
3270     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3271     if (isize > 1) {
3272       cisrow[ii] = isrow[i];
3273       ++ii;
3274     }
3275   }
3276   /*
3277     Allocate the necessary arrays to hold the resulting parallel matrices as well as the intermediate
3278     array of sequential matrices underlying the resulting parallel matrices.
3279     Which arrays to allocate is based on the value of MatReuse scall and whether ISs are sorted and/or
3280     contain duplicates.
3281 
3282     There are as many diag matrices as there are original index sets. There are only as many parallel
3283     and off-diag matrices, as there are parallel (comm size > 1) index sets.
3284 
3285     ARRAYS that can hold Seq matrices get allocated in any event -- either here or by getsubmats_seq():
3286     - If the array of MPI matrices already exists and is being reused, we need to allocate the array
3287       and extract the underlying seq matrices into it to serve as placeholders, into which getsubmats_seq
3288       will deposite the extracted diag and off-diag parts. Thus, we allocate the A&B arrays and fill them
3289       with A[i] and B[ii] extracted from the corresponding MPI submat.
3290     - However, if the rows, A's column indices or B's column indices are not sorted, the extracted A[i] & B[ii]
3291       will have a different order from what getsubmats_seq expects.  To handle this case -- indicated
3292       by a nonzero isrow_p[i], iscol_p[i], or ciscol_p[ii] -- we duplicate A[i] --> AA[i], B[ii] --> BB[ii]
3293       (retrieve composed AA[i] or BB[ii]) and reuse them here. AA[i] and BB[ii] are then used to permute its
3294       values into A[i] and B[ii] sitting inside the corresponding submat.
3295     - If no reuse is taking place then getsubmats_seq will allocate the A&B arrays and create the corresponding
3296       A[i], B[ii], AA[i] or BB[ii] matrices.
3297   */
3298   /* Parallel matrix array is allocated here only if no reuse is taking place. If reused, it is passed in by the caller. */
3299   if (scall == MAT_INITIAL_MATRIX) {
3300     ierr = PetscMalloc1(ismax,submat);CHKERRQ(ierr);
3301   }
3302 
3303   /* Now obtain the sequential A and B submatrices separately. */
3304   /* scall=MAT_REUSE_MATRIX is not handled yet, because getsubmats_seq() requires reuse of A and B */
3305   ierr = (*getsubmats_seq)(C,ismax,isrow,iscol,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
3306   ierr = (*getsubmats_seq)(C,cismax,cisrow,ciscol,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
3307 
3308   /*
3309     If scall == MAT_REUSE_MATRIX AND the permutations are NULL, we are done, since the sequential
3310     matrices A & B have been extracted directly into the parallel matrices containing them, or
3311     simply into the sequential matrix identical with the corresponding A (if isize == 1).
3312     Note that in that case colmap doesn't need to be rebuilt, since the matrices are expected
3313     to have the same sparsity pattern.
3314     Otherwise, A and/or B have to be properly embedded into C's index spaces and the correct colmap
3315     must be constructed for C. This is done by setseqmat(s).
3316   */
3317   for (i = 0, ii = 0; i < ismax; ++i) {
3318     /*
3319        TODO: cache ciscol, permutation ISs and maybe cisrow? What about isrow & iscol?
3320        That way we can avoid sorting and computing permutations when reusing.
3321        To this end:
3322         - remove the old cache, if it exists, when extracting submatrices with MAT_INITIAL_MATRIX
3323 	- if caching arrays to hold the ISs, make and compose a container for them so that it can
3324 	  be destroyed upon destruction of C (use PetscContainerUserDestroy() to clear out the contents).
3325     */
3326     MatStructure pattern;
3327     pattern = DIFFERENT_NONZERO_PATTERN;
3328 
3329     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3330     /* Construct submat[i] from the Seq pieces A (and B, if necessary). */
3331     if (isize > 1) {
3332       if (scall == MAT_INITIAL_MATRIX) {
3333 	ierr = MatCreate(((PetscObject)isrow[i])->comm,(*submat)+i);CHKERRQ(ierr);
3334 	ierr = MatSetSizes((*submat)[i],A[i]->rmap->n,A[i]->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3335 	ierr = MatSetType((*submat)[i],MATMPIAIJ);CHKERRQ(ierr);
3336 	ierr = PetscLayoutSetUp((*submat)[i]->rmap);CHKERRQ(ierr);
3337 	ierr = PetscLayoutSetUp((*submat)[i]->cmap);CHKERRQ(ierr);
3338       }
3339       /*
3340 	For each parallel isrow[i], insert the extracted sequential matrices into the parallel matrix.
3341       */
3342       {
3343 	Mat AA,BB;
3344         AA = A[i];
3345         BB = B[ii];
3346 	if (AA || BB) {
3347 	  ierr = setseqmats((*submat)[i],isrow_p[i],iscol_p[i],ciscol_p[ii],pattern,AA,BB);CHKERRQ(ierr);
3348 	  ierr = MatAssemblyBegin((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3349 	  ierr = MatAssemblyEnd((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3350 	}
3351 
3352         ierr = MatDestroy(&AA);CHKERRQ(ierr);
3353       }
3354       ierr = ISDestroy(ciscol+ii);CHKERRQ(ierr);
3355       ierr = ISDestroy(ciscol_p+ii);CHKERRQ(ierr);
3356       ++ii;
3357     } else { /* if (isize == 1) */
3358       if (scall == MAT_REUSE_MATRIX) {
3359         ierr = MatDestroy(&(*submat)[i]);CHKERRQ(ierr);
3360       }
3361       if (isrow_p[i] || iscol_p[i]) {
3362         ierr = MatDuplicate(A[i],MAT_DO_NOT_COPY_VALUES,(*submat)+i);CHKERRQ(ierr);
3363         ierr = setseqmat((*submat)[i],isrow_p[i],iscol_p[i],pattern,A[i]);CHKERRQ(ierr);
3364 	/* Otherwise A is extracted straight into (*submats)[i]. */
3365 	/* TODO: Compose A[i] on (*submat([i] for future use, if ((isrow_p[i] || iscol_p[i]) && MAT_INITIAL_MATRIX). */
3366 	ierr = MatDestroy(A+i);CHKERRQ(ierr);
3367       } else (*submat)[i] = A[i];
3368     }
3369     ierr = ISDestroy(&isrow_p[i]);CHKERRQ(ierr);
3370     ierr = ISDestroy(&iscol_p[i]);CHKERRQ(ierr);
3371   }
3372   ierr = PetscFree2(cisrow,ciscol);CHKERRQ(ierr);
3373   ierr = PetscFree2(isrow_p,iscol_p);CHKERRQ(ierr);
3374   ierr = PetscFree(ciscol_p);CHKERRQ(ierr);
3375   ierr = PetscFree(A);CHKERRQ(ierr);
3376   ierr = MatDestroySubMatrices(cismax,&B);CHKERRQ(ierr);
3377   PetscFunctionReturn(0);
3378 }
3379 
3380 PetscErrorCode MatGetSubMatricesMPI_MPIAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
3381 {
3382   PetscErrorCode ierr;
3383 
3384   PetscFunctionBegin;
3385   ierr = MatGetSubMatricesMPI_MPIXAIJ(C,ismax,isrow,iscol,scall,submat,MatGetSubMatrices_MPIAIJ,MatGetSeqMats_MPIAIJ,MatSetSeqMat_SeqAIJ,MatSetSeqMats_MPIAIJ);CHKERRQ(ierr);
3386   PetscFunctionReturn(0);
3387 }
3388