xref: /petsc/src/mat/impls/aij/mpi/mpiov.c (revision b360545fa64ec79fb6783c6f542b37bac312292f)
1 /*
2    Routines to compute overlapping regions of a parallel MPI matrix
3   and to find submatrices that were shared across processors.
4 */
5 #include <../src/mat/impls/aij/seq/aij.h>
6 #include <../src/mat/impls/aij/mpi/mpiaij.h>
7 #include <petscbt.h>
8 #include <petscsf.h>
9 
10 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once(Mat,PetscInt,IS*);
11 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local(Mat,PetscInt,char**,PetscInt*,PetscInt**,PetscTable*);
12 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive(Mat,PetscInt,PetscInt**,PetscInt**,PetscInt*);
13 extern PetscErrorCode MatGetRow_MPIAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);
14 extern PetscErrorCode MatRestoreRow_MPIAIJ(Mat,PetscInt,PetscInt*,PetscInt**,PetscScalar**);
15 
16 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once_Scalable(Mat,PetscInt,IS*);
17 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local_Scalable(Mat,PetscInt,IS*);
18 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Send_Scalable(Mat,PetscInt,PetscMPIInt,PetscMPIInt *,PetscInt *, PetscInt *,PetscInt **,PetscInt **);
19 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive_Scalable(Mat,PetscInt,IS*,PetscInt,PetscInt *);
20 
21 
22 PetscErrorCode MatIncreaseOverlap_MPIAIJ(Mat C,PetscInt imax,IS is[],PetscInt ov)
23 {
24   PetscErrorCode ierr;
25   PetscInt       i;
26 
27   PetscFunctionBegin;
28   if (ov < 0) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap specified");
29   for (i=0; i<ov; ++i) {
30     ierr = MatIncreaseOverlap_MPIAIJ_Once(C,imax,is);CHKERRQ(ierr);
31   }
32   PetscFunctionReturn(0);
33 }
34 
35 PetscErrorCode MatIncreaseOverlap_MPIAIJ_Scalable(Mat C,PetscInt imax,IS is[],PetscInt ov)
36 {
37   PetscErrorCode ierr;
38   PetscInt       i;
39 
40   PetscFunctionBegin;
41   if (ov < 0) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap specified");
42   for (i=0; i<ov; ++i) {
43     ierr = MatIncreaseOverlap_MPIAIJ_Once_Scalable(C,imax,is);CHKERRQ(ierr);
44   }
45   PetscFunctionReturn(0);
46 }
47 
48 
49 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once_Scalable(Mat mat,PetscInt nidx,IS is[])
50 {
51   PetscErrorCode   ierr;
52   MPI_Comm         comm;
53   PetscInt        *length,length_i,tlength,*remoterows,nrrows,reducednrrows,*rrow_ranks,*rrow_isids,i,j,owner;
54   PetscInt         *tosizes,*tosizes_temp,*toffsets,*fromsizes,*todata,*fromdata;
55   PetscInt         nrecvrows,*sbsizes = 0,*sbdata = 0;
56   const PetscInt  *indices_i,**indices;
57   PetscLayout      rmap;
58   PetscMPIInt      rank,size,*toranks,*fromranks,nto,nfrom;
59   PetscSF          sf;
60   PetscSFNode     *remote;
61 
62   PetscFunctionBegin;
63   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
64   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
65   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
66   /* get row map to determine where rows should be going */
67   ierr = MatGetLayouts(mat,&rmap,NULL);CHKERRQ(ierr);
68   /* retrieve IS data and put all together so that we
69    * can optimize communication
70    *  */
71   ierr = PetscCalloc2(nidx,(PetscInt ***)&indices,nidx,&length);CHKERRQ(ierr);
72   for (i=0,tlength=0; i<nidx; i++){
73     ierr = ISGetLocalSize(is[i],&length[i]);CHKERRQ(ierr);
74     tlength += length[i];
75     ierr = ISGetIndices(is[i],&indices[i]);CHKERRQ(ierr);
76   }
77   /* find these rows on remote processors */
78   ierr = PetscCalloc3(tlength,&remoterows,tlength,&rrow_ranks,tlength,&rrow_isids);CHKERRQ(ierr);
79   ierr = PetscCalloc3(size,&toranks,2*size,&tosizes,size,&tosizes_temp);CHKERRQ(ierr);
80   nrrows = 0;
81   for (i=0; i<nidx; i++){
82     length_i     = length[i];
83     indices_i    = indices[i];
84     for (j=0; j<length_i; j++){
85       owner = -1;
86       ierr = PetscLayoutFindOwner(rmap,indices_i[j],&owner);CHKERRQ(ierr);
87       /* remote processors */
88       if (owner != rank){
89         tosizes_temp[owner]++; /* number of rows to owner */
90         rrow_ranks[nrrows]  = owner; /* processor */
91         rrow_isids[nrrows]   = i; /* is id */
92         remoterows[nrrows++] = indices_i[j]; /* row */
93       }
94     }
95     ierr = ISRestoreIndices(is[i],&indices[i]);CHKERRQ(ierr);
96   }
97   ierr = PetscFree2(indices,length);CHKERRQ(ierr);
98   /* test if we need to exchange messages
99    * generally speaking, we do not need to exchange
100    * data when overlap is 1
101    * */
102   ierr = MPIU_Allreduce(&nrrows,&reducednrrows,1,MPIU_INT,MPIU_MAX,comm);CHKERRQ(ierr);
103   /* we do not have any messages
104    * It usually corresponds to overlap 1
105    * */
106   if (!reducednrrows){
107     ierr = PetscFree3(toranks,tosizes,tosizes_temp);CHKERRQ(ierr);
108     ierr = PetscFree3(remoterows,rrow_ranks,rrow_isids);CHKERRQ(ierr);
109     ierr = MatIncreaseOverlap_MPIAIJ_Local_Scalable(mat,nidx,is);CHKERRQ(ierr);
110     PetscFunctionReturn(0);
111   }
112   nto = 0;
113   /* send sizes and ranks for building a two-sided communcation */
114   for (i=0; i<size; i++){
115    if (tosizes_temp[i]){
116      tosizes[nto*2]  = tosizes_temp[i]*2; /* size */
117      tosizes_temp[i] = nto; /* a map from processor to index */
118      toranks[nto++]  = i; /* processor */
119    }
120   }
121   ierr = PetscCalloc1(nto+1,&toffsets);CHKERRQ(ierr);
122   for (i=0; i<nto; i++){
123     toffsets[i+1]  = toffsets[i]+tosizes[2*i]; /* offsets */
124     tosizes[2*i+1] = toffsets[i]; /* offsets to send */
125   }
126   /* send information to other processors */
127   ierr = PetscCommBuildTwoSided(comm,2,MPIU_INT,nto,toranks,tosizes,&nfrom,&fromranks,&fromsizes);CHKERRQ(ierr);
128   nrecvrows = 0;
129   for (i=0; i<nfrom; i++) nrecvrows += fromsizes[2*i];
130   ierr = PetscMalloc1(nrecvrows,&remote);CHKERRQ(ierr);
131   nrecvrows = 0;
132   for (i=0; i<nfrom; i++){
133     for (j=0; j<fromsizes[2*i]; j++){
134       remote[nrecvrows].rank    = fromranks[i];
135       remote[nrecvrows++].index = fromsizes[2*i+1]+j;
136     }
137   }
138   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
139   ierr = PetscSFSetGraph(sf,nrecvrows,nrecvrows,NULL,PETSC_OWN_POINTER,remote,PETSC_OWN_POINTER);CHKERRQ(ierr);
140   /* use two-sided communication by default since OPENMPI has some bugs for one-sided one */
141   ierr = PetscSFSetType(sf,PETSCSFBASIC);CHKERRQ(ierr);
142   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
143   /* message pair <no of is, row>  */
144   ierr = PetscCalloc2(2*nrrows,&todata,nrecvrows,&fromdata);CHKERRQ(ierr);
145   for (i=0; i<nrrows; i++){
146     owner = rrow_ranks[i]; /* processor */
147     j     = tosizes_temp[owner]; /* index */
148     todata[toffsets[j]++] = rrow_isids[i];
149     todata[toffsets[j]++] = remoterows[i];
150   }
151   ierr = PetscFree3(toranks,tosizes,tosizes_temp);CHKERRQ(ierr);
152   ierr = PetscFree3(remoterows,rrow_ranks,rrow_isids);CHKERRQ(ierr);
153   ierr = PetscFree(toffsets);CHKERRQ(ierr);
154   ierr = PetscSFBcastBegin(sf,MPIU_INT,todata,fromdata);CHKERRQ(ierr);
155   ierr = PetscSFBcastEnd(sf,MPIU_INT,todata,fromdata);CHKERRQ(ierr);
156   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
157   /* send rows belonging to the remote so that then we could get the overlapping data back */
158   ierr = MatIncreaseOverlap_MPIAIJ_Send_Scalable(mat,nidx,nfrom,fromranks,fromsizes,fromdata,&sbsizes,&sbdata);CHKERRQ(ierr);
159   ierr = PetscFree2(todata,fromdata);CHKERRQ(ierr);
160   ierr = PetscFree(fromsizes);CHKERRQ(ierr);
161   ierr = PetscCommBuildTwoSided(comm,2,MPIU_INT,nfrom,fromranks,sbsizes,&nto,&toranks,&tosizes);CHKERRQ(ierr);
162   ierr = PetscFree(fromranks);CHKERRQ(ierr);
163   nrecvrows = 0;
164   for (i=0; i<nto; i++) nrecvrows += tosizes[2*i];
165   ierr = PetscCalloc1(nrecvrows,&todata);CHKERRQ(ierr);
166   ierr = PetscMalloc1(nrecvrows,&remote);CHKERRQ(ierr);
167   nrecvrows = 0;
168   for (i=0; i<nto; i++){
169     for (j=0; j<tosizes[2*i]; j++){
170       remote[nrecvrows].rank    = toranks[i];
171       remote[nrecvrows++].index = tosizes[2*i+1]+j;
172     }
173   }
174   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
175   ierr = PetscSFSetGraph(sf,nrecvrows,nrecvrows,NULL,PETSC_OWN_POINTER,remote,PETSC_OWN_POINTER);CHKERRQ(ierr);
176   /* use two-sided communication by default since OPENMPI has some bugs for one-sided one */
177   ierr = PetscSFSetType(sf,PETSCSFBASIC);CHKERRQ(ierr);
178   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
179   /* overlap communication and computation */
180   ierr = PetscSFBcastBegin(sf,MPIU_INT,sbdata,todata);CHKERRQ(ierr);
181   ierr = MatIncreaseOverlap_MPIAIJ_Local_Scalable(mat,nidx,is);CHKERRQ(ierr);
182   ierr = PetscSFBcastEnd(sf,MPIU_INT,sbdata,todata);CHKERRQ(ierr);
183   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
184   ierr = PetscFree2(sbdata,sbsizes);CHKERRQ(ierr);
185   ierr = MatIncreaseOverlap_MPIAIJ_Receive_Scalable(mat,nidx,is,nrecvrows,todata);CHKERRQ(ierr);
186   ierr = PetscFree(toranks);CHKERRQ(ierr);
187   ierr = PetscFree(tosizes);CHKERRQ(ierr);
188   ierr = PetscFree(todata);CHKERRQ(ierr);
189   PetscFunctionReturn(0);
190 }
191 
192 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive_Scalable(Mat mat,PetscInt nidx, IS is[], PetscInt nrecvs, PetscInt *recvdata)
193 {
194   PetscInt         *isz,isz_i,i,j,is_id, data_size;
195   PetscInt          col,lsize,max_lsize,*indices_temp, *indices_i;
196   const PetscInt   *indices_i_temp;
197   PetscErrorCode    ierr;
198 
199   PetscFunctionBegin;
200   max_lsize = 0;
201   ierr = PetscMalloc1(nidx,&isz);CHKERRQ(ierr);
202   for (i=0; i<nidx; i++){
203     ierr = ISGetLocalSize(is[i],&lsize);CHKERRQ(ierr);
204     max_lsize = lsize>max_lsize ? lsize:max_lsize;
205     isz[i]    = lsize;
206   }
207   ierr = PetscMalloc1((max_lsize+nrecvs)*nidx,&indices_temp);CHKERRQ(ierr);
208   for (i=0; i<nidx; i++){
209     ierr = ISGetIndices(is[i],&indices_i_temp);CHKERRQ(ierr);
210     ierr = PetscMemcpy(indices_temp+i*(max_lsize+nrecvs),indices_i_temp, sizeof(PetscInt)*isz[i]);CHKERRQ(ierr);
211     ierr = ISRestoreIndices(is[i],&indices_i_temp);CHKERRQ(ierr);
212     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
213   }
214   /* retrieve information to get row id and its overlap */
215   for (i=0; i<nrecvs; ){
216     is_id      = recvdata[i++];
217     data_size  = recvdata[i++];
218     indices_i  = indices_temp+(max_lsize+nrecvs)*is_id;
219     isz_i      = isz[is_id];
220     for (j=0; j< data_size; j++){
221       col = recvdata[i++];
222       indices_i[isz_i++] = col;
223     }
224     isz[is_id] = isz_i;
225   }
226   /* remove duplicate entities */
227   for (i=0; i<nidx; i++){
228     indices_i  = indices_temp+(max_lsize+nrecvs)*i;
229     isz_i      = isz[i];
230     ierr = PetscSortRemoveDupsInt(&isz_i,indices_i);CHKERRQ(ierr);
231     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz_i,indices_i,PETSC_COPY_VALUES,&is[i]);CHKERRQ(ierr);
232   }
233   ierr = PetscFree(isz);CHKERRQ(ierr);
234   ierr = PetscFree(indices_temp);CHKERRQ(ierr);
235   PetscFunctionReturn(0);
236 }
237 
238 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Send_Scalable(Mat mat,PetscInt nidx, PetscMPIInt nfrom,PetscMPIInt *fromranks,PetscInt *fromsizes, PetscInt *fromrows, PetscInt **sbrowsizes, PetscInt **sbrows)
239 {
240   PetscLayout       rmap,cmap;
241   PetscInt          i,j,k,l,*rows_i,*rows_data_ptr,**rows_data,max_fszs,rows_pos,*rows_pos_i;
242   PetscInt          is_id,tnz,an,bn,rstart,cstart,row,start,end,col,totalrows,*sbdata;
243   PetscInt         *indv_counts,indvc_ij,*sbsizes,*indices_tmp,*offsets;
244   const PetscInt   *gcols,*ai,*aj,*bi,*bj;
245   Mat               amat,bmat;
246   PetscMPIInt       rank;
247   PetscBool         done;
248   MPI_Comm          comm;
249   PetscErrorCode    ierr;
250 
251   PetscFunctionBegin;
252   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
253   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
254   ierr = MatMPIAIJGetSeqAIJ(mat,&amat,&bmat,&gcols);CHKERRQ(ierr);
255   /* Even if the mat is symmetric, we still assume it is not symmetric */
256   ierr = MatGetRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
257   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
258   ierr = MatGetRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
259   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
260   /* total number of nonzero values is used to estimate the memory usage in the next step */
261   tnz  = ai[an]+bi[bn];
262   ierr = MatGetLayouts(mat,&rmap,&cmap);CHKERRQ(ierr);
263   ierr = PetscLayoutGetRange(rmap,&rstart,NULL);CHKERRQ(ierr);
264   ierr = PetscLayoutGetRange(cmap,&cstart,NULL);CHKERRQ(ierr);
265   /* to find the longest message */
266   max_fszs = 0;
267   for (i=0; i<nfrom; i++) max_fszs = fromsizes[2*i]>max_fszs ? fromsizes[2*i]:max_fszs;
268   /* better way to estimate number of nonzero in the mat??? */
269   ierr = PetscCalloc5(max_fszs*nidx,&rows_data_ptr,nidx,&rows_data,nidx,&rows_pos_i,nfrom*nidx,&indv_counts,tnz,&indices_tmp);CHKERRQ(ierr);
270   for (i=0; i<nidx; i++) rows_data[i] = rows_data_ptr+max_fszs*i;
271   rows_pos  = 0;
272   totalrows = 0;
273   for (i=0; i<nfrom; i++){
274     ierr = PetscMemzero(rows_pos_i,sizeof(PetscInt)*nidx);CHKERRQ(ierr);
275     /* group data together */
276     for (j=0; j<fromsizes[2*i]; j+=2){
277       is_id                       = fromrows[rows_pos++];/* no of is */
278       rows_i                      = rows_data[is_id];
279       rows_i[rows_pos_i[is_id]++] = fromrows[rows_pos++];/* row */
280     }
281     /* estimate a space to avoid multiple allocations  */
282     for (j=0; j<nidx; j++){
283       indvc_ij = 0;
284       rows_i   = rows_data[j];
285       for (l=0; l<rows_pos_i[j]; l++){
286         row    = rows_i[l]-rstart;
287         start  = ai[row];
288         end    = ai[row+1];
289         for (k=start; k<end; k++){ /* Amat */
290           col = aj[k] + cstart;
291           indices_tmp[indvc_ij++] = col;/* do not count the rows from the original rank */
292         }
293         start = bi[row];
294         end   = bi[row+1];
295         for (k=start; k<end; k++) { /* Bmat */
296           col = gcols[bj[k]];
297           indices_tmp[indvc_ij++] = col;
298         }
299       }
300       ierr = PetscSortRemoveDupsInt(&indvc_ij,indices_tmp);CHKERRQ(ierr);
301       indv_counts[i*nidx+j] = indvc_ij;
302       totalrows            += indvc_ij;
303     }
304   }
305   /* message triple <no of is, number of rows, rows> */
306   ierr = PetscCalloc2(totalrows+nidx*nfrom*2,&sbdata,2*nfrom,&sbsizes);CHKERRQ(ierr);
307   totalrows = 0;
308   rows_pos  = 0;
309   /* use this code again */
310   for (i=0;i<nfrom;i++){
311     ierr = PetscMemzero(rows_pos_i,sizeof(PetscInt)*nidx);CHKERRQ(ierr);
312     for (j=0; j<fromsizes[2*i]; j+=2){
313       is_id                       = fromrows[rows_pos++];
314       rows_i                      = rows_data[is_id];
315       rows_i[rows_pos_i[is_id]++] = fromrows[rows_pos++];
316     }
317     /* add data  */
318     for (j=0; j<nidx; j++){
319       if (!indv_counts[i*nidx+j]) continue;
320       indvc_ij = 0;
321       sbdata[totalrows++] = j;
322       sbdata[totalrows++] = indv_counts[i*nidx+j];
323       sbsizes[2*i]       += 2;
324       rows_i              = rows_data[j];
325       for (l=0; l<rows_pos_i[j]; l++){
326         row   = rows_i[l]-rstart;
327         start = ai[row];
328         end   = ai[row+1];
329         for (k=start; k<end; k++){ /* Amat */
330           col = aj[k] + cstart;
331           indices_tmp[indvc_ij++] = col;
332         }
333         start = bi[row];
334         end   = bi[row+1];
335         for (k=start; k<end; k++) { /* Bmat */
336           col = gcols[bj[k]];
337           indices_tmp[indvc_ij++] = col;
338         }
339       }
340       ierr = PetscSortRemoveDupsInt(&indvc_ij,indices_tmp);CHKERRQ(ierr);
341       sbsizes[2*i]  += indvc_ij;
342       ierr = PetscMemcpy(sbdata+totalrows,indices_tmp,sizeof(PetscInt)*indvc_ij);CHKERRQ(ierr);
343       totalrows += indvc_ij;
344     }
345   }
346   ierr = PetscCalloc1(nfrom+1,&offsets);CHKERRQ(ierr);
347   for (i=0; i<nfrom; i++){
348     offsets[i+1]   = offsets[i] + sbsizes[2*i];
349     sbsizes[2*i+1] = offsets[i];
350   }
351   ierr = PetscFree(offsets);CHKERRQ(ierr);
352   if (sbrowsizes) *sbrowsizes = sbsizes;
353   if (sbrows) *sbrows = sbdata;
354   ierr = PetscFree5(rows_data_ptr,rows_data,rows_pos_i,indv_counts,indices_tmp);CHKERRQ(ierr);
355   ierr = MatRestoreRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
356   ierr = MatRestoreRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
357   PetscFunctionReturn(0);
358 }
359 
360 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local_Scalable(Mat mat,PetscInt nidx, IS is[])
361 {
362   const PetscInt   *gcols,*ai,*aj,*bi,*bj, *indices;
363   PetscInt          tnz,an,bn,i,j,row,start,end,rstart,cstart,col,k,*indices_temp;
364   PetscInt          lsize,lsize_tmp,owner;
365   PetscMPIInt       rank;
366   Mat               amat,bmat;
367   PetscBool         done;
368   PetscLayout       cmap,rmap;
369   MPI_Comm          comm;
370   PetscErrorCode    ierr;
371 
372   PetscFunctionBegin;
373   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
374   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
375   ierr = MatMPIAIJGetSeqAIJ(mat,&amat,&bmat,&gcols);CHKERRQ(ierr);
376   ierr = MatGetRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
377   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
378   ierr = MatGetRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
379   if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"can not get row IJ \n");
380   /* is it a safe way to compute number of nonzero values ? */
381   tnz  = ai[an]+bi[bn];
382   ierr = MatGetLayouts(mat,&rmap,&cmap);CHKERRQ(ierr);
383   ierr = PetscLayoutGetRange(rmap,&rstart,NULL);CHKERRQ(ierr);
384   ierr = PetscLayoutGetRange(cmap,&cstart,NULL);CHKERRQ(ierr);
385   /* it is a better way to estimate memory than the old implementation
386    * where global size of matrix is used
387    * */
388   ierr = PetscMalloc1(tnz,&indices_temp);CHKERRQ(ierr);
389   for (i=0; i<nidx; i++) {
390     ierr = ISGetLocalSize(is[i],&lsize);CHKERRQ(ierr);
391     ierr = ISGetIndices(is[i],&indices);CHKERRQ(ierr);
392     lsize_tmp = 0;
393     for (j=0; j<lsize; j++) {
394       owner = -1;
395       row   = indices[j];
396       ierr = PetscLayoutFindOwner(rmap,row,&owner);CHKERRQ(ierr);
397       if (owner != rank) continue;
398       /* local number */
399       row  -= rstart;
400       start = ai[row];
401       end   = ai[row+1];
402       for (k=start; k<end; k++) { /* Amat */
403         col = aj[k] + cstart;
404         indices_temp[lsize_tmp++] = col;
405       }
406       start = bi[row];
407       end   = bi[row+1];
408       for (k=start; k<end; k++) { /* Bmat */
409         col = gcols[bj[k]];
410         indices_temp[lsize_tmp++] = col;
411       }
412     }
413    ierr = ISRestoreIndices(is[i],&indices);CHKERRQ(ierr);
414    ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
415    ierr = PetscSortRemoveDupsInt(&lsize_tmp,indices_temp);CHKERRQ(ierr);
416    ierr = ISCreateGeneral(PETSC_COMM_SELF,lsize_tmp,indices_temp,PETSC_COPY_VALUES,&is[i]);CHKERRQ(ierr);
417   }
418   ierr = PetscFree(indices_temp);CHKERRQ(ierr);
419   ierr = MatRestoreRowIJ(amat,0,PETSC_FALSE,PETSC_FALSE,&an,&ai,&aj,&done);CHKERRQ(ierr);
420   ierr = MatRestoreRowIJ(bmat,0,PETSC_FALSE,PETSC_FALSE,&bn,&bi,&bj,&done);CHKERRQ(ierr);
421   PetscFunctionReturn(0);
422 }
423 
424 
425 /*
426   Sample message format:
427   If a processor A wants processor B to process some elements corresponding
428   to index sets is[1],is[5]
429   mesg [0] = 2   (no of index sets in the mesg)
430   -----------
431   mesg [1] = 1 => is[1]
432   mesg [2] = sizeof(is[1]);
433   -----------
434   mesg [3] = 5  => is[5]
435   mesg [4] = sizeof(is[5]);
436   -----------
437   mesg [5]
438   mesg [n]  datas[1]
439   -----------
440   mesg[n+1]
441   mesg[m]  data(is[5])
442   -----------
443 
444   Notes:
445   nrqs - no of requests sent (or to be sent out)
446   nrqr - no of requests recieved (which have to be or which have been processed
447 */
448 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Once(Mat C,PetscInt imax,IS is[])
449 {
450   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
451   PetscMPIInt    *w1,*w2,nrqr,*w3,*w4,*onodes1,*olengths1,*onodes2,*olengths2;
452   const PetscInt **idx,*idx_i;
453   PetscInt       *n,**data,len;
454 #if defined(PETSC_USE_CTABLE)
455   PetscTable     *table_data,table_data_i;
456   PetscInt       *tdata,tcount,tcount_max;
457 #else
458   PetscInt       *data_i,*d_p;
459 #endif
460   PetscErrorCode ierr;
461   PetscMPIInt    size,rank,tag1,tag2;
462   PetscInt       M,i,j,k,**rbuf,row,proc = 0,nrqs,msz,**outdat,**ptr;
463   PetscInt       *ctr,*pa,*tmp,*isz,*isz1,**xdata,**rbuf2;
464   PetscBT        *table;
465   MPI_Comm       comm;
466   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2;
467   MPI_Status     *s_status,*recv_status;
468   char           *t_p;
469 
470   PetscFunctionBegin;
471   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
472   size = c->size;
473   rank = c->rank;
474   M    = C->rmap->N;
475 
476   ierr = PetscObjectGetNewTag((PetscObject)C,&tag1);CHKERRQ(ierr);
477   ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
478 
479   ierr = PetscMalloc2(imax,&idx,imax,&n);CHKERRQ(ierr);
480 
481   for (i=0; i<imax; i++) {
482     ierr = ISGetIndices(is[i],&idx[i]);CHKERRQ(ierr);
483     ierr = ISGetLocalSize(is[i],&n[i]);CHKERRQ(ierr);
484   }
485 
486   /* evaluate communication - mesg to who,length of mesg, and buffer space
487      required. Based on this, buffers are allocated, and data copied into them  */
488   ierr = PetscMalloc4(size,&w1,size,&w2,size,&w3,size,&w4);CHKERRQ(ierr);
489   ierr = PetscMemzero(w1,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
490   ierr = PetscMemzero(w2,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
491   ierr = PetscMemzero(w3,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
492   for (i=0; i<imax; i++) {
493     ierr  = PetscMemzero(w4,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialise work vector*/
494     idx_i = idx[i];
495     len   = n[i];
496     for (j=0; j<len; j++) {
497       row = idx_i[j];
498       if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Index set cannot have negative entries");
499       ierr = PetscLayoutFindOwner(C->rmap,row,&proc);CHKERRQ(ierr);
500       w4[proc]++;
501     }
502     for (j=0; j<size; j++) {
503       if (w4[j]) { w1[j] += w4[j]; w3[j]++;}
504     }
505   }
506 
507   nrqs     = 0;              /* no of outgoing messages */
508   msz      = 0;              /* total mesg length (for all proc */
509   w1[rank] = 0;              /* no mesg sent to intself */
510   w3[rank] = 0;
511   for (i=0; i<size; i++) {
512     if (w1[i])  {w2[i] = 1; nrqs++;} /* there exists a message to proc i */
513   }
514   /* pa - is list of processors to communicate with */
515   ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr);
516   for (i=0,j=0; i<size; i++) {
517     if (w1[i]) {pa[j] = i; j++;}
518   }
519 
520   /* Each message would have a header = 1 + 2*(no of IS) + data */
521   for (i=0; i<nrqs; i++) {
522     j      = pa[i];
523     w1[j] += w2[j] + 2*w3[j];
524     msz   += w1[j];
525   }
526 
527   /* Determine the number of messages to expect, their lengths, from from-ids */
528   ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
529   ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
530 
531   /* Now post the Irecvs corresponding to these messages */
532   ierr = PetscPostIrecvInt(comm,tag1,nrqr,onodes1,olengths1,&rbuf,&r_waits1);CHKERRQ(ierr);
533 
534   /* Allocate Memory for outgoing messages */
535   ierr = PetscMalloc4(size,&outdat,size,&ptr,msz,&tmp,size,&ctr);CHKERRQ(ierr);
536   ierr = PetscMemzero(outdat,size*sizeof(PetscInt*));CHKERRQ(ierr);
537   ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
538 
539   {
540     PetscInt *iptr = tmp,ict  = 0;
541     for (i=0; i<nrqs; i++) {
542       j         = pa[i];
543       iptr     +=  ict;
544       outdat[j] = iptr;
545       ict       = w1[j];
546     }
547   }
548 
549   /* Form the outgoing messages */
550   /* plug in the headers */
551   for (i=0; i<nrqs; i++) {
552     j            = pa[i];
553     outdat[j][0] = 0;
554     ierr         = PetscMemzero(outdat[j]+1,2*w3[j]*sizeof(PetscInt));CHKERRQ(ierr);
555     ptr[j]       = outdat[j] + 2*w3[j] + 1;
556   }
557 
558   /* Memory for doing local proc's work */
559   {
560     PetscInt M_BPB_imax = 0;
561 #if defined(PETSC_USE_CTABLE)
562     ierr = PetscIntMultError((M/PETSC_BITS_PER_BYTE+1),imax, &M_BPB_imax);CHKERRQ(ierr);
563     ierr = PetscMalloc1(imax,&table_data);CHKERRQ(ierr);
564     for (i=0; i<imax; i++) {
565       ierr = PetscTableCreate(n[i]+1,M+1,&table_data[i]);CHKERRQ(ierr);
566     }
567     ierr = PetscCalloc4(imax,&table, imax,&data, imax,&isz, M_BPB_imax,&t_p);CHKERRQ(ierr);
568     for (i=0; i<imax; i++) {
569       table[i] = t_p + (M/PETSC_BITS_PER_BYTE+1)*i;
570     }
571 #else
572     PetscInt Mimax = 0;
573     ierr = PetscIntMultError(M,imax, &Mimax);CHKERRQ(ierr);
574     ierr = PetscIntMultError((M/PETSC_BITS_PER_BYTE+1),imax, &M_BPB_imax);CHKERRQ(ierr);
575     ierr = PetscCalloc5(imax,&table, imax,&data, imax,&isz, Mimax,&d_p, M_BPB_imax,&t_p);CHKERRQ(ierr);
576     for (i=0; i<imax; i++) {
577       table[i] = t_p + (M/PETSC_BITS_PER_BYTE+1)*i;
578       data[i]  = d_p + M*i;
579     }
580 #endif
581   }
582 
583   /* Parse the IS and update local tables and the outgoing buf with the data */
584   {
585     PetscInt n_i,isz_i,*outdat_j,ctr_j;
586     PetscBT  table_i;
587 
588     for (i=0; i<imax; i++) {
589       ierr    = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
590       n_i     = n[i];
591       table_i = table[i];
592       idx_i   = idx[i];
593 #if defined(PETSC_USE_CTABLE)
594       table_data_i = table_data[i];
595 #else
596       data_i  = data[i];
597 #endif
598       isz_i   = isz[i];
599       for (j=0; j<n_i; j++) {   /* parse the indices of each IS */
600         row  = idx_i[j];
601         ierr = PetscLayoutFindOwner(C->rmap,row,&proc);CHKERRQ(ierr);
602         if (proc != rank) { /* copy to the outgoing buffer */
603           ctr[proc]++;
604           *ptr[proc] = row;
605           ptr[proc]++;
606         } else if (!PetscBTLookupSet(table_i,row)) {
607 #if defined(PETSC_USE_CTABLE)
608           ierr = PetscTableAdd(table_data_i,row+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
609 #else
610           data_i[isz_i] = row; /* Update the local table */
611 #endif
612           isz_i++;
613         }
614       }
615       /* Update the headers for the current IS */
616       for (j=0; j<size; j++) { /* Can Optimise this loop by using pa[] */
617         if ((ctr_j = ctr[j])) {
618           outdat_j        = outdat[j];
619           k               = ++outdat_j[0];
620           outdat_j[2*k]   = ctr_j;
621           outdat_j[2*k-1] = i;
622         }
623       }
624       isz[i] = isz_i;
625     }
626   }
627 
628   /*  Now  post the sends */
629   ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
630   for (i=0; i<nrqs; ++i) {
631     j    = pa[i];
632     ierr = MPI_Isend(outdat[j],w1[j],MPIU_INT,j,tag1,comm,s_waits1+i);CHKERRQ(ierr);
633   }
634 
635   /* No longer need the original indices */
636   for (i=0; i<imax; ++i) {
637     ierr = ISRestoreIndices(is[i],idx+i);CHKERRQ(ierr);
638   }
639   ierr = PetscFree2(idx,n);CHKERRQ(ierr);
640 
641   for (i=0; i<imax; ++i) {
642     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
643   }
644 
645   /* Do Local work */
646 #if defined(PETSC_USE_CTABLE)
647   ierr = MatIncreaseOverlap_MPIAIJ_Local(C,imax,table,isz,NULL,table_data);CHKERRQ(ierr);
648 #else
649   ierr = MatIncreaseOverlap_MPIAIJ_Local(C,imax,table,isz,data,NULL);CHKERRQ(ierr);
650 #endif
651 
652   /* Receive messages */
653   ierr = PetscMalloc1(nrqr+1,&recv_status);CHKERRQ(ierr);
654   if (nrqr) {ierr = MPI_Waitall(nrqr,r_waits1,recv_status);CHKERRQ(ierr);}
655 
656   ierr = PetscMalloc1(nrqs+1,&s_status);CHKERRQ(ierr);
657   if (nrqs) {ierr = MPI_Waitall(nrqs,s_waits1,s_status);CHKERRQ(ierr);}
658 
659   /* Phase 1 sends are complete - deallocate buffers */
660   ierr = PetscFree4(outdat,ptr,tmp,ctr);CHKERRQ(ierr);
661   ierr = PetscFree4(w1,w2,w3,w4);CHKERRQ(ierr);
662 
663   ierr = PetscMalloc1(nrqr+1,&xdata);CHKERRQ(ierr);
664   ierr = PetscMalloc1(nrqr+1,&isz1);CHKERRQ(ierr);
665   ierr = MatIncreaseOverlap_MPIAIJ_Receive(C,nrqr,rbuf,xdata,isz1);CHKERRQ(ierr);
666   ierr = PetscFree(rbuf[0]);CHKERRQ(ierr);
667   ierr = PetscFree(rbuf);CHKERRQ(ierr);
668 
669 
670   /* Send the data back */
671   /* Do a global reduction to know the buffer space req for incoming messages */
672   {
673     PetscMPIInt *rw1;
674 
675     ierr = PetscCalloc1(size,&rw1);CHKERRQ(ierr);
676 
677     for (i=0; i<nrqr; ++i) {
678       proc = recv_status[i].MPI_SOURCE;
679 
680       if (proc != onodes1[i]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPI_SOURCE mismatch");
681       rw1[proc] = isz1[i];
682     }
683     ierr = PetscFree(onodes1);CHKERRQ(ierr);
684     ierr = PetscFree(olengths1);CHKERRQ(ierr);
685 
686     /* Determine the number of messages to expect, their lengths, from from-ids */
687     ierr = PetscGatherMessageLengths(comm,nrqr,nrqs,rw1,&onodes2,&olengths2);CHKERRQ(ierr);
688     ierr = PetscFree(rw1);CHKERRQ(ierr);
689   }
690   /* Now post the Irecvs corresponding to these messages */
691   ierr = PetscPostIrecvInt(comm,tag2,nrqs,onodes2,olengths2,&rbuf2,&r_waits2);CHKERRQ(ierr);
692 
693   /* Now  post the sends */
694   ierr = PetscMalloc1(nrqr+1,&s_waits2);CHKERRQ(ierr);
695   for (i=0; i<nrqr; ++i) {
696     j    = recv_status[i].MPI_SOURCE;
697     ierr = MPI_Isend(xdata[i],isz1[i],MPIU_INT,j,tag2,comm,s_waits2+i);CHKERRQ(ierr);
698   }
699 
700   /* receive work done on other processors */
701   {
702     PetscInt    is_no,ct1,max,*rbuf2_i,isz_i,jmax;
703     PetscMPIInt idex;
704     PetscBT     table_i;
705     MPI_Status  *status2;
706 
707     ierr = PetscMalloc1((PetscMax(nrqr,nrqs)+1),&status2);CHKERRQ(ierr);
708     for (i=0; i<nrqs; ++i) {
709       ierr = MPI_Waitany(nrqs,r_waits2,&idex,status2+i);CHKERRQ(ierr);
710       /* Process the message */
711       rbuf2_i = rbuf2[idex];
712       ct1     = 2*rbuf2_i[0]+1;
713       jmax    = rbuf2[idex][0];
714       for (j=1; j<=jmax; j++) {
715         max     = rbuf2_i[2*j];
716         is_no   = rbuf2_i[2*j-1];
717         isz_i   = isz[is_no];
718         table_i = table[is_no];
719 #if defined(PETSC_USE_CTABLE)
720         table_data_i = table_data[is_no];
721 #else
722         data_i  = data[is_no];
723 #endif
724         for (k=0; k<max; k++,ct1++) {
725           row = rbuf2_i[ct1];
726           if (!PetscBTLookupSet(table_i,row)) {
727 #if defined(PETSC_USE_CTABLE)
728             ierr = PetscTableAdd(table_data_i,row+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
729 #else
730             data_i[isz_i] = row;
731 #endif
732             isz_i++;
733           }
734         }
735         isz[is_no] = isz_i;
736       }
737     }
738 
739     if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits2,status2);CHKERRQ(ierr);}
740     ierr = PetscFree(status2);CHKERRQ(ierr);
741   }
742 
743 #if defined(PETSC_USE_CTABLE)
744   tcount_max = 0;
745   for (i=0; i<imax; ++i) {
746     table_data_i = table_data[i];
747     ierr = PetscTableGetCount(table_data_i,&tcount);CHKERRQ(ierr);
748     if (tcount_max < tcount) tcount_max = tcount;
749   }
750   ierr = PetscMalloc1(tcount_max+1,&tdata);CHKERRQ(ierr);
751 #endif
752 
753   for (i=0; i<imax; ++i) {
754 #if defined(PETSC_USE_CTABLE)
755     PetscTablePosition tpos;
756     table_data_i = table_data[i];
757 
758     ierr = PetscTableGetHeadPosition(table_data_i,&tpos);CHKERRQ(ierr);
759     while (tpos) {
760       ierr = PetscTableGetNext(table_data_i,&tpos,&k,&j);CHKERRQ(ierr);
761       tdata[--j] = --k;
762     }
763     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz[i],tdata,PETSC_COPY_VALUES,is+i);CHKERRQ(ierr);
764 #else
765     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz[i],data[i],PETSC_COPY_VALUES,is+i);CHKERRQ(ierr);
766 #endif
767   }
768 
769   ierr = PetscFree(onodes2);CHKERRQ(ierr);
770   ierr = PetscFree(olengths2);CHKERRQ(ierr);
771 
772   ierr = PetscFree(pa);CHKERRQ(ierr);
773   ierr = PetscFree(rbuf2[0]);CHKERRQ(ierr);
774   ierr = PetscFree(rbuf2);CHKERRQ(ierr);
775   ierr = PetscFree(s_waits1);CHKERRQ(ierr);
776   ierr = PetscFree(r_waits1);CHKERRQ(ierr);
777   ierr = PetscFree(s_waits2);CHKERRQ(ierr);
778   ierr = PetscFree(r_waits2);CHKERRQ(ierr);
779   ierr = PetscFree(s_status);CHKERRQ(ierr);
780   ierr = PetscFree(recv_status);CHKERRQ(ierr);
781   ierr = PetscFree(xdata[0]);CHKERRQ(ierr);
782   ierr = PetscFree(xdata);CHKERRQ(ierr);
783   ierr = PetscFree(isz1);CHKERRQ(ierr);
784 #if defined(PETSC_USE_CTABLE)
785   for (i=0; i<imax; i++) {
786     ierr = PetscTableDestroy((PetscTable*)&table_data[i]);CHKERRQ(ierr);
787   }
788   ierr = PetscFree(table_data);CHKERRQ(ierr);
789   ierr = PetscFree(tdata);CHKERRQ(ierr);
790   ierr = PetscFree4(table,data,isz,t_p);CHKERRQ(ierr);
791 #else
792   ierr = PetscFree5(table,data,isz,d_p,t_p);CHKERRQ(ierr);
793 #endif
794   PetscFunctionReturn(0);
795 }
796 
797 /*
798    MatIncreaseOverlap_MPIAIJ_Local - Called by MatincreaseOverlap, to do
799        the work on the local processor.
800 
801      Inputs:
802       C      - MAT_MPIAIJ;
803       imax - total no of index sets processed at a time;
804       table  - an array of char - size = m bits.
805 
806      Output:
807       isz    - array containing the count of the solution elements corresponding
808                to each index set;
809       data or table_data  - pointer to the solutions
810 */
811 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Local(Mat C,PetscInt imax,PetscBT *table,PetscInt *isz,PetscInt **data,PetscTable *table_data)
812 {
813   Mat_MPIAIJ *c = (Mat_MPIAIJ*)C->data;
814   Mat        A  = c->A,B = c->B;
815   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
816   PetscInt   start,end,val,max,rstart,cstart,*ai,*aj;
817   PetscInt   *bi,*bj,*garray,i,j,k,row,isz_i;
818   PetscBT    table_i;
819 #if defined(PETSC_USE_CTABLE)
820   PetscTable         table_data_i;
821   PetscErrorCode     ierr;
822   PetscTablePosition tpos;
823   PetscInt           tcount,*tdata;
824 #else
825   PetscInt           *data_i;
826 #endif
827 
828   PetscFunctionBegin;
829   rstart = C->rmap->rstart;
830   cstart = C->cmap->rstart;
831   ai     = a->i;
832   aj     = a->j;
833   bi     = b->i;
834   bj     = b->j;
835   garray = c->garray;
836 
837   for (i=0; i<imax; i++) {
838 #if defined(PETSC_USE_CTABLE)
839     /* copy existing entries of table_data_i into tdata[] */
840     table_data_i = table_data[i];
841     ierr = PetscTableGetCount(table_data_i,&tcount);CHKERRQ(ierr);
842     if (tcount != isz[i]) SETERRQ3(PETSC_COMM_SELF,0," tcount %d != isz[%d] %d",tcount,i,isz[i]);
843 
844     ierr = PetscMalloc1(tcount,&tdata);CHKERRQ(ierr);
845     ierr = PetscTableGetHeadPosition(table_data_i,&tpos);CHKERRQ(ierr);
846     while (tpos) {
847       ierr = PetscTableGetNext(table_data_i,&tpos,&row,&j);CHKERRQ(ierr);
848       tdata[--j] = --row;
849       if (j > tcount - 1) SETERRQ2(PETSC_COMM_SELF,0," j %d >= tcount %d",j,tcount);
850     }
851 #else
852     data_i  = data[i];
853 #endif
854     table_i = table[i];
855     isz_i   = isz[i];
856     max     = isz[i];
857 
858     for (j=0; j<max; j++) {
859 #if defined(PETSC_USE_CTABLE)
860       row   = tdata[j] - rstart;
861 #else
862       row   = data_i[j] - rstart;
863 #endif
864       start = ai[row];
865       end   = ai[row+1];
866       for (k=start; k<end; k++) { /* Amat */
867         val = aj[k] + cstart;
868         if (!PetscBTLookupSet(table_i,val)) {
869 #if defined(PETSC_USE_CTABLE)
870           ierr = PetscTableAdd(table_data_i,val+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
871 #else
872           data_i[isz_i] = val;
873 #endif
874           isz_i++;
875         }
876       }
877       start = bi[row];
878       end   = bi[row+1];
879       for (k=start; k<end; k++) { /* Bmat */
880         val = garray[bj[k]];
881         if (!PetscBTLookupSet(table_i,val)) {
882 #if defined(PETSC_USE_CTABLE)
883           ierr = PetscTableAdd(table_data_i,val+1,isz_i+1,INSERT_VALUES);CHKERRQ(ierr);
884 #else
885           data_i[isz_i] = val;
886 #endif
887           isz_i++;
888         }
889       }
890     }
891     isz[i] = isz_i;
892 
893 #if defined(PETSC_USE_CTABLE)
894     ierr = PetscFree(tdata);CHKERRQ(ierr);
895 #endif
896   }
897   PetscFunctionReturn(0);
898 }
899 
900 /*
901       MatIncreaseOverlap_MPIAIJ_Receive - Process the recieved messages,
902          and return the output
903 
904          Input:
905            C    - the matrix
906            nrqr - no of messages being processed.
907            rbuf - an array of pointers to the recieved requests
908 
909          Output:
910            xdata - array of messages to be sent back
911            isz1  - size of each message
912 
913   For better efficiency perhaps we should malloc separately each xdata[i],
914 then if a remalloc is required we need only copy the data for that one row
915 rather then all previous rows as it is now where a single large chunck of
916 memory is used.
917 
918 */
919 static PetscErrorCode MatIncreaseOverlap_MPIAIJ_Receive(Mat C,PetscInt nrqr,PetscInt **rbuf,PetscInt **xdata,PetscInt * isz1)
920 {
921   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
922   Mat            A  = c->A,B = c->B;
923   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
924   PetscErrorCode ierr;
925   PetscInt       rstart,cstart,*ai,*aj,*bi,*bj,*garray,i,j,k;
926   PetscInt       row,total_sz,ct,ct1,ct2,ct3,mem_estimate,oct2,l,start,end;
927   PetscInt       val,max1,max2,m,no_malloc =0,*tmp,new_estimate,ctr;
928   PetscInt       *rbuf_i,kmax,rbuf_0;
929   PetscBT        xtable;
930 
931   PetscFunctionBegin;
932   m      = C->rmap->N;
933   rstart = C->rmap->rstart;
934   cstart = C->cmap->rstart;
935   ai     = a->i;
936   aj     = a->j;
937   bi     = b->i;
938   bj     = b->j;
939   garray = c->garray;
940 
941 
942   for (i=0,ct=0,total_sz=0; i<nrqr; ++i) {
943     rbuf_i =  rbuf[i];
944     rbuf_0 =  rbuf_i[0];
945     ct    += rbuf_0;
946     for (j=1; j<=rbuf_0; j++) total_sz += rbuf_i[2*j];
947   }
948 
949   if (C->rmap->n) max1 = ct*(a->nz + b->nz)/C->rmap->n;
950   else max1 = 1;
951   mem_estimate = 3*((total_sz > max1 ? total_sz : max1)+1);
952   ierr         = PetscMalloc1(mem_estimate,&xdata[0]);CHKERRQ(ierr);
953   ++no_malloc;
954   ierr = PetscBTCreate(m,&xtable);CHKERRQ(ierr);
955   ierr = PetscMemzero(isz1,nrqr*sizeof(PetscInt));CHKERRQ(ierr);
956 
957   ct3 = 0;
958   for (i=0; i<nrqr; i++) { /* for easch mesg from proc i */
959     rbuf_i =  rbuf[i];
960     rbuf_0 =  rbuf_i[0];
961     ct1    =  2*rbuf_0+1;
962     ct2    =  ct1;
963     ct3   += ct1;
964     for (j=1; j<=rbuf_0; j++) { /* for each IS from proc i*/
965       ierr = PetscBTMemzero(m,xtable);CHKERRQ(ierr);
966       oct2 = ct2;
967       kmax = rbuf_i[2*j];
968       for (k=0; k<kmax; k++,ct1++) {
969         row = rbuf_i[ct1];
970         if (!PetscBTLookupSet(xtable,row)) {
971           if (!(ct3 < mem_estimate)) {
972             new_estimate = (PetscInt)(1.5*mem_estimate)+1;
973             ierr         = PetscMalloc1(new_estimate,&tmp);CHKERRQ(ierr);
974             ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(PetscInt));CHKERRQ(ierr);
975             ierr         = PetscFree(xdata[0]);CHKERRQ(ierr);
976             xdata[0]     = tmp;
977             mem_estimate = new_estimate; ++no_malloc;
978             for (ctr=1; ctr<=i; ctr++) xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];
979           }
980           xdata[i][ct2++] = row;
981           ct3++;
982         }
983       }
984       for (k=oct2,max2=ct2; k<max2; k++) {
985         row   = xdata[i][k] - rstart;
986         start = ai[row];
987         end   = ai[row+1];
988         for (l=start; l<end; l++) {
989           val = aj[l] + cstart;
990           if (!PetscBTLookupSet(xtable,val)) {
991             if (!(ct3 < mem_estimate)) {
992               new_estimate = (PetscInt)(1.5*mem_estimate)+1;
993               ierr         = PetscMalloc1(new_estimate,&tmp);CHKERRQ(ierr);
994               ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(PetscInt));CHKERRQ(ierr);
995               ierr         = PetscFree(xdata[0]);CHKERRQ(ierr);
996               xdata[0]     = tmp;
997               mem_estimate = new_estimate; ++no_malloc;
998               for (ctr=1; ctr<=i; ctr++) xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];
999             }
1000             xdata[i][ct2++] = val;
1001             ct3++;
1002           }
1003         }
1004         start = bi[row];
1005         end   = bi[row+1];
1006         for (l=start; l<end; l++) {
1007           val = garray[bj[l]];
1008           if (!PetscBTLookupSet(xtable,val)) {
1009             if (!(ct3 < mem_estimate)) {
1010               new_estimate = (PetscInt)(1.5*mem_estimate)+1;
1011               ierr         = PetscMalloc1(new_estimate,&tmp);CHKERRQ(ierr);
1012               ierr         = PetscMemcpy(tmp,xdata[0],mem_estimate*sizeof(PetscInt));CHKERRQ(ierr);
1013               ierr         = PetscFree(xdata[0]);CHKERRQ(ierr);
1014               xdata[0]     = tmp;
1015               mem_estimate = new_estimate; ++no_malloc;
1016               for (ctr =1; ctr <=i; ctr++) xdata[ctr] = xdata[ctr-1] + isz1[ctr-1];
1017             }
1018             xdata[i][ct2++] = val;
1019             ct3++;
1020           }
1021         }
1022       }
1023       /* Update the header*/
1024       xdata[i][2*j]   = ct2 - oct2; /* Undo the vector isz1 and use only a var*/
1025       xdata[i][2*j-1] = rbuf_i[2*j-1];
1026     }
1027     xdata[i][0] = rbuf_0;
1028     xdata[i+1]  = xdata[i] + ct2;
1029     isz1[i]     = ct2; /* size of each message */
1030   }
1031   ierr = PetscBTDestroy(&xtable);CHKERRQ(ierr);
1032   ierr = PetscInfo3(C,"Allocated %D bytes, required %D bytes, no of mallocs = %D\n",mem_estimate,ct3,no_malloc);CHKERRQ(ierr);
1033   PetscFunctionReturn(0);
1034 }
1035 /* -------------------------------------------------------------------------*/
1036 extern PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool*,Mat*);
1037 extern PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat,MatAssemblyType);
1038 /*
1039     Every processor gets the entire matrix
1040 */
1041 PetscErrorCode MatGetSubMatrix_MPIAIJ_All(Mat A,MatGetSubMatrixOption flag,MatReuse scall,Mat *Bin[])
1042 {
1043   Mat            B;
1044   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1045   Mat_SeqAIJ     *b,*ad = (Mat_SeqAIJ*)a->A->data,*bd = (Mat_SeqAIJ*)a->B->data;
1046   PetscErrorCode ierr;
1047   PetscMPIInt    size,rank,*recvcounts = 0,*displs = 0;
1048   PetscInt       sendcount,i,*rstarts = A->rmap->range,n,cnt,j;
1049   PetscInt       m,*b_sendj,*garray = a->garray,*lens,*jsendbuf,*a_jsendbuf,*b_jsendbuf;
1050   MatScalar      *sendbuf,*recvbuf,*a_sendbuf,*b_sendbuf;
1051 
1052   PetscFunctionBegin;
1053   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRQ(ierr);
1054   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
1055 
1056   if (scall == MAT_INITIAL_MATRIX) {
1057     /* ----------------------------------------------------------------
1058          Tell every processor the number of nonzeros per row
1059     */
1060     ierr = PetscMalloc1(A->rmap->N,&lens);CHKERRQ(ierr);
1061     for (i=A->rmap->rstart; i<A->rmap->rend; i++) {
1062       lens[i] = ad->i[i-A->rmap->rstart+1] - ad->i[i-A->rmap->rstart] + bd->i[i-A->rmap->rstart+1] - bd->i[i-A->rmap->rstart];
1063     }
1064     ierr      = PetscMalloc2(size,&recvcounts,size,&displs);CHKERRQ(ierr);
1065     for (i=0; i<size; i++) {
1066       recvcounts[i] = A->rmap->range[i+1] - A->rmap->range[i];
1067       displs[i]     = A->rmap->range[i];
1068     }
1069 #if defined(PETSC_HAVE_MPI_IN_PLACE)
1070     ierr = MPI_Allgatherv(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,lens,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1071 #else
1072     sendcount = A->rmap->rend - A->rmap->rstart;
1073     ierr = MPI_Allgatherv(lens+A->rmap->rstart,sendcount,MPIU_INT,lens,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1074 #endif
1075     /* ---------------------------------------------------------------
1076          Create the sequential matrix of the same type as the local block diagonal
1077     */
1078     ierr  = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
1079     ierr  = MatSetSizes(B,A->rmap->N,A->cmap->N,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1080     ierr  = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
1081     ierr  = MatSetType(B,((PetscObject)a->A)->type_name);CHKERRQ(ierr);
1082     ierr  = MatSeqAIJSetPreallocation(B,0,lens);CHKERRQ(ierr);
1083     ierr  = PetscMalloc1(1,Bin);CHKERRQ(ierr);
1084     **Bin = B;
1085     b     = (Mat_SeqAIJ*)B->data;
1086 
1087     /*--------------------------------------------------------------------
1088        Copy my part of matrix column indices over
1089     */
1090     sendcount  = ad->nz + bd->nz;
1091     jsendbuf   = b->j + b->i[rstarts[rank]];
1092     a_jsendbuf = ad->j;
1093     b_jsendbuf = bd->j;
1094     n          = A->rmap->rend - A->rmap->rstart;
1095     cnt        = 0;
1096     for (i=0; i<n; i++) {
1097 
1098       /* put in lower diagonal portion */
1099       m = bd->i[i+1] - bd->i[i];
1100       while (m > 0) {
1101         /* is it above diagonal (in bd (compressed) numbering) */
1102         if (garray[*b_jsendbuf] > A->rmap->rstart + i) break;
1103         jsendbuf[cnt++] = garray[*b_jsendbuf++];
1104         m--;
1105       }
1106 
1107       /* put in diagonal portion */
1108       for (j=ad->i[i]; j<ad->i[i+1]; j++) {
1109         jsendbuf[cnt++] = A->rmap->rstart + *a_jsendbuf++;
1110       }
1111 
1112       /* put in upper diagonal portion */
1113       while (m-- > 0) {
1114         jsendbuf[cnt++] = garray[*b_jsendbuf++];
1115       }
1116     }
1117     if (cnt != sendcount) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Corrupted PETSc matrix: nz given %D actual nz %D",sendcount,cnt);
1118 
1119     /*--------------------------------------------------------------------
1120        Gather all column indices to all processors
1121     */
1122     for (i=0; i<size; i++) {
1123       recvcounts[i] = 0;
1124       for (j=A->rmap->range[i]; j<A->rmap->range[i+1]; j++) {
1125         recvcounts[i] += lens[j];
1126       }
1127     }
1128     displs[0] = 0;
1129     for (i=1; i<size; i++) {
1130       displs[i] = displs[i-1] + recvcounts[i-1];
1131     }
1132 #if defined(PETSC_HAVE_MPI_IN_PLACE)
1133     ierr = MPI_Allgatherv(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,b->j,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1134 #else
1135     ierr = MPI_Allgatherv(jsendbuf,sendcount,MPIU_INT,b->j,recvcounts,displs,MPIU_INT,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1136 #endif
1137     /*--------------------------------------------------------------------
1138         Assemble the matrix into useable form (note numerical values not yet set)
1139     */
1140     /* set the b->ilen (length of each row) values */
1141     ierr = PetscMemcpy(b->ilen,lens,A->rmap->N*sizeof(PetscInt));CHKERRQ(ierr);
1142     /* set the b->i indices */
1143     b->i[0] = 0;
1144     for (i=1; i<=A->rmap->N; i++) {
1145       b->i[i] = b->i[i-1] + lens[i-1];
1146     }
1147     ierr = PetscFree(lens);CHKERRQ(ierr);
1148     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1149     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1150 
1151   } else {
1152     B = **Bin;
1153     b = (Mat_SeqAIJ*)B->data;
1154   }
1155 
1156   /*--------------------------------------------------------------------
1157        Copy my part of matrix numerical values into the values location
1158   */
1159   if (flag == MAT_GET_VALUES) {
1160     sendcount = ad->nz + bd->nz;
1161     sendbuf   = b->a + b->i[rstarts[rank]];
1162     a_sendbuf = ad->a;
1163     b_sendbuf = bd->a;
1164     b_sendj   = bd->j;
1165     n         = A->rmap->rend - A->rmap->rstart;
1166     cnt       = 0;
1167     for (i=0; i<n; i++) {
1168 
1169       /* put in lower diagonal portion */
1170       m = bd->i[i+1] - bd->i[i];
1171       while (m > 0) {
1172         /* is it above diagonal (in bd (compressed) numbering) */
1173         if (garray[*b_sendj] > A->rmap->rstart + i) break;
1174         sendbuf[cnt++] = *b_sendbuf++;
1175         m--;
1176         b_sendj++;
1177       }
1178 
1179       /* put in diagonal portion */
1180       for (j=ad->i[i]; j<ad->i[i+1]; j++) {
1181         sendbuf[cnt++] = *a_sendbuf++;
1182       }
1183 
1184       /* put in upper diagonal portion */
1185       while (m-- > 0) {
1186         sendbuf[cnt++] = *b_sendbuf++;
1187         b_sendj++;
1188       }
1189     }
1190     if (cnt != sendcount) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Corrupted PETSc matrix: nz given %D actual nz %D",sendcount,cnt);
1191 
1192     /* -----------------------------------------------------------------
1193        Gather all numerical values to all processors
1194     */
1195     if (!recvcounts) {
1196       ierr = PetscMalloc2(size,&recvcounts,size,&displs);CHKERRQ(ierr);
1197     }
1198     for (i=0; i<size; i++) {
1199       recvcounts[i] = b->i[rstarts[i+1]] - b->i[rstarts[i]];
1200     }
1201     displs[0] = 0;
1202     for (i=1; i<size; i++) {
1203       displs[i] = displs[i-1] + recvcounts[i-1];
1204     }
1205     recvbuf = b->a;
1206 #if defined(PETSC_HAVE_MPI_IN_PLACE)
1207     ierr = MPI_Allgatherv(MPI_IN_PLACE,0,MPI_DATATYPE_NULL,recvbuf,recvcounts,displs,MPIU_SCALAR,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1208 #else
1209     ierr = MPI_Allgatherv(sendbuf,sendcount,MPIU_SCALAR,recvbuf,recvcounts,displs,MPIU_SCALAR,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
1210 #endif
1211   }  /* endof (flag == MAT_GET_VALUES) */
1212   ierr = PetscFree2(recvcounts,displs);CHKERRQ(ierr);
1213 
1214   if (A->symmetric) {
1215     ierr = MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
1216   } else if (A->hermitian) {
1217     ierr = MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
1218   } else if (A->structurally_symmetric) {
1219     ierr = MatSetOption(B,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
1220   }
1221   PetscFunctionReturn(0);
1222 }
1223 PetscErrorCode MatDestroy_MPIAIJ_MatGetSubmatrices(Mat C)
1224 {
1225   PetscErrorCode ierr;
1226   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
1227   Mat_SubMat     *submatj = c->submatis1;
1228   PetscInt       i;
1229 
1230   PetscFunctionBegin;
1231   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
1232     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
1233 
1234     for (i=0; i<submatj->nrqr; ++i) {
1235       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
1236     }
1237     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
1238 
1239     if (submatj->rbuf1) {
1240       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
1241       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
1242     }
1243 
1244     for (i=0; i<submatj->nrqs; ++i) {
1245       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
1246     }
1247     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
1248     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
1249   }
1250 
1251 #if defined(PETSC_USE_CTABLE)
1252   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
1253   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
1254   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
1255 #else
1256   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
1257 #endif
1258 
1259   if (!submatj->allcolumns) {
1260 #if defined(PETSC_USE_CTABLE)
1261     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
1262 #else
1263     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
1264 #endif
1265   }
1266   ierr = submatj->destroy(C);CHKERRQ(ierr);
1267   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
1268 
1269   ierr = PetscFree(submatj);CHKERRQ(ierr);
1270   PetscFunctionReturn(0);
1271 }
1272 
1273 PetscErrorCode MatGetSubMatrices_MPIAIJ_SingleIS_Local(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,PetscBool allcolumns,Mat *submats)
1274 {
1275   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
1276   Mat            submat,A = c->A,B = c->B;
1277   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data,*subc;
1278   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,nzA,nzB;
1279   PetscInt       cstart = C->cmap->rstart,cend = C->cmap->rend,rstart = C->rmap->rstart,*bmap = c->garray;
1280   const PetscInt *icol,*irow;
1281   PetscInt       nrow,ncol,start;
1282   PetscErrorCode ierr;
1283   PetscMPIInt    rank,size,tag1,tag2,tag3,tag4,*w1,*w2,nrqr;
1284   PetscInt       **sbuf1,**sbuf2,i,j,k,l,ct1,ct2,ct3,**rbuf1,row,proc;
1285   PetscInt       nrqs=0,msz,**ptr,*req_size,*ctr,*pa,*tmp,tcol,*iptr;
1286   PetscInt       **rbuf3,*req_source1,*req_source2,**sbuf_aj,**rbuf2,max1,nnz;
1287   PetscInt       *lens,rmax,ncols,*cols,Crow;
1288 #if defined(PETSC_USE_CTABLE)
1289   PetscTable     cmap,rmap;
1290   PetscInt       *cmap_loc,*rmap_loc;
1291 #else
1292   PetscInt       *cmap,*rmap;
1293 #endif
1294   PetscInt       ctr_j,*sbuf1_j,*sbuf_aj_i,*rbuf1_i,kmax,*sbuf1_i,*rbuf2_i,*rbuf3_i;
1295   PetscInt       *cworkB,lwrite,*subcols,*row2proc;
1296   PetscScalar    *vworkA,*vworkB,*a_a = a->a,*b_a = b->a,*subvals=NULL;
1297   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2,*r_waits3;
1298   MPI_Request    *r_waits4,*s_waits3 = NULL,*s_waits4;
1299   MPI_Status     *r_status1,*r_status2,*s_status1,*s_status3 = NULL,*s_status2;
1300   MPI_Status     *r_status3 = NULL,*r_status4,*s_status4;
1301   MPI_Comm       comm;
1302   PetscScalar    **rbuf4,**sbuf_aa,*vals,*sbuf_aa_i,*rbuf4_i;
1303   PetscMPIInt    *onodes1,*olengths1,idex,end;
1304   Mat_SubMat     *smatis1;
1305   PetscBool      isrowsorted;
1306 
1307   PetscFunctionBegin;
1308   if (ismax != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"This routine only works when all processes have ismax=1");
1309 
1310   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1311   size = c->size;
1312   rank = c->rank;
1313 
1314   ierr = ISSorted(isrow[0],&isrowsorted);CHKERRQ(ierr);
1315   if (!isrowsorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"isrow[0] must be sorted");
1316 
1317   ierr = ISGetIndices(isrow[0],&irow);CHKERRQ(ierr);
1318   ierr = ISGetLocalSize(isrow[0],&nrow);CHKERRQ(ierr);
1319   if (allcolumns) {
1320     icol = NULL;
1321     ncol = C->cmap->N;
1322   } else {
1323     ierr = ISGetIndices(iscol[0],&icol);CHKERRQ(ierr);
1324     ierr = ISGetLocalSize(iscol[0],&ncol);CHKERRQ(ierr);
1325   }
1326 
1327   if (scall == MAT_INITIAL_MATRIX) {
1328     PetscInt *sbuf2_i,*cworkA,lwrite,ctmp;
1329 
1330     /* Get some new tags to keep the communication clean */
1331     tag1 = ((PetscObject)C)->tag;
1332     ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
1333     ierr = PetscObjectGetNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
1334 
1335     /* evaluate communication - mesg to who, length of mesg, and buffer space
1336      required. Based on this, buffers are allocated, and data copied into them */
1337     ierr = PetscCalloc2(size,&w1,size,&w2);CHKERRQ(ierr);
1338     ierr = PetscMalloc1(nrow,&row2proc);CHKERRQ(ierr);
1339 
1340     /* w1[proc] = num of rows owned by proc -- to be requested */
1341     proc = 0;
1342     nrqs = 0; /* num of outgoing messages */
1343     for (j=0; j<nrow; j++) {
1344       row  = irow[j]; /* sorted! */
1345       while (row >= C->rmap->range[proc+1]) proc++;
1346       w1[proc]++;
1347       row2proc[j] = proc; /* map row index to proc */
1348 
1349       if (proc != rank && !w2[proc]) {
1350         w2[proc] = 1; nrqs++;
1351       }
1352     }
1353     w1[rank] = 0;  /* rows owned by self will not be requested */
1354 
1355     ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr); /*(proc -array)*/
1356     for (proc=0,j=0; proc<size; proc++) {
1357       if (w1[proc]) { pa[j++] = proc;}
1358     }
1359 
1360     /* Each message would have a header = 1 + 2*(num of IS) + data (here,num of IS = 1) */
1361     msz = 0;              /* total mesg length (for all procs) */
1362     for (i=0; i<nrqs; i++) {
1363       proc      = pa[i];
1364       w1[proc] += 3;
1365       msz      += w1[proc];
1366     }
1367     ierr = PetscInfo2(0,"Number of outgoing messages %D Total message length %D\n",nrqs,msz);CHKERRQ(ierr);
1368 
1369     /* Determine nrqr, the number of messages to expect, their lengths, from from-ids */
1370     /* if w2[proc]=1, a message of length w1[proc] will be sent to proc; */
1371     ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
1372 
1373     /* Input: nrqs: nsend; nrqr: nrecv; w1: msg length to be sent;
1374        Output: onodes1: recv node-ids; olengths1: corresponding recv message length */
1375     ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
1376 
1377     /* Now post the Irecvs corresponding to these messages */
1378     ierr = PetscPostIrecvInt(comm,tag1,nrqr,onodes1,olengths1,&rbuf1,&r_waits1);CHKERRQ(ierr);
1379 
1380     ierr = PetscFree(onodes1);CHKERRQ(ierr);
1381     ierr = PetscFree(olengths1);CHKERRQ(ierr);
1382 
1383     /* Allocate Memory for outgoing messages */
1384     ierr = PetscMalloc4(size,&sbuf1,size,&ptr,2*msz,&tmp,size,&ctr);CHKERRQ(ierr);
1385     ierr = PetscMemzero(sbuf1,size*sizeof(PetscInt*));CHKERRQ(ierr);
1386     ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
1387 
1388     /* subf1[pa[0]] = tmp, subf1[pa[i]] = subf1[pa[i-1]] + w1[pa[i-1]] */
1389     iptr = tmp;
1390     for (i=0; i<nrqs; i++) {
1391       proc        = pa[i];
1392       sbuf1[proc] = iptr;
1393       iptr       += w1[proc];
1394     }
1395 
1396     /* Form the outgoing messages */
1397     /* Initialize the header space */
1398     for (i=0; i<nrqs; i++) {
1399       proc      = pa[i];
1400       ierr      = PetscMemzero(sbuf1[proc],3*sizeof(PetscInt));CHKERRQ(ierr);
1401       ptr[proc] = sbuf1[proc] + 3;
1402     }
1403 
1404     /* Parse the isrow and copy data into outbuf */
1405     ierr = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
1406     for (j=0; j<nrow; j++) {  /* parse the indices of each IS */
1407       proc = row2proc[j];
1408       if (proc != rank) { /* copy to the outgoing buf*/
1409         *ptr[proc] = irow[j];
1410         ctr[proc]++; ptr[proc]++;
1411       }
1412     }
1413 
1414     /* Update the headers for the current IS */
1415     for (j=0; j<size; j++) { /* Can Optimise this loop too */
1416       if ((ctr_j = ctr[j])) {
1417         sbuf1_j        = sbuf1[j];
1418         k              = ++sbuf1_j[0];
1419         sbuf1_j[2*k]   = ctr_j;
1420         sbuf1_j[2*k-1] = 0;
1421       }
1422     }
1423 
1424     /* Now post the sends */
1425     ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
1426     for (i=0; i<nrqs; ++i) {
1427       proc = pa[i];
1428       ierr = MPI_Isend(sbuf1[proc],w1[proc],MPIU_INT,proc,tag1,comm,s_waits1+i);CHKERRQ(ierr);
1429     }
1430 
1431     /* Post Receives to capture the buffer size */
1432     ierr = PetscMalloc4(nrqs+1,&r_status2,nrqr+1,&s_waits2,nrqs+1,&r_waits2,nrqr+1,&s_status2);CHKERRQ(ierr);
1433     ierr = PetscMalloc3(nrqs+1,&req_source2,nrqs+1,&rbuf2,nrqs+1,&rbuf3);CHKERRQ(ierr);
1434 
1435     rbuf2[0] = tmp + msz;
1436     for (i=1; i<nrqs; ++i) rbuf2[i] = rbuf2[i-1] + w1[pa[i-1]];
1437 
1438     for (i=0; i<nrqs; ++i) {
1439       proc = pa[i];
1440       ierr = MPI_Irecv(rbuf2[i],w1[proc],MPIU_INT,proc,tag2,comm,r_waits2+i);CHKERRQ(ierr);
1441     }
1442 
1443     ierr = PetscFree2(w1,w2);CHKERRQ(ierr);
1444 
1445     /* Send to other procs the buf size they should allocate */
1446     /* Receive messages*/
1447     ierr = PetscMalloc1(nrqr+1,&r_status1);CHKERRQ(ierr);
1448     ierr = PetscMalloc3(nrqr,&sbuf2,nrqr,&req_size,nrqr,&req_source1);CHKERRQ(ierr);
1449 
1450     ierr = MPI_Waitall(nrqr,r_waits1,r_status1);CHKERRQ(ierr);
1451     for (i=0; i<nrqr; ++i) {
1452       req_size[i] = 0;
1453       rbuf1_i        = rbuf1[i];
1454       start          = 2*rbuf1_i[0] + 1;
1455       ierr           = MPI_Get_count(r_status1+i,MPIU_INT,&end);CHKERRQ(ierr);
1456       ierr           = PetscMalloc1(end+1,&sbuf2[i]);CHKERRQ(ierr);
1457       sbuf2_i        = sbuf2[i];
1458       for (j=start; j<end; j++) {
1459         k            = rbuf1_i[j] - rstart;
1460         ncols        = ai[k+1] - ai[k] + bi[k+1] - bi[k];
1461         sbuf2_i[j]   = ncols;
1462         req_size[i] += ncols;
1463       }
1464       req_source1[i] = r_status1[i].MPI_SOURCE;
1465 
1466       /* form the header */
1467       sbuf2_i[0] = req_size[i];
1468       for (j=1; j<start; j++) sbuf2_i[j] = rbuf1_i[j];
1469 
1470       ierr = MPI_Isend(sbuf2_i,end,MPIU_INT,req_source1[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
1471     }
1472 
1473     ierr = PetscFree(r_status1);CHKERRQ(ierr);
1474     ierr = PetscFree(r_waits1);CHKERRQ(ierr);
1475 
1476     /* rbuf2 is received, Post recv column indices a->j */
1477     ierr = MPI_Waitall(nrqs,r_waits2,r_status2);CHKERRQ(ierr);
1478 
1479     ierr = PetscMalloc4(nrqs+1,&r_waits3,nrqr+1,&s_waits3,nrqs+1,&r_status3,nrqr+1,&s_status3);CHKERRQ(ierr);
1480     for (i=0; i<nrqs; ++i) {
1481       ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf3[i]);CHKERRQ(ierr);
1482       req_source2[i] = r_status2[i].MPI_SOURCE;
1483       ierr = MPI_Irecv(rbuf3[i],rbuf2[i][0],MPIU_INT,req_source2[i],tag3,comm,r_waits3+i);CHKERRQ(ierr);
1484     }
1485 
1486     /* Wait on sends1 and sends2 */
1487     ierr = PetscMalloc1(nrqs+1,&s_status1);CHKERRQ(ierr);
1488     ierr = MPI_Waitall(nrqs,s_waits1,s_status1);CHKERRQ(ierr);
1489     ierr = PetscFree(s_waits1);CHKERRQ(ierr);
1490     ierr = PetscFree(s_status1);CHKERRQ(ierr);
1491 
1492     ierr = MPI_Waitall(nrqr,s_waits2,s_status2);CHKERRQ(ierr);
1493     ierr = PetscFree4(r_status2,s_waits2,r_waits2,s_status2);CHKERRQ(ierr);
1494 
1495     /* Now allocate sending buffers for a->j, and send them off */
1496     ierr = PetscMalloc1(nrqr+1,&sbuf_aj);CHKERRQ(ierr);
1497     for (i=0,j=0; i<nrqr; i++) j += req_size[i];
1498     ierr = PetscMalloc1(j+1,&sbuf_aj[0]);CHKERRQ(ierr);
1499     for (i=1; i<nrqr; i++) sbuf_aj[i] = sbuf_aj[i-1] + req_size[i-1];
1500 
1501     for (i=0; i<nrqr; i++) { /* for each requested message */
1502       rbuf1_i   = rbuf1[i];
1503       sbuf_aj_i = sbuf_aj[i];
1504       ct1       = 2*rbuf1_i[0] + 1;
1505       ct2       = 0;
1506       /* max1=rbuf1_i[0]; if (max1 != 1) SETERRQ1(PETSC_COMM_SELF,0,"max1 %d != 1",max1); */
1507 
1508       kmax = rbuf1[i][2];
1509       for (k=0; k<kmax; k++,ct1++) { /* for each row */
1510         row    = rbuf1_i[ct1] - rstart;
1511         nzA    = ai[row+1] - ai[row];
1512         nzB    = bi[row+1] - bi[row];
1513         ncols  = nzA + nzB;
1514         cworkA = aj + ai[row]; cworkB = bj + bi[row];
1515 
1516         /* load the column indices for this row into cols*/
1517         cols = sbuf_aj_i + ct2;
1518 
1519         lwrite = 0;
1520         for (l=0; l<nzB; l++) {
1521           if ((ctmp = bmap[cworkB[l]]) < cstart) cols[lwrite++] = ctmp;
1522         }
1523         for (l=0; l<nzA; l++) cols[lwrite++] = cstart + cworkA[l];
1524         for (l=0; l<nzB; l++) {
1525           if ((ctmp = bmap[cworkB[l]]) >= cend) cols[lwrite++] = ctmp;
1526         }
1527 
1528         ct2 += ncols;
1529       }
1530       ierr = MPI_Isend(sbuf_aj_i,req_size[i],MPIU_INT,req_source1[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
1531     }
1532 
1533     /* create column map (cmap): global col of C -> local col of submat */
1534 #if defined(PETSC_USE_CTABLE)
1535     if (!allcolumns) {
1536       ierr = PetscTableCreate(ncol+1,C->cmap->N+1,&cmap);CHKERRQ(ierr);
1537       ierr = PetscCalloc1(C->cmap->n,&cmap_loc);CHKERRQ(ierr);
1538       for (j=0; j<ncol; j++) { /* use array cmap_loc[] for local col indices */
1539         if (icol[j] >= cstart && icol[j] <cend) {
1540           cmap_loc[icol[j] - cstart] = j+1;
1541         } else { /* use PetscTable for non-local col indices */
1542           ierr = PetscTableAdd(cmap,icol[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
1543         }
1544       }
1545     } else {
1546       cmap     = NULL;
1547       cmap_loc = NULL;
1548     }
1549     ierr = PetscCalloc1(C->rmap->n,&rmap_loc);CHKERRQ(ierr);
1550 #else
1551     if (!allcolumns) {
1552       ierr   = PetscCalloc1(C->cmap->N,&cmap);CHKERRQ(ierr);
1553       for (j=0; j<ncol; j++) cmap[icol[j]] = j+1;
1554     } else {
1555       cmap = NULL;
1556     }
1557 #endif
1558 
1559     /* Create lens for MatSeqAIJSetPreallocation() */
1560     ierr = PetscCalloc1(nrow,&lens);CHKERRQ(ierr);
1561 
1562     /* Compute lens from local part of C */
1563     for (j=0; j<nrow; j++) {
1564       row  = irow[j];
1565       proc = row2proc[j];
1566       if (proc == rank) {
1567         /* diagonal part A = c->A */
1568         ncols = ai[row-rstart+1] - ai[row-rstart];
1569         cols  = aj + ai[row-rstart];
1570         if (!allcolumns) {
1571           for (k=0; k<ncols; k++) {
1572 #if defined(PETSC_USE_CTABLE)
1573             tcol = cmap_loc[cols[k]];
1574 #else
1575             tcol = cmap[cols[k]+cstart];
1576 #endif
1577             if (tcol) lens[j]++;
1578           }
1579         } else { /* allcolumns */
1580           lens[j] = ncols;
1581         }
1582 
1583         /* off-diagonal part B = c->B */
1584         ncols = bi[row-rstart+1] - bi[row-rstart];
1585         cols  = bj + bi[row-rstart];
1586         if (!allcolumns) {
1587           for (k=0; k<ncols; k++) {
1588 #if defined(PETSC_USE_CTABLE)
1589             ierr = PetscTableFind(cmap,bmap[cols[k]]+1,&tcol);CHKERRQ(ierr);
1590 #else
1591             tcol = cmap[bmap[cols[k]]];
1592 #endif
1593             if (tcol) lens[j]++;
1594           }
1595         } else { /* allcolumns */
1596           lens[j] += ncols;
1597         }
1598       }
1599     }
1600 
1601     /* Create row map (rmap): global row of C -> local row of submat */
1602 #if defined(PETSC_USE_CTABLE)
1603     ierr = PetscTableCreate(nrow+1,C->rmap->N+1,&rmap);CHKERRQ(ierr);
1604     for (j=0; j<nrow; j++) {
1605       row  = irow[j];
1606       proc = row2proc[j];
1607       if (proc == rank) { /* a local row */
1608         rmap_loc[row - rstart] = j;
1609       } else {
1610         ierr = PetscTableAdd(rmap,irow[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
1611       }
1612     }
1613 #else
1614     ierr = PetscCalloc1(C->rmap->N,&rmap);CHKERRQ(ierr);
1615     for (j=0; j<nrow; j++) {
1616       rmap[irow[j]] = j;
1617     }
1618 #endif
1619 
1620     /* Update lens from offproc data */
1621     /* recv a->j is done */
1622     ierr    = MPI_Waitall(nrqs,r_waits3,r_status3);CHKERRQ(ierr);
1623     for (i=0; i<nrqs; i++) {
1624       proc    = pa[i];
1625       sbuf1_i = sbuf1[proc];
1626       /* jmax    = sbuf1_i[0]; if (jmax != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"jmax !=1"); */
1627       ct1     = 2 + 1;
1628       ct2     = 0;
1629       rbuf2_i = rbuf2[i]; /* received length of C->j */
1630       rbuf3_i = rbuf3[i]; /* received C->j */
1631 
1632       /* is_no  = sbuf1_i[2*j-1]; if (is_no != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_no !=0"); */
1633       max1   = sbuf1_i[2];
1634       for (k=0; k<max1; k++,ct1++) {
1635 #if defined(PETSC_USE_CTABLE)
1636         ierr = PetscTableFind(rmap,sbuf1_i[ct1]+1,&row);CHKERRQ(ierr);
1637         row--;
1638         if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"row not found in table");
1639 #else
1640         row = rmap[sbuf1_i[ct1]]; /* the row index in submat */
1641 #endif
1642         /* Now, store row index of submat in sbuf1_i[ct1] */
1643         sbuf1_i[ct1] = row;
1644 
1645         nnz = rbuf2_i[ct1];
1646         if (!allcolumns) {
1647           for (l=0; l<nnz; l++,ct2++) {
1648 #if defined(PETSC_USE_CTABLE)
1649             if (rbuf3_i[ct2] >= cstart && rbuf3_i[ct2] <cend) {
1650               tcol = cmap_loc[rbuf3_i[ct2] - cstart];
1651             } else {
1652               ierr = PetscTableFind(cmap,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
1653             }
1654 #else
1655             tcol = cmap[rbuf3_i[ct2]]; /* column index in submat */
1656 #endif
1657             if (tcol) lens[row]++;
1658           }
1659         } else { /* allcolumns */
1660           lens[row] += nnz;
1661         }
1662       }
1663     }
1664     ierr = MPI_Waitall(nrqr,s_waits3,s_status3);CHKERRQ(ierr);
1665     ierr = PetscFree4(r_waits3,s_waits3,r_status3,s_status3);CHKERRQ(ierr);
1666 
1667     /* Create the submatrices */
1668     ierr = MatCreate(PETSC_COMM_SELF,&submat);CHKERRQ(ierr);
1669     ierr = MatSetSizes(submat,nrow,ncol,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1670 
1671     ierr = ISGetBlockSize(isrow[0],&i);CHKERRQ(ierr);
1672     ierr = ISGetBlockSize(iscol[0],&j);CHKERRQ(ierr);
1673     ierr = MatSetBlockSizes(submat,i,j);CHKERRQ(ierr);
1674     ierr = MatSetType(submat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1675     ierr = MatSeqAIJSetPreallocation(submat,0,lens);CHKERRQ(ierr);
1676 
1677     /* create struct Mat_SubMat and attached it to submat */
1678     ierr = PetscNew(&smatis1);CHKERRQ(ierr);
1679     subc = (Mat_SeqAIJ*)submat->data;
1680     subc->submatis1 = smatis1;
1681 
1682     smatis1->id          = 0;
1683     smatis1->nrqs        = nrqs;
1684     smatis1->nrqr        = nrqr;
1685     smatis1->rbuf1       = rbuf1;
1686     smatis1->rbuf2       = rbuf2;
1687     smatis1->rbuf3       = rbuf3;
1688     smatis1->sbuf2       = sbuf2;
1689     smatis1->req_source2 = req_source2;
1690 
1691     smatis1->sbuf1       = sbuf1;
1692     smatis1->ptr         = ptr;
1693     smatis1->tmp         = tmp;
1694     smatis1->ctr         = ctr;
1695 
1696     smatis1->pa           = pa;
1697     smatis1->req_size     = req_size;
1698     smatis1->req_source1  = req_source1;
1699 
1700     smatis1->allcolumns  = allcolumns;
1701     smatis1->row2proc    = row2proc;
1702     smatis1->rmap        = rmap;
1703     smatis1->cmap        = cmap;
1704 #if defined(PETSC_USE_CTABLE)
1705     smatis1->rmap_loc    = rmap_loc;
1706     smatis1->cmap_loc    = cmap_loc;
1707 #endif
1708 
1709     smatis1->destroy     = submat->ops->destroy;
1710     submat->ops->destroy = MatDestroy_MPIAIJ_MatGetSubmatrices;
1711     submat->factortype   = C->factortype;
1712 
1713     /* compute rmax */
1714     rmax = 0;
1715     for (i=0; i<nrow; i++) rmax = PetscMax(rmax,lens[i]);
1716 
1717   } else { /* scall == MAT_REUSE_MATRIX */
1718     submat = submats[0];
1719     if (submat->rmap->n != nrow || submat->cmap->n != ncol) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
1720 
1721     subc    = (Mat_SeqAIJ*)submat->data;
1722     rmax    = subc->rmax;
1723     smatis1 = subc->submatis1;
1724     nrqs        = smatis1->nrqs;
1725     nrqr        = smatis1->nrqr;
1726     rbuf1       = smatis1->rbuf1;
1727     rbuf2       = smatis1->rbuf2;
1728     rbuf3       = smatis1->rbuf3;
1729     req_source2 = smatis1->req_source2;
1730 
1731     sbuf1     = smatis1->sbuf1;
1732     sbuf2     = smatis1->sbuf2;
1733     ptr       = smatis1->ptr;
1734     tmp       = smatis1->tmp;
1735     ctr       = smatis1->ctr;
1736 
1737     pa         = smatis1->pa;
1738     req_size   = smatis1->req_size;
1739     req_source1 = smatis1->req_source1;
1740 
1741     allcolumns = smatis1->allcolumns;
1742     row2proc   = smatis1->row2proc;
1743     rmap       = smatis1->rmap;
1744     cmap       = smatis1->cmap;
1745 #if defined(PETSC_USE_CTABLE)
1746     rmap_loc   = smatis1->rmap_loc;
1747     cmap_loc   = smatis1->cmap_loc;
1748 #endif
1749   }
1750 
1751   /* Post recv matrix values */
1752   ierr = PetscMalloc3(nrqs+1,&rbuf4, rmax,&subcols, rmax,&subvals);CHKERRQ(ierr);
1753   ierr = PetscMalloc4(nrqs+1,&r_waits4,nrqr+1,&s_waits4,nrqs+1,&r_status4,nrqr+1,&s_status4);CHKERRQ(ierr);
1754   ierr = PetscObjectGetNewTag((PetscObject)C,&tag4);CHKERRQ(ierr);
1755   for (i=0; i<nrqs; ++i) {
1756     ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf4[i]);CHKERRQ(ierr);
1757     ierr = MPI_Irecv(rbuf4[i],rbuf2[i][0],MPIU_SCALAR,req_source2[i],tag4,comm,r_waits4+i);CHKERRQ(ierr);
1758   }
1759 
1760   /* Allocate sending buffers for a->a, and send them off */
1761   ierr = PetscMalloc1(nrqr+1,&sbuf_aa);CHKERRQ(ierr);
1762   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
1763   ierr = PetscMalloc1(j+1,&sbuf_aa[0]);CHKERRQ(ierr);
1764   for (i=1; i<nrqr; i++) sbuf_aa[i] = sbuf_aa[i-1] + req_size[i-1];
1765 
1766   for (i=0; i<nrqr; i++) {
1767     rbuf1_i   = rbuf1[i];
1768     sbuf_aa_i = sbuf_aa[i];
1769     ct1       = 2*rbuf1_i[0]+1;
1770     ct2       = 0;
1771     /* max1=rbuf1_i[0]; if (max1 != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"max1 !=1"); */
1772 
1773     kmax = rbuf1_i[2];
1774     for (k=0; k<kmax; k++,ct1++) {
1775       row = rbuf1_i[ct1] - rstart;
1776       nzA = ai[row+1] - ai[row];
1777       nzB = bi[row+1] - bi[row];
1778       ncols  = nzA + nzB;
1779       cworkB = bj + bi[row];
1780       vworkA = a_a + ai[row];
1781       vworkB = b_a + bi[row];
1782 
1783       /* load the column values for this row into vals*/
1784       vals = sbuf_aa_i + ct2;
1785 
1786       lwrite = 0;
1787       for (l=0; l<nzB; l++) {
1788         if ((bmap[cworkB[l]]) < cstart) vals[lwrite++] = vworkB[l];
1789       }
1790       for (l=0; l<nzA; l++) vals[lwrite++] = vworkA[l];
1791       for (l=0; l<nzB; l++) {
1792         if ((bmap[cworkB[l]]) >= cend) vals[lwrite++] = vworkB[l];
1793       }
1794 
1795       ct2 += ncols;
1796     }
1797     ierr = MPI_Isend(sbuf_aa_i,req_size[i],MPIU_SCALAR,req_source1[i],tag4,comm,s_waits4+i);CHKERRQ(ierr);
1798   }
1799 
1800   /* Assemble submat */
1801   /* First assemble the local rows */
1802   for (j=0; j<nrow; j++) {
1803     row  = irow[j];
1804     proc = row2proc[j];
1805     if (proc == rank) {
1806       Crow = row - rstart;  /* local row index of C */
1807 #if defined(PETSC_USE_CTABLE)
1808       row = rmap_loc[Crow]; /* row index of submat */
1809 #else
1810       row = rmap[row];
1811 #endif
1812 
1813       if (allcolumns) {
1814         /* diagonal part A = c->A */
1815         ncols = ai[Crow+1] - ai[Crow];
1816         cols  = aj + ai[Crow];
1817         vals  = a->a + ai[Crow];
1818         i     = 0;
1819         for (k=0; k<ncols; k++) {
1820           subcols[i]   = cols[k] + cstart;
1821           subvals[i++] = vals[k];
1822         }
1823 
1824         /* off-diagonal part B = c->B */
1825         ncols = bi[Crow+1] - bi[Crow];
1826         cols  = bj + bi[Crow];
1827         vals  = b->a + bi[Crow];
1828         for (k=0; k<ncols; k++) {
1829           subcols[i]   = bmap[cols[k]];
1830           subvals[i++] = vals[k];
1831         }
1832 
1833         ierr = MatSetValues_SeqAIJ(submat,1,&row,i,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1834 
1835       } else { /* !allcolumns */
1836 #if defined(PETSC_USE_CTABLE)
1837         /* diagonal part A = c->A */
1838         ncols = ai[Crow+1] - ai[Crow];
1839         cols  = aj + ai[Crow];
1840         vals  = a->a + ai[Crow];
1841         i     = 0;
1842         for (k=0; k<ncols; k++) {
1843           tcol = cmap_loc[cols[k]];
1844           if (tcol) {
1845             subcols[i]   = --tcol;
1846             subvals[i++] = vals[k];
1847           }
1848         }
1849 
1850         /* off-diagonal part B = c->B */
1851         ncols = bi[Crow+1] - bi[Crow];
1852         cols  = bj + bi[Crow];
1853         vals  = b->a + bi[Crow];
1854         for (k=0; k<ncols; k++) {
1855           ierr = PetscTableFind(cmap,bmap[cols[k]]+1,&tcol);CHKERRQ(ierr);
1856           if (tcol) {
1857             subcols[i]   = --tcol;
1858             subvals[i++] = vals[k];
1859           }
1860         }
1861 #else
1862         /* diagonal part A = c->A */
1863         ncols = ai[Crow+1] - ai[Crow];
1864         cols  = aj + ai[Crow];
1865         vals  = a->a + ai[Crow];
1866         i     = 0;
1867         for (k=0; k<ncols; k++) {
1868           tcol = cmap[cols[k]+cstart];
1869           if (tcol) {
1870             subcols[i]   = --tcol;
1871             subvals[i++] = vals[k];
1872           }
1873         }
1874 
1875         /* off-diagonal part B = c->B */
1876         ncols = bi[Crow+1] - bi[Crow];
1877         cols  = bj + bi[Crow];
1878         vals  = b->a + bi[Crow];
1879         for (k=0; k<ncols; k++) {
1880           tcol = cmap[bmap[cols[k]]];
1881           if (tcol) {
1882             subcols[i]   = --tcol;
1883             subvals[i++] = vals[k];
1884           }
1885         }
1886 #endif
1887         ierr = MatSetValues_SeqAIJ(submat,1,&row,i,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1888       }
1889     }
1890   }
1891 
1892   /* Now assemble the off-proc rows */
1893   for (i=0; i<nrqs; i++) { /* for each requested message */
1894     /* recv values from other processes */
1895     ierr    = MPI_Waitany(nrqs,r_waits4,&idex,r_status4+i);CHKERRQ(ierr);
1896     proc    = pa[idex];
1897     sbuf1_i = sbuf1[proc];
1898     /* jmax    = sbuf1_i[0]; if (jmax != 1)SETERRQ1(PETSC_COMM_SELF,0,"jmax %d != 1",jmax); */
1899     ct1     = 2 + 1;
1900     ct2     = 0; /* count of received C->j */
1901     ct3     = 0; /* count of received C->j that will be inserted into submat */
1902     rbuf2_i = rbuf2[idex]; /* int** received length of C->j from other processes */
1903     rbuf3_i = rbuf3[idex]; /* int** received C->j from other processes */
1904     rbuf4_i = rbuf4[idex]; /* scalar** received C->a from other processes */
1905 
1906     /* is_no = sbuf1_i[2*j-1]; if (is_no != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_no !=0"); */
1907     max1 = sbuf1_i[2];             /* num of rows */
1908     for (k=0; k<max1; k++,ct1++) { /* for each recved row */
1909       row = sbuf1_i[ct1]; /* row index of submat */
1910       if (!allcolumns) {
1911         idex = 0;
1912         if (scall == MAT_INITIAL_MATRIX) {
1913           nnz  = rbuf2_i[ct1]; /* num of C entries in this row */
1914           for (l=0; l<nnz; l++,ct2++) { /* for each recved column */
1915 #if defined(PETSC_USE_CTABLE)
1916             if (rbuf3_i[ct2] >= cstart && rbuf3_i[ct2] <cend) {
1917               tcol = cmap_loc[rbuf3_i[ct2] - cstart];
1918             } else {
1919               ierr = PetscTableFind(cmap,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
1920             }
1921 #else
1922             tcol = cmap[rbuf3_i[ct2]];
1923 #endif
1924             if (tcol) {
1925               subcols[idex]   = --tcol;
1926               subvals[idex++] = rbuf4_i[ct2];
1927 
1928               /* We receive an entire column of C, but a subset of it needs to be inserted into submat.
1929                For reuse, we replace received C->j with index that should be inserted to submat */
1930               rbuf3_i[ct3++] = ct2;
1931             }
1932           }
1933           ierr = MatSetValues_SeqAIJ(submat,1,&row,idex,subcols,subvals,INSERT_VALUES);CHKERRQ(ierr);
1934 
1935         } else { /* scall == MAT_REUSE_MATRIX */
1936           submat = submats[0];
1937           subc   = (Mat_SeqAIJ*)submat->data;
1938 
1939           nnz = subc->i[row+1] - subc->i[row]; /* num of submat entries in this row */
1940           for (l=0; l<nnz; l++) {
1941             ct2 = rbuf3_i[ct3++]; /* index of rbuf4_i[] which needs to be inserted into submat */
1942             subvals[idex++] = rbuf4_i[ct2];
1943           }
1944 
1945           bj = subc->j + subc->i[row];
1946           ierr = MatSetValues_SeqAIJ(submat,1,&row,nnz,bj,subvals,INSERT_VALUES);CHKERRQ(ierr);
1947         }
1948       } else { /* allcolumns */
1949         nnz  = rbuf2_i[ct1]; /* num of C entries in this row */
1950         ierr = MatSetValues_SeqAIJ(submat,1,&row,nnz,rbuf3_i+ct2,rbuf4_i+ct2,INSERT_VALUES);CHKERRQ(ierr);
1951         ct2 += nnz;
1952       }
1953     }
1954   }
1955 
1956   /* sending a->a are done */
1957   ierr = MPI_Waitall(nrqr,s_waits4,s_status4);CHKERRQ(ierr);
1958   ierr = PetscFree4(r_waits4,s_waits4,r_status4,s_status4);CHKERRQ(ierr);
1959 
1960   ierr = MatAssemblyBegin(submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1961   ierr = MatAssemblyEnd(submat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1962   submats[0] = submat;
1963 
1964   /* Restore the indices */
1965   ierr = ISRestoreIndices(isrow[0],&irow);CHKERRQ(ierr);
1966   if (!allcolumns) {
1967     ierr = ISRestoreIndices(iscol[0],&icol);CHKERRQ(ierr);
1968   }
1969 
1970   /* Destroy allocated memory */
1971   for (i=0; i<nrqs; ++i) {
1972     ierr = PetscFree3(rbuf4[i],subcols,subvals);CHKERRQ(ierr);
1973   }
1974   ierr = PetscFree3(rbuf4,subcols,subvals);CHKERRQ(ierr);
1975   ierr = PetscFree(sbuf_aa[0]);CHKERRQ(ierr);
1976   ierr = PetscFree(sbuf_aa);CHKERRQ(ierr);
1977 
1978   if (scall == MAT_INITIAL_MATRIX) {
1979     ierr = PetscFree(lens);CHKERRQ(ierr);
1980     ierr = PetscFree(sbuf_aj[0]);CHKERRQ(ierr);
1981     ierr = PetscFree(sbuf_aj);CHKERRQ(ierr);
1982   }
1983   PetscFunctionReturn(0);
1984 }
1985 
1986 PetscErrorCode MatGetSubMatrices_MPIAIJ_SingleIS(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
1987 {
1988   PetscErrorCode ierr;
1989   PetscInt       ncol;
1990   PetscBool      colflag,allcolumns=PETSC_FALSE;
1991 
1992   PetscFunctionBegin;
1993   /* Allocate memory to hold all the submatrices */
1994   if (scall == MAT_INITIAL_MATRIX) {
1995     ierr = PetscMalloc1(1,submat);CHKERRQ(ierr);
1996   }
1997 
1998   /* Check for special case: each processor gets entire matrix columns */
1999   ierr = ISIdentity(iscol[0],&colflag);CHKERRQ(ierr);
2000   ierr = ISGetLocalSize(iscol[0],&ncol);CHKERRQ(ierr);
2001   if (colflag && ncol == C->cmap->N) allcolumns = PETSC_TRUE;
2002 
2003   ierr = MatGetSubMatrices_MPIAIJ_SingleIS_Local(C,ismax,isrow,iscol,scall,allcolumns,*submat);CHKERRQ(ierr);
2004   PetscFunctionReturn(0);
2005 }
2006 
2007 PetscErrorCode MatGetSubMatrices_MPIAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
2008 {
2009   PetscErrorCode ierr;
2010   PetscInt       nmax,nstages_local,nstages,i,pos,max_no,nrow,ncol;
2011   PetscBool      rowflag,colflag,wantallmatrix=PETSC_FALSE,twantallmatrix,*allcolumns;
2012 
2013   PetscFunctionBegin;
2014 #if 0
2015   /* Check for special case: each processor gets entire matrix */
2016   if (C->submat_singleis) { /* flag is set in PCSetUp_ASM() to skip several MPIU_Allreduce() */
2017     ierr = MatGetSubMatrices_MPIAIJ_SingleIS(C,ismax,isrow,iscol,scall,submat);CHKERRQ(ierr);
2018     PetscFunctionReturn(0);
2019   }
2020 #endif
2021 
2022   if (ismax == 1 && C->rmap->N == C->cmap->N) {
2023     ierr = ISIdentity(*isrow,&rowflag);CHKERRQ(ierr);
2024     ierr = ISIdentity(*iscol,&colflag);CHKERRQ(ierr);
2025     ierr = ISGetLocalSize(*isrow,&nrow);CHKERRQ(ierr);
2026     ierr = ISGetLocalSize(*iscol,&ncol);CHKERRQ(ierr);
2027     if (rowflag && colflag && nrow == C->rmap->N && ncol == C->cmap->N) {
2028       wantallmatrix = PETSC_TRUE;
2029 
2030       ierr = PetscOptionsGetBool(((PetscObject)C)->options,((PetscObject)C)->prefix,"-use_fast_submatrix",&wantallmatrix,NULL);CHKERRQ(ierr);
2031     }
2032   }
2033   ierr = MPIU_Allreduce(&wantallmatrix,&twantallmatrix,1,MPIU_BOOL,MPI_MIN,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
2034   if (twantallmatrix) {
2035     ierr = MatGetSubMatrix_MPIAIJ_All(C,MAT_GET_VALUES,scall,submat);CHKERRQ(ierr);
2036     PetscFunctionReturn(0);
2037   }
2038 
2039   /* Allocate memory to hold all the submatrices */
2040   if (scall == MAT_INITIAL_MATRIX) {
2041     ierr = PetscMalloc1(ismax+1,submat);CHKERRQ(ierr);
2042   }
2043 
2044   if (scall == MAT_REUSE_MATRIX && !ismax) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"n=0 is not supported for MatGetSubMatrices(mat,n,isrow,iscol,MAT_REUSE_MATRIX,...). Set n=1 with zero-length isrow and iscolumn instead");
2045 
2046   /* Check for special case: each processor gets entire matrix columns */
2047   ierr = PetscMalloc1(ismax+1,&allcolumns);CHKERRQ(ierr);
2048   for (i=0; i<ismax; i++) {
2049     ierr = ISIdentity(iscol[i],&colflag);CHKERRQ(ierr);
2050     ierr = ISGetLocalSize(iscol[i],&ncol);CHKERRQ(ierr);
2051     if (colflag && ncol == C->cmap->N) {
2052       allcolumns[i] = PETSC_TRUE;
2053     } else {
2054       allcolumns[i] = PETSC_FALSE;
2055     }
2056   }
2057 
2058   /* Determine the number of stages through which submatrices are done */
2059   nmax = 20*1000000 / (C->cmap->N * sizeof(PetscInt));
2060 
2061   /*
2062      Each stage will extract nmax submatrices.
2063      nmax is determined by the matrix column dimension.
2064      If the original matrix has 20M columns, only one submatrix per stage is allowed, etc.
2065   */
2066   if (!nmax) nmax = 1;
2067   nstages_local = ismax/nmax + ((ismax % nmax) ? 1 : 0);
2068 
2069   /* Make sure every processor loops through the nstages */
2070   ierr = MPIU_Allreduce(&nstages_local,&nstages,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
2071 
2072   for (i=0,pos=0; i<nstages; i++) {
2073     if (pos+nmax <= ismax) max_no = nmax;
2074     else if (pos == ismax) max_no = 0;
2075     else                   max_no = ismax-pos;
2076     ierr = MatGetSubMatrices_MPIAIJ_Local(C,max_no,isrow+pos,iscol+pos,scall,allcolumns+pos,*submat+pos);CHKERRQ(ierr);
2077     pos += max_no;
2078   }
2079 
2080   ierr = PetscFree(allcolumns);CHKERRQ(ierr);
2081   PetscFunctionReturn(0);
2082 }
2083 
2084 /* -------------------------------------------------------------------------*/
2085 PetscErrorCode MatGetSubMatrices_MPIAIJ_Local(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,PetscBool *allcolumns,Mat *submats)
2086 {
2087   Mat_MPIAIJ     *c = (Mat_MPIAIJ*)C->data;
2088   Mat            A  = c->A;
2089   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)c->B->data,*mat;
2090   const PetscInt **icol,**irow;
2091   PetscInt       *nrow,*ncol,start;
2092   PetscErrorCode ierr;
2093   PetscMPIInt    rank,size,tag0,tag2,tag3,tag4,*w1,*w2,*w3,*w4,nrqr;
2094   PetscInt       **sbuf1,**sbuf2,i,j,k,l,ct1,ct2,**rbuf1,row,proc;
2095   PetscInt       nrqs,msz,**ptr,*req_size,*ctr,*pa,*tmp,tcol;
2096   PetscInt       **rbuf3,*req_source1,*req_source2,**sbuf_aj,**rbuf2,max1,max2;
2097   PetscInt       **lens,is_no,ncols,*cols,mat_i,*mat_j,tmp2,jmax;
2098 #if defined(PETSC_USE_CTABLE)
2099   PetscTable     *cmap,cmap_i=NULL,*rmap,rmap_i;
2100 #else
2101   PetscInt       **cmap,*cmap_i=NULL,**rmap,*rmap_i;
2102 #endif
2103   const PetscInt *irow_i;
2104   PetscInt       ctr_j,*sbuf1_j,*sbuf_aj_i,*rbuf1_i,kmax,*lens_i;
2105   MPI_Request    *s_waits1,*r_waits1,*s_waits2,*r_waits2,*r_waits3;
2106   MPI_Request    *r_waits4,*s_waits3,*s_waits4;
2107   MPI_Status     *r_status1,*r_status2,*s_status1,*s_status3,*s_status2;
2108   MPI_Status     *r_status3,*r_status4,*s_status4;
2109   MPI_Comm       comm;
2110   PetscScalar    **rbuf4,**sbuf_aa,*vals,*mat_a,*sbuf_aa_i;
2111   PetscMPIInt    *onodes1,*olengths1,end;
2112   PetscInt       **row2proc,*row2proc_i;
2113   Mat_SubMat     **smats,*smat_i;
2114   PetscBool      *issorted;
2115 
2116   PetscFunctionBegin;
2117   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2118   size = c->size;
2119   rank = c->rank;
2120   //if (ismax == 0) printf("[%d] MatGetSubMatrices_MPIAIJ_Local, scall %d, ismax = 0!!! \n",rank,scall);
2121   //printf("[%d] MatGetSubMatrices_MPIAIJ_Local, scall %d\n",rank,scall);
2122 
2123   ierr = PetscMalloc4(ismax,&irow,ismax,&icol,ismax,&nrow,ismax,&ncol);CHKERRQ(ierr);
2124   ierr = PetscMalloc1(ismax,&issorted);CHKERRQ(ierr);
2125 
2126   for (i=0; i<ismax; i++) {
2127     ierr = ISSorted(isrow[i],&issorted[i]);CHKERRQ(ierr);
2128 
2129     ierr = ISGetIndices(isrow[i],&irow[i]);CHKERRQ(ierr);
2130     ierr = ISGetLocalSize(isrow[i],&nrow[i]);CHKERRQ(ierr);
2131     if (allcolumns[i]) {
2132       icol[i] = NULL;
2133       ncol[i] = C->cmap->N;
2134     } else {
2135       ierr = ISGetIndices(iscol[i],&icol[i]);CHKERRQ(ierr);
2136       ierr = ISGetLocalSize(iscol[i],&ncol[i]);CHKERRQ(ierr);
2137     }
2138   }
2139 
2140   ierr = PetscMalloc1(ismax,&smats);CHKERRQ(ierr);
2141   ierr = PetscMalloc1(ismax,&row2proc);CHKERRQ(ierr);
2142   ierr = PetscMalloc1(ismax,&cmap);CHKERRQ(ierr);
2143   ierr = PetscMalloc1(ismax,&rmap);CHKERRQ(ierr);
2144 
2145   if (scall == MAT_REUSE_MATRIX) {
2146     /* Assumes new rows are same length as the old rows,hence bug! */
2147     for (i=0; i<ismax; i++) {
2148       mat = (Mat_SeqAIJ*)(submats[i]->data);
2149       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");
2150 
2151       /* Initial matrix as if empty -- rm later!!! */
2152       ierr = PetscMemzero(mat->ilen,submats[i]->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2153 
2154       /* Initial matrix as if empty */
2155       submats[i]->factortype = C->factortype;
2156 
2157       smat_i   = mat->submatis1;
2158       smats[i] = smat_i;
2159 
2160       nrqs        = smat_i->nrqs;
2161       nrqr        = smat_i->nrqr;
2162       rbuf1       = smat_i->rbuf1;
2163       rbuf2       = smat_i->rbuf2;
2164       rbuf3       = smat_i->rbuf3;
2165       req_source2 = smat_i->req_source2;
2166 
2167       sbuf1     = smat_i->sbuf1;
2168       sbuf2     = smat_i->sbuf2;
2169       ptr       = smat_i->ptr;
2170       tmp       = smat_i->tmp;
2171       ctr       = smat_i->ctr;
2172 
2173       pa          = smat_i->pa;
2174       req_size    = smat_i->req_size;
2175       req_source1 = smat_i->req_source1;
2176 
2177       allcolumns[i] = smat_i->allcolumns;
2178       row2proc[i]   = smat_i->row2proc;
2179       rmap[i]       = smat_i->rmap;
2180       cmap[i]       = smat_i->cmap;
2181 #if defined(PETSC_USE_CTABLE)
2182       //rmap_loc   = smat_i->rmap_loc;
2183       //cmap_loc   = smat_i->cmap_loc;
2184 #endif
2185     }
2186   }
2187 
2188   if (scall == MAT_INITIAL_MATRIX) {
2189     /* Get some new tags to keep the communication clean */
2190     ierr = PetscObjectGetNewTag((PetscObject)C,&tag2);CHKERRQ(ierr);
2191     ierr = PetscObjectGetNewTag((PetscObject)C,&tag3);CHKERRQ(ierr);
2192 
2193   /* evaluate communication - mesg to who, length of mesg, and buffer space
2194      required. Based on this, buffers are allocated, and data copied into them*/
2195   ierr = PetscMalloc4(size,&w1,size,&w2,size,&w3,size,&w4);CHKERRQ(ierr);   /* mesg size */
2196   ierr = PetscMemzero(w1,size*sizeof(PetscMPIInt));CHKERRQ(ierr);   /* initialize work vector*/
2197   ierr = PetscMemzero(w2,size*sizeof(PetscMPIInt));CHKERRQ(ierr);   /* initialize work vector*/
2198   ierr = PetscMemzero(w3,size*sizeof(PetscMPIInt));CHKERRQ(ierr);   /* initialize work vector*/
2199 
2200   for (i=0; i<ismax; i++) {
2201     ierr   = PetscMemzero(w4,size*sizeof(PetscMPIInt));CHKERRQ(ierr); /* initialize work vector*/
2202     jmax   = nrow[i];
2203     irow_i = irow[i];
2204 
2205     ierr   = PetscMalloc1(jmax,&row2proc_i);CHKERRQ(ierr);
2206     row2proc[i] = row2proc_i;
2207 
2208     if (issorted[i]) proc = 0;
2209     for (j=0; j<jmax; j++) {
2210       if (!issorted[i]) proc = 0;
2211       row = irow_i[j];
2212       while (row >= C->rmap->range[proc+1]) proc++;
2213       w4[proc]++;
2214       row2proc_i[j] = proc; /* map row index to proc */
2215     }
2216     for (j=0; j<size; j++) {
2217       if (w4[j]) { w1[j] += w4[j];  w3[j]++;}
2218     }
2219   }
2220 
2221   nrqs     = 0;              /* no of outgoing messages */
2222   msz      = 0;              /* total mesg length (for all procs) */
2223   w1[rank] = 0;              /* no mesg sent to self */
2224   w3[rank] = 0;
2225   for (i=0; i<size; i++) {
2226     if (w1[i])  { w2[i] = 1; nrqs++;} /* there exists a message to proc i */
2227   }
2228   ierr = PetscMalloc1(nrqs+1,&pa);CHKERRQ(ierr); /*(proc -array)*/
2229   for (i=0,j=0; i<size; i++) {
2230     if (w1[i]) { pa[j] = i; j++; }
2231   }
2232 
2233   /* Each message would have a header = 1 + 2*(no of IS) + data */
2234   for (i=0; i<nrqs; i++) {
2235     j      = pa[i];
2236     w1[j] += w2[j] + 2* w3[j];
2237     msz   += w1[j];
2238   }
2239   ierr = PetscInfo2(0,"Number of outgoing messages %D Total message length %D\n",nrqs,msz);CHKERRQ(ierr);
2240 
2241   /* Determine the number of messages to expect, their lengths, from from-ids */
2242   ierr = PetscGatherNumberOfMessages(comm,w2,w1,&nrqr);CHKERRQ(ierr);
2243   ierr = PetscGatherMessageLengths(comm,nrqs,nrqr,w1,&onodes1,&olengths1);CHKERRQ(ierr);
2244 
2245   /* Now post the Irecvs corresponding to these messages */
2246   tag0 = ((PetscObject)C)->tag;
2247   ierr = PetscPostIrecvInt(comm,tag0,nrqr,onodes1,olengths1,&rbuf1,&r_waits1);CHKERRQ(ierr);
2248 
2249   ierr = PetscFree(onodes1);CHKERRQ(ierr);
2250   ierr = PetscFree(olengths1);CHKERRQ(ierr);
2251 
2252   /* Allocate Memory for outgoing messages */
2253   ierr = PetscMalloc4(size,&sbuf1,size,&ptr,2*msz,&tmp,size,&ctr);CHKERRQ(ierr);
2254   ierr = PetscMemzero(sbuf1,size*sizeof(PetscInt*));CHKERRQ(ierr);
2255   ierr = PetscMemzero(ptr,size*sizeof(PetscInt*));CHKERRQ(ierr);
2256 
2257   {
2258     PetscInt *iptr = tmp;
2259     k    = 0;
2260     for (i=0; i<nrqs; i++) {
2261       j        = pa[i];
2262       iptr    += k;
2263       sbuf1[j] = iptr;
2264       k        = w1[j];
2265     }
2266   }
2267 
2268   /* Form the outgoing messages */
2269   /* Initialize the header space */
2270   for (i=0; i<nrqs; i++) {
2271     j           = pa[i];
2272     sbuf1[j][0] = 0;
2273     ierr        = PetscMemzero(sbuf1[j]+1,2*w3[j]*sizeof(PetscInt));CHKERRQ(ierr);
2274     ptr[j]      = sbuf1[j] + 2*w3[j] + 1;
2275   }
2276 
2277   /* Parse the isrow and copy data into outbuf */
2278   for (i=0; i<ismax; i++) {
2279     row2proc_i = row2proc[i];
2280     ierr   = PetscMemzero(ctr,size*sizeof(PetscInt));CHKERRQ(ierr);
2281     irow_i = irow[i];
2282     jmax   = nrow[i];
2283     for (j=0; j<jmax; j++) {  /* parse the indices of each IS */
2284       proc = row2proc_i[j];
2285       if (proc != rank) { /* copy to the outgoing buf*/
2286         ctr[proc]++;
2287         *ptr[proc] = irow_i[j];
2288         ptr[proc]++;
2289       }
2290     }
2291     /* Update the headers for the current IS */
2292     for (j=0; j<size; j++) { /* Can Optimise this loop too */
2293       if ((ctr_j = ctr[j])) {
2294         sbuf1_j        = sbuf1[j];
2295         k              = ++sbuf1_j[0];
2296         sbuf1_j[2*k]   = ctr_j;
2297         sbuf1_j[2*k-1] = i;
2298       }
2299     }
2300   }
2301 
2302   /*  Now  post the sends */
2303   ierr = PetscMalloc1(nrqs+1,&s_waits1);CHKERRQ(ierr);
2304   for (i=0; i<nrqs; ++i) {
2305     j    = pa[i];
2306     ierr = MPI_Isend(sbuf1[j],w1[j],MPIU_INT,j,tag0,comm,s_waits1+i);CHKERRQ(ierr);
2307   }
2308 
2309   /* Post Receives to capture the buffer size */
2310   ierr = PetscMalloc1(nrqs+1,&r_waits2);CHKERRQ(ierr);
2311   ierr = PetscMalloc3(nrqs+1,&req_source2,nrqs+1,&rbuf2,nrqs+1,&rbuf3);CHKERRQ(ierr);
2312   rbuf2[0] = tmp + msz;
2313   for (i=1; i<nrqs; ++i) {
2314     rbuf2[i] = rbuf2[i-1]+w1[pa[i-1]];
2315   }
2316   for (i=0; i<nrqs; ++i) {
2317     j    = pa[i];
2318     ierr = MPI_Irecv(rbuf2[i],w1[j],MPIU_INT,j,tag2,comm,r_waits2+i);CHKERRQ(ierr);
2319   }
2320 
2321   /* Send to other procs the buf size they should allocate */
2322   /* Receive messages*/
2323   ierr = PetscMalloc1(nrqr+1,&s_waits2);CHKERRQ(ierr);
2324   ierr = PetscMalloc1(nrqr+1,&r_status1);CHKERRQ(ierr);
2325   ierr = PetscMalloc3(nrqr,&sbuf2,nrqr,&req_size,nrqr,&req_source1);CHKERRQ(ierr);
2326   {
2327     PetscInt   *sAi = a->i,*sBi = b->i,id,rstart = C->rmap->rstart;
2328     PetscInt   *sbuf2_i;
2329 
2330     ierr = MPI_Waitall(nrqr,r_waits1,r_status1);CHKERRQ(ierr);
2331     for (i=0; i<nrqr; ++i) {
2332       req_size[i] = 0;
2333       rbuf1_i        = rbuf1[i];
2334       start          = 2*rbuf1_i[0] + 1;
2335       ierr           = MPI_Get_count(r_status1+i,MPIU_INT,&end);CHKERRQ(ierr);
2336       ierr           = PetscMalloc1(end+1,&sbuf2[i]);CHKERRQ(ierr);
2337       sbuf2_i        = sbuf2[i];
2338       for (j=start; j<end; j++) {
2339         id              = rbuf1_i[j] - rstart;
2340         ncols           = sAi[id+1] - sAi[id] + sBi[id+1] - sBi[id];
2341         sbuf2_i[j]      = ncols;
2342         req_size[i] += ncols;
2343       }
2344       req_source1[i] = r_status1[i].MPI_SOURCE;
2345       /* form the header */
2346       sbuf2_i[0] = req_size[i];
2347       for (j=1; j<start; j++) sbuf2_i[j] = rbuf1_i[j];
2348 
2349       ierr = MPI_Isend(sbuf2_i,end,MPIU_INT,req_source1[i],tag2,comm,s_waits2+i);CHKERRQ(ierr);
2350     }
2351   }
2352   ierr = PetscFree(r_status1);CHKERRQ(ierr);
2353   ierr = PetscFree(r_waits1);CHKERRQ(ierr);
2354 
2355   /* Receive messages*/
2356   ierr = PetscMalloc1(nrqs+1,&r_waits3);CHKERRQ(ierr);
2357   ierr = PetscMalloc1(nrqs+1,&r_status2);CHKERRQ(ierr);
2358 
2359   ierr = MPI_Waitall(nrqs,r_waits2,r_status2);CHKERRQ(ierr);
2360   for (i=0; i<nrqs; ++i) {
2361     ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf3[i]);CHKERRQ(ierr);
2362     req_source2[i] = r_status2[i].MPI_SOURCE;
2363     ierr = MPI_Irecv(rbuf3[i],rbuf2[i][0],MPIU_INT,req_source2[i],tag3,comm,r_waits3+i);CHKERRQ(ierr);
2364   }
2365   ierr = PetscFree(r_status2);CHKERRQ(ierr);
2366   ierr = PetscFree(r_waits2);CHKERRQ(ierr);
2367 
2368   /* Wait on sends1 and sends2 */
2369   ierr = PetscMalloc1(nrqs+1,&s_status1);CHKERRQ(ierr);
2370   ierr = PetscMalloc1(nrqr+1,&s_status2);CHKERRQ(ierr);
2371 
2372   if (nrqs) {ierr = MPI_Waitall(nrqs,s_waits1,s_status1);CHKERRQ(ierr);}
2373   if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits2,s_status2);CHKERRQ(ierr);}
2374   ierr = PetscFree(s_status1);CHKERRQ(ierr);
2375   ierr = PetscFree(s_status2);CHKERRQ(ierr);
2376   ierr = PetscFree(s_waits1);CHKERRQ(ierr);
2377   ierr = PetscFree(s_waits2);CHKERRQ(ierr);
2378 
2379   /* Now allocate sending buffers for a->j, and send them off */
2380   ierr = PetscMalloc1(nrqr+1,&sbuf_aj);CHKERRQ(ierr);
2381   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
2382   ierr = PetscMalloc1(j+1,&sbuf_aj[0]);CHKERRQ(ierr);
2383   for (i=1; i<nrqr; i++) sbuf_aj[i] = sbuf_aj[i-1] + req_size[i-1];
2384 
2385   ierr = PetscMalloc1(nrqr+1,&s_waits3);CHKERRQ(ierr);
2386   {
2387     PetscInt nzA,nzB,*a_i = a->i,*b_i = b->i,lwrite;
2388     PetscInt *cworkA,*cworkB,cstart = C->cmap->rstart,rstart = C->rmap->rstart,*bmap = c->garray;
2389     PetscInt cend = C->cmap->rend;
2390     PetscInt *a_j = a->j,*b_j = b->j,ctmp;
2391 
2392     for (i=0; i<nrqr; i++) {
2393       rbuf1_i   = rbuf1[i];
2394       sbuf_aj_i = sbuf_aj[i];
2395       ct1       = 2*rbuf1_i[0] + 1;
2396       ct2       = 0;
2397       for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
2398         kmax = rbuf1[i][2*j];
2399         for (k=0; k<kmax; k++,ct1++) {
2400           row    = rbuf1_i[ct1] - rstart;
2401           nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
2402           ncols  = nzA + nzB;
2403           cworkA = a_j + a_i[row]; cworkB = b_j + b_i[row];
2404 
2405           /* load the column indices for this row into cols*/
2406           cols = sbuf_aj_i + ct2;
2407 
2408           lwrite = 0;
2409           for (l=0; l<nzB; l++) {
2410             if ((ctmp = bmap[cworkB[l]]) < cstart) cols[lwrite++] = ctmp;
2411           }
2412           for (l=0; l<nzA; l++) cols[lwrite++] = cstart + cworkA[l];
2413           for (l=0; l<nzB; l++) {
2414             if ((ctmp = bmap[cworkB[l]]) >= cend) cols[lwrite++] = ctmp;
2415           }
2416 
2417           ct2 += ncols;
2418         }
2419       }
2420       ierr = MPI_Isend(sbuf_aj_i,req_size[i],MPIU_INT,req_source1[i],tag3,comm,s_waits3+i);CHKERRQ(ierr);
2421     }
2422   }
2423   ierr = PetscMalloc1(nrqs+1,&r_status3);CHKERRQ(ierr);
2424   ierr = PetscMalloc1(nrqr+1,&s_status3);CHKERRQ(ierr);
2425 
2426   if (scall == MAT_INITIAL_MATRIX) {
2427     /* create col map: global col of C -> local col of submatrices */
2428     const PetscInt *icol_i;
2429 #if defined(PETSC_USE_CTABLE)
2430     for (i=0; i<ismax; i++) {
2431       if (!allcolumns[i]) {
2432         ierr = PetscTableCreate(ncol[i]+1,C->cmap->N+1,&cmap[i]);CHKERRQ(ierr);
2433 
2434         jmax   = ncol[i];
2435         icol_i = icol[i];
2436         cmap_i = cmap[i];
2437         for (j=0; j<jmax; j++) {
2438           ierr = PetscTableAdd(cmap[i],icol_i[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
2439         }
2440       } else cmap[i] = NULL;
2441     }
2442 #else
2443     for (i=0; i<ismax; i++) {
2444       if (!allcolumns[i]) {
2445         ierr   = PetscMalloc1(C->cmap->N,&cmap[i]);CHKERRQ(ierr);
2446         ierr   = PetscMemzero(cmap[i],C->cmap->N*sizeof(PetscInt));CHKERRQ(ierr);
2447         jmax   = ncol[i];
2448         icol_i = icol[i];
2449         cmap_i = cmap[i];
2450         for (j=0; j<jmax; j++) {
2451           cmap_i[icol_i[j]] = j+1;
2452         }
2453       } else cmap[i] = NULL;
2454     }
2455 #endif
2456   }
2457 
2458   //if (scall == MAT_INITIAL_MATRIX) {
2459   /* Create lens which is required for MatCreate... */
2460   for (i=0,j=0; i<ismax; i++) j += nrow[i];
2461   ierr = PetscMalloc1(ismax,&lens);CHKERRQ(ierr);
2462   if (ismax) {
2463     ierr = PetscMalloc1(j,&lens[0]);CHKERRQ(ierr);
2464     ierr = PetscMemzero(lens[0],j*sizeof(PetscInt));CHKERRQ(ierr);
2465   }
2466   for (i=1; i<ismax; i++) lens[i] = lens[i-1] + nrow[i-1];
2467 
2468   /* Update lens from local data */
2469   for (i=0; i<ismax; i++) {
2470     row2proc_i = row2proc[i];
2471     jmax = nrow[i];
2472     if (!allcolumns[i]) cmap_i = cmap[i];
2473     irow_i = irow[i];
2474     lens_i = lens[i];
2475     for (j=0; j<jmax; j++) {
2476       row = irow_i[j];
2477       proc = row2proc_i[j];
2478       if (proc == rank) {
2479         ierr = MatGetRow_MPIAIJ(C,row,&ncols,&cols,0);CHKERRQ(ierr);
2480         if (!allcolumns[i]) {
2481           for (k=0; k<ncols; k++) {
2482 #if defined(PETSC_USE_CTABLE)
2483             ierr = PetscTableFind(cmap_i,cols[k]+1,&tcol);CHKERRQ(ierr);
2484 #else
2485             tcol = cmap_i[cols[k]];
2486 #endif
2487             if (tcol) lens_i[j]++;
2488           }
2489         } else { /* allcolumns */
2490           lens_i[j] = ncols;
2491         }
2492         ierr = MatRestoreRow_MPIAIJ(C,row,&ncols,&cols,0);CHKERRQ(ierr);
2493       }
2494     }
2495   }
2496   //}
2497 
2498   /* Create row map: global row of C -> local row of submatrices */
2499   if (scall == MAT_INITIAL_MATRIX) {
2500 #if defined(PETSC_USE_CTABLE)
2501     for (i=0; i<ismax; i++) {
2502       ierr   = PetscTableCreate(nrow[i]+1,C->rmap->N+1,&rmap[i]);CHKERRQ(ierr);
2503       irow_i = irow[i];
2504       jmax   = nrow[i];
2505       for (j=0; j<jmax; j++) {
2506       ierr = PetscTableAdd(rmap[i],irow_i[j]+1,j+1,INSERT_VALUES);CHKERRQ(ierr);
2507       }
2508     }
2509 #else
2510     if (ismax) {
2511       ierr = PetscMalloc1(ismax*C->rmap->N,&rmap[0]);CHKERRQ(ierr);
2512       ierr = PetscMemzero(rmap[0],ismax*C->rmap->N*sizeof(PetscInt));CHKERRQ(ierr);
2513     }
2514     for (i=1; i<ismax; i++) rmap[i] = rmap[i-1] + C->rmap->N;
2515     for (i=0; i<ismax; i++) {
2516       rmap_i = rmap[i];
2517       irow_i = irow[i];
2518       jmax   = nrow[i];
2519       for (j=0; j<jmax; j++) {
2520         rmap_i[irow_i[j]] = j;
2521       }
2522     }
2523 #endif
2524   }
2525 
2526   /* Update lens from offproc data */
2527   {
2528     PetscInt *rbuf2_i,*rbuf3_i,*sbuf1_i;
2529 
2530     ierr    = MPI_Waitall(nrqs,r_waits3,r_status3);CHKERRQ(ierr);
2531     for (tmp2=0; tmp2<nrqs; tmp2++) {
2532       sbuf1_i = sbuf1[pa[tmp2]];
2533       jmax    = sbuf1_i[0];
2534       ct1     = 2*jmax+1;
2535       ct2     = 0;
2536       rbuf2_i = rbuf2[tmp2];
2537       rbuf3_i = rbuf3[tmp2];
2538       for (j=1; j<=jmax; j++) {
2539         is_no  = sbuf1_i[2*j-1];
2540         max1   = sbuf1_i[2*j];
2541         lens_i = lens[is_no];
2542         if (!allcolumns[is_no]) cmap_i = cmap[is_no];
2543         rmap_i = rmap[is_no];
2544         for (k=0; k<max1; k++,ct1++) {
2545 #if defined(PETSC_USE_CTABLE)
2546           ierr = PetscTableFind(rmap_i,sbuf1_i[ct1]+1,&row);CHKERRQ(ierr);
2547           row--;
2548           if (row < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"row not found in table");
2549 #else
2550           row = rmap_i[sbuf1_i[ct1]]; /* the val in the new matrix to be */
2551 #endif
2552           max2 = rbuf2_i[ct1];
2553           for (l=0; l<max2; l++,ct2++) {
2554             if (!allcolumns[is_no]) {
2555 #if defined(PETSC_USE_CTABLE)
2556               ierr = PetscTableFind(cmap_i,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
2557 #else
2558               tcol = cmap_i[rbuf3_i[ct2]];
2559 #endif
2560               if (tcol) lens_i[row]++;
2561             } else { /* allcolumns */
2562               lens_i[row]++; /* lens_i[row] += max2 ? */
2563             }
2564           }
2565         }
2566       }
2567     }
2568   }
2569   ierr = PetscFree(r_status3);CHKERRQ(ierr);
2570   ierr = PetscFree(r_waits3);CHKERRQ(ierr);
2571   if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits3,s_status3);CHKERRQ(ierr);}
2572   ierr = PetscFree(s_status3);CHKERRQ(ierr);
2573   ierr = PetscFree(s_waits3);CHKERRQ(ierr);
2574 
2575   } // endof scall == MAT_INITIAL_MATRIX
2576 
2577   /* Create the submatrices */
2578   if (scall == MAT_INITIAL_MATRIX) {
2579     for (i=0; i<ismax; i++) {
2580       PetscInt    rbs,cbs;
2581       Mat_SeqAIJ* subc;
2582 
2583       ierr = ISGetBlockSize(isrow[i],&rbs);CHKERRQ(ierr);
2584       ierr = ISGetBlockSize(iscol[i],&cbs);CHKERRQ(ierr);
2585 
2586       ierr = MatCreate(PETSC_COMM_SELF,submats+i);CHKERRQ(ierr);
2587       ierr = MatSetSizes(submats[i],nrow[i],ncol[i],PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2588 
2589       ierr = MatSetBlockSizes(submats[i],rbs,cbs);CHKERRQ(ierr);
2590       ierr = MatSetType(submats[i],((PetscObject)A)->type_name);CHKERRQ(ierr);
2591       ierr = MatSeqAIJSetPreallocation(submats[i],0,lens[i]);CHKERRQ(ierr);
2592 
2593       /* create struct Mat_SubMat and attached it to submat */
2594       ierr = PetscNew(&smat_i);CHKERRQ(ierr);
2595       subc = (Mat_SeqAIJ*)submats[i]->data;
2596       subc->submatis1 = smat_i;
2597       smats[i]        = smat_i;
2598 
2599       smat_i->destroy          = submats[i]->ops->destroy;
2600       submats[i]->ops->destroy = MatDestroy_MPIAIJ_MatGetSubmatrices;
2601       submats[i]->factortype   = C->factortype;
2602 
2603       smat_i->id          = i;
2604       smat_i->nrqs        = nrqs;
2605       smat_i->nrqr        = nrqr;
2606       smat_i->rbuf1       = rbuf1;
2607       smat_i->rbuf2       = rbuf2;
2608       smat_i->rbuf3       = rbuf3;
2609       smat_i->sbuf2       = sbuf2;
2610       smat_i->req_source2 = req_source2;
2611 
2612       smat_i->sbuf1       = sbuf1;
2613       smat_i->ptr         = ptr;
2614       smat_i->tmp         = tmp;
2615       smat_i->ctr         = ctr;
2616 
2617       smat_i->pa           = pa;
2618       smat_i->req_size     = req_size;
2619       smat_i->req_source1  = req_source1;
2620 
2621       smat_i->allcolumns  = allcolumns[i];
2622       smat_i->row2proc    = row2proc[i];
2623       smat_i->rmap        = rmap[i];
2624       smat_i->cmap        = cmap[i];
2625 #if defined(PETSC_USE_CTABLE)
2626       smat_i->rmap_loc    = NULL;//rmap_loc;
2627       smat_i->cmap_loc    = NULL;//cmap_loc;
2628 #endif
2629 
2630     }
2631   } // endof scall == MAT_INITIAL_MATRIX
2632 
2633   /* Post recv matrix values */
2634   ierr = PetscObjectGetNewTag((PetscObject)C,&tag4);CHKERRQ(ierr);
2635   ierr = PetscMalloc1(nrqs+1,&rbuf4);CHKERRQ(ierr);
2636   ierr = PetscMalloc1(nrqs+1,&r_waits4);CHKERRQ(ierr);
2637   ierr = PetscMalloc1(nrqs+1,&r_status4);CHKERRQ(ierr);
2638   ierr = PetscMalloc1(nrqr+1,&s_status4);CHKERRQ(ierr);
2639   for (i=0; i<nrqs; ++i) {
2640     ierr = PetscMalloc1(rbuf2[i][0]+1,&rbuf4[i]);CHKERRQ(ierr);
2641     ierr = MPI_Irecv(rbuf4[i],rbuf2[i][0],MPIU_SCALAR,req_source2[i],tag4,comm,r_waits4+i);CHKERRQ(ierr);
2642   }
2643 
2644   /* Allocate sending buffers for a->a, and send them off */
2645   ierr = PetscMalloc1(nrqr+1,&sbuf_aa);CHKERRQ(ierr);
2646   for (i=0,j=0; i<nrqr; i++) j += req_size[i];
2647   ierr = PetscMalloc1(j+1,&sbuf_aa[0]);CHKERRQ(ierr);
2648   for (i=1; i<nrqr; i++) sbuf_aa[i] = sbuf_aa[i-1] + req_size[i-1];
2649 
2650   ierr = PetscMalloc1(nrqr+1,&s_waits4);CHKERRQ(ierr);
2651   {
2652     PetscInt    nzA,nzB,*a_i = a->i,*b_i = b->i, *cworkB,lwrite;
2653     PetscInt    cstart = C->cmap->rstart,rstart = C->rmap->rstart,*bmap = c->garray;
2654     PetscInt    cend   = C->cmap->rend;
2655     PetscInt    *b_j   = b->j;
2656     PetscScalar *vworkA,*vworkB,*a_a = a->a,*b_a = b->a;
2657 
2658     for (i=0; i<nrqr; i++) {
2659       rbuf1_i   = rbuf1[i];
2660       sbuf_aa_i = sbuf_aa[i];
2661       ct1       = 2*rbuf1_i[0]+1;
2662       ct2       = 0;
2663       for (j=1,max1=rbuf1_i[0]; j<=max1; j++) {
2664         kmax = rbuf1_i[2*j];
2665         for (k=0; k<kmax; k++,ct1++) {
2666           row    = rbuf1_i[ct1] - rstart;
2667           nzA    = a_i[row+1] - a_i[row];     nzB = b_i[row+1] - b_i[row];
2668           ncols  = nzA + nzB;
2669           cworkB = b_j + b_i[row];
2670           vworkA = a_a + a_i[row];
2671           vworkB = b_a + b_i[row];
2672 
2673           /* load the column values for this row into vals*/
2674           vals = sbuf_aa_i+ct2;
2675 
2676           lwrite = 0;
2677           for (l=0; l<nzB; l++) {
2678             if ((bmap[cworkB[l]]) < cstart) vals[lwrite++] = vworkB[l];
2679           }
2680           for (l=0; l<nzA; l++) vals[lwrite++] = vworkA[l];
2681           for (l=0; l<nzB; l++) {
2682             if ((bmap[cworkB[l]]) >= cend) vals[lwrite++] = vworkB[l];
2683           }
2684 
2685           ct2 += ncols;
2686         }
2687       }
2688       ierr = MPI_Isend(sbuf_aa_i,req_size[i],MPIU_SCALAR,req_source1[i],tag4,comm,s_waits4+i);CHKERRQ(ierr);
2689     }
2690   }
2691 
2692   if (!ismax) {
2693     ierr = PetscFree(rbuf1[0]);CHKERRQ(ierr);
2694     ierr = PetscFree(rbuf1);CHKERRQ(ierr);
2695   }
2696 
2697   /* Assemble the matrices */
2698   /* First assemble the local rows */
2699   {
2700     PetscInt    ilen_row,*imat_ilen,*imat_j,*imat_i,old_row;
2701     PetscScalar *imat_a;
2702 
2703     for (i=0; i<ismax; i++) {
2704       row2proc_i = row2proc[i];
2705       mat       = (Mat_SeqAIJ*)submats[i]->data;
2706       imat_ilen = mat->ilen;
2707       imat_j    = mat->j;
2708       imat_i    = mat->i;
2709       imat_a    = mat->a;
2710 
2711       if (!allcolumns[i]) cmap_i = cmap[i];
2712       rmap_i = rmap[i];
2713       irow_i = irow[i];
2714       jmax   = nrow[i];
2715       for (j=0; j<jmax; j++) {
2716         row  = irow_i[j];
2717         proc = row2proc_i[j];
2718         if (proc == rank) {
2719           old_row = row;
2720 #if defined(PETSC_USE_CTABLE)
2721           ierr = PetscTableFind(rmap_i,row+1,&row);CHKERRQ(ierr);
2722           row--;
2723 #else
2724           row = rmap_i[row];
2725 #endif
2726           ilen_row = imat_ilen[row];
2727           ierr     = MatGetRow_MPIAIJ(C,old_row,&ncols,&cols,&vals);CHKERRQ(ierr);
2728           mat_i    = imat_i[row];
2729           mat_a    = imat_a + mat_i;
2730           mat_j    = imat_j + mat_i;
2731           if (!allcolumns[i]) {
2732             for (k=0; k<ncols; k++) {
2733 #if defined(PETSC_USE_CTABLE)
2734               ierr = PetscTableFind(cmap_i,cols[k]+1,&tcol);CHKERRQ(ierr);
2735 #else
2736               tcol = cmap_i[cols[k]];
2737 #endif
2738               if (tcol) {
2739                 *mat_j++ = tcol - 1;
2740                 *mat_a++ = vals[k];
2741                 ilen_row++;
2742               }
2743             }
2744           } else { /* allcolumns */
2745             for (k=0; k<ncols; k++) {
2746               *mat_j++ = cols[k];  /* global col index! */
2747               *mat_a++ = vals[k];
2748               ilen_row++;
2749             }
2750           }
2751           ierr = MatRestoreRow_MPIAIJ(C,old_row,&ncols,&cols,&vals);CHKERRQ(ierr);
2752 
2753           imat_ilen[row] = ilen_row;
2754         }
2755       }
2756     }
2757   }
2758 
2759   /*   Now assemble the off proc rows*/
2760   {
2761     PetscInt    *sbuf1_i,*rbuf2_i,*rbuf3_i,*imat_ilen,ilen;
2762     PetscInt    *imat_j,*imat_i;
2763     PetscScalar *imat_a,*rbuf4_i;
2764 
2765     ierr    = MPI_Waitall(nrqs,r_waits4,r_status4);CHKERRQ(ierr);
2766     for (tmp2=0; tmp2<nrqs; tmp2++) {
2767       sbuf1_i = sbuf1[pa[tmp2]];
2768       jmax    = sbuf1_i[0];
2769       ct1     = 2*jmax + 1;
2770       ct2     = 0;
2771       rbuf2_i = rbuf2[tmp2];
2772       rbuf3_i = rbuf3[tmp2];
2773       rbuf4_i = rbuf4[tmp2];
2774       for (j=1; j<=jmax; j++) {
2775         is_no     = sbuf1_i[2*j-1];
2776         rmap_i    = rmap[is_no];
2777         if (!allcolumns[is_no]) cmap_i = cmap[is_no];
2778         mat       = (Mat_SeqAIJ*)submats[is_no]->data;
2779         imat_ilen = mat->ilen;
2780         imat_j    = mat->j;
2781         imat_i    = mat->i;
2782         imat_a    = mat->a;
2783         max1      = sbuf1_i[2*j];
2784         for (k=0; k<max1; k++,ct1++) {
2785           row = sbuf1_i[ct1];
2786 #if defined(PETSC_USE_CTABLE)
2787           ierr = PetscTableFind(rmap_i,row+1,&row);CHKERRQ(ierr);
2788           row--;
2789 #else
2790           row = rmap_i[row];
2791 #endif
2792           ilen  = imat_ilen[row];
2793           mat_i = imat_i[row];
2794           mat_a = imat_a + mat_i;
2795           mat_j = imat_j + mat_i;
2796           max2  = rbuf2_i[ct1];
2797           if (!allcolumns[is_no]) {
2798             for (l=0; l<max2; l++,ct2++) {
2799 
2800 #if defined(PETSC_USE_CTABLE)
2801               ierr = PetscTableFind(cmap_i,rbuf3_i[ct2]+1,&tcol);CHKERRQ(ierr);
2802 #else
2803               tcol = cmap_i[rbuf3_i[ct2]];
2804 #endif
2805               if (tcol) {
2806                 *mat_j++ = tcol - 1;
2807                 *mat_a++ = rbuf4_i[ct2];
2808                 ilen++;
2809               }
2810             }
2811           } else { /* allcolumns */
2812             for (l=0; l<max2; l++,ct2++) {
2813               *mat_j++ = rbuf3_i[ct2]; /* same global column index of C */
2814               *mat_a++ = rbuf4_i[ct2];
2815               ilen++;
2816             }
2817           }
2818           imat_ilen[row] = ilen;
2819         }
2820       }
2821     }
2822   }
2823 
2824   /* sort the rows */
2825   {
2826     PetscInt    *imat_ilen,*imat_j,*imat_i;
2827     PetscScalar *imat_a;
2828 
2829     for (i=0; i<ismax; i++) {
2830       mat       = (Mat_SeqAIJ*)submats[i]->data;
2831       imat_j    = mat->j;
2832       imat_i    = mat->i;
2833       imat_a    = mat->a;
2834       imat_ilen = mat->ilen;
2835 
2836       if (allcolumns[i]) continue;
2837       jmax = nrow[i];
2838       for (j=0; j<jmax; j++) {
2839         PetscInt ilen;
2840 
2841         mat_i = imat_i[j];
2842         mat_a = imat_a + mat_i;
2843         mat_j = imat_j + mat_i;
2844         ilen  = imat_ilen[j];
2845         ierr  = PetscSortIntWithScalarArray(ilen,mat_j,mat_a);CHKERRQ(ierr);
2846       }
2847     }
2848   }
2849 
2850   ierr = PetscFree(r_status4);CHKERRQ(ierr);
2851   ierr = PetscFree(r_waits4);CHKERRQ(ierr);
2852   if (nrqr) {ierr = MPI_Waitall(nrqr,s_waits4,s_status4);CHKERRQ(ierr);}
2853   ierr = PetscFree(s_waits4);CHKERRQ(ierr);
2854   ierr = PetscFree(s_status4);CHKERRQ(ierr);
2855 
2856   /* Restore the indices */
2857   for (i=0; i<ismax; i++) {
2858     ierr = ISRestoreIndices(isrow[i],irow+i);CHKERRQ(ierr);
2859     if (!allcolumns[i]) {
2860       ierr = ISRestoreIndices(iscol[i],icol+i);CHKERRQ(ierr);
2861     }
2862   }
2863 
2864   /* Destroy allocated memory */
2865   ierr = PetscFree4(irow,icol,nrow,ncol);CHKERRQ(ierr);
2866   if (scall == MAT_INITIAL_MATRIX) {
2867     ierr = PetscFree4(w1,w2,w3,w4);CHKERRQ(ierr);
2868   }
2869 
2870   if (!ismax) {
2871     ierr = PetscFree(pa);CHKERRQ(ierr);
2872 
2873     ierr = PetscFree4(sbuf1,ptr,tmp,ctr);CHKERRQ(ierr);
2874     for (i=0; i<nrqr; ++i) {
2875       ierr = PetscFree(sbuf2[i]);CHKERRQ(ierr);
2876     }
2877     for (i=0; i<nrqs; ++i) {
2878       ierr = PetscFree(rbuf3[i]);CHKERRQ(ierr);
2879     }
2880 
2881     ierr = PetscFree3(sbuf2,req_size,req_source1);CHKERRQ(ierr);
2882     ierr = PetscFree3(req_source2,rbuf2,rbuf3);CHKERRQ(ierr);
2883   }
2884 
2885   for (i=0; i<nrqs; ++i) {
2886     ierr = PetscFree(rbuf4[i]);CHKERRQ(ierr);
2887   }
2888   ierr = PetscFree(rbuf4);CHKERRQ(ierr);
2889 
2890   if (scall == MAT_INITIAL_MATRIX) {
2891     ierr = PetscFree(sbuf_aj[0]);CHKERRQ(ierr);
2892     ierr = PetscFree(sbuf_aj);CHKERRQ(ierr);
2893   }
2894   ierr = PetscFree(sbuf_aa[0]);CHKERRQ(ierr);
2895   ierr = PetscFree(sbuf_aa);CHKERRQ(ierr);
2896 
2897   ierr = PetscFree(rmap);CHKERRQ(ierr);
2898   ierr = PetscFree(cmap);CHKERRQ(ierr);
2899 
2900   if (scall == MAT_INITIAL_MATRIX) {
2901     if (ismax) {ierr = PetscFree(lens[0]);CHKERRQ(ierr);}
2902     ierr = PetscFree(lens);CHKERRQ(ierr);
2903   }
2904 
2905   for (i=0; i<ismax; i++) {
2906     ierr = MatAssemblyBegin(submats[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2907     ierr = MatAssemblyEnd(submats[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2908   }
2909 
2910   ierr = PetscFree(issorted);CHKERRQ(ierr);
2911   ierr = PetscFree(row2proc);CHKERRQ(ierr);
2912   ierr = PetscFree(smats);CHKERRQ(ierr);
2913   PetscFunctionReturn(0);
2914 }
2915 
2916 /*
2917  Permute A & B into C's *local* index space using rowemb,dcolemb for A and rowemb,ocolemb for B.
2918  Embeddings are supposed to be injections and the above implies that the range of rowemb is a subset
2919  of [0,m), dcolemb is in [0,n) and ocolemb is in [N-n).
2920  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A&B.
2921  After that B's columns are mapped into C's global column space, so that C is in the "disassembled"
2922  state, and needs to be "assembled" later by compressing B's column space.
2923 
2924  This function may be called in lieu of preallocation, so C should not be expected to be preallocated.
2925  Following this call, C->A & C->B have been created, even if empty.
2926  */
2927 PetscErrorCode MatSetSeqMats_MPIAIJ(Mat C,IS rowemb,IS dcolemb,IS ocolemb,MatStructure pattern,Mat A,Mat B)
2928 {
2929   /* If making this function public, change the error returned in this function away from _PLIB. */
2930   PetscErrorCode ierr;
2931   Mat_MPIAIJ     *aij;
2932   Mat_SeqAIJ     *Baij;
2933   PetscBool      seqaij,Bdisassembled;
2934   PetscInt       m,n,*nz,i,j,ngcol,col,rstart,rend,shift,count;
2935   PetscScalar    v;
2936   const PetscInt *rowindices,*colindices;
2937 
2938   PetscFunctionBegin;
2939   /* Check to make sure the component matrices (and embeddings) are compatible with C. */
2940   if (A) {
2941     ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
2942     if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diagonal matrix is of wrong type");
2943     if (rowemb) {
2944       ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
2945       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);
2946     } else {
2947       if (C->rmap->n != A->rmap->n) {
2948 	SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag seq matrix is row-incompatible with the MPIAIJ matrix");
2949       }
2950     }
2951     if (dcolemb) {
2952       ierr = ISGetLocalSize(dcolemb,&n);CHKERRQ(ierr);
2953       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);
2954     } else {
2955       if (C->cmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag seq matrix is col-incompatible with the MPIAIJ matrix");
2956     }
2957   }
2958   if (B) {
2959     ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
2960     if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diagonal matrix is of wrong type");
2961     if (rowemb) {
2962       ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
2963       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);
2964     } else {
2965       if (C->rmap->n != B->rmap->n) {
2966 	SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Off-diag seq matrix is row-incompatible with the MPIAIJ matrix");
2967       }
2968     }
2969     if (ocolemb) {
2970       ierr = ISGetLocalSize(ocolemb,&n);CHKERRQ(ierr);
2971       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);
2972     } else {
2973       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");
2974     }
2975   }
2976 
2977   aij    = (Mat_MPIAIJ*)(C->data);
2978   if (!aij->A) {
2979     /* Mimic parts of MatMPIAIJSetPreallocation() */
2980     ierr   = MatCreate(PETSC_COMM_SELF,&aij->A);CHKERRQ(ierr);
2981     ierr   = MatSetSizes(aij->A,C->rmap->n,C->cmap->n,C->rmap->n,C->cmap->n);CHKERRQ(ierr);
2982     ierr   = MatSetBlockSizesFromMats(aij->A,C,C);CHKERRQ(ierr);
2983     ierr   = MatSetType(aij->A,MATSEQAIJ);CHKERRQ(ierr);
2984     ierr   = PetscLogObjectParent((PetscObject)C,(PetscObject)aij->A);CHKERRQ(ierr);
2985   }
2986   if (A) {
2987     ierr   = MatSetSeqMat_SeqAIJ(aij->A,rowemb,dcolemb,pattern,A);CHKERRQ(ierr);
2988   } else {
2989     ierr = MatSetUp(aij->A);CHKERRQ(ierr);
2990   }
2991   if (B) { /* Destroy the old matrix or the column map, depending on the sparsity pattern. */
2992     /*
2993       If pattern == DIFFERENT_NONZERO_PATTERN, we reallocate B and
2994       need to "disassemble" B -- convert it to using C's global indices.
2995       To insert the values we take the safer, albeit more expensive, route of MatSetValues().
2996 
2997       If pattern == SUBSET_NONZERO_PATTERN, we do not "disassemble" B and do not reallocate;
2998       we MatZeroValues(B) first, so there may be a bunch of zeros that, perhaps, could be compacted out.
2999 
3000       TODO: Put B's values into aij->B's aij structure in place using the embedding ISs?
3001       At least avoid calling MatSetValues() and the implied searches?
3002     */
3003 
3004     if (B && pattern == DIFFERENT_NONZERO_PATTERN) {
3005 #if defined(PETSC_USE_CTABLE)
3006       ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
3007 #else
3008       ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
3009       /* A bit of a HACK: ideally we should deal with case aij->B all in one code block below. */
3010       if (aij->B) {
3011         ierr = PetscLogObjectMemory((PetscObject)C,-aij->B->cmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3012       }
3013 #endif
3014       ngcol = 0;
3015       if (aij->lvec) {
3016 	ierr = VecGetSize(aij->lvec,&ngcol);CHKERRQ(ierr);
3017       }
3018       if (aij->garray) {
3019 	ierr = PetscFree(aij->garray);CHKERRQ(ierr);
3020 	ierr = PetscLogObjectMemory((PetscObject)C,-ngcol*sizeof(PetscInt));CHKERRQ(ierr);
3021       }
3022       ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
3023       ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
3024     }
3025     if (aij->B && B && pattern == DIFFERENT_NONZERO_PATTERN) {
3026       ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
3027     }
3028     if (aij->B && B && pattern == SUBSET_NONZERO_PATTERN) {
3029       ierr = MatZeroEntries(aij->B);CHKERRQ(ierr);
3030     }
3031   }
3032   Bdisassembled = PETSC_FALSE;
3033   if (!aij->B) {
3034     ierr = MatCreate(PETSC_COMM_SELF,&aij->B);CHKERRQ(ierr);
3035     ierr = PetscLogObjectParent((PetscObject)C,(PetscObject)aij->B);CHKERRQ(ierr);
3036     ierr = MatSetSizes(aij->B,C->rmap->n,C->cmap->N,C->rmap->n,C->cmap->N);CHKERRQ(ierr);
3037     ierr = MatSetBlockSizesFromMats(aij->B,B,B);CHKERRQ(ierr);
3038     ierr = MatSetType(aij->B,MATSEQAIJ);CHKERRQ(ierr);
3039     Bdisassembled = PETSC_TRUE;
3040   }
3041   if (B) {
3042     Baij = (Mat_SeqAIJ*)(B->data);
3043     if (pattern == DIFFERENT_NONZERO_PATTERN) {
3044       ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
3045       for (i=0; i<B->rmap->n; i++) {
3046 	nz[i] = Baij->i[i+1] - Baij->i[i];
3047       }
3048       ierr = MatSeqAIJSetPreallocation(aij->B,0,nz);CHKERRQ(ierr);
3049       ierr = PetscFree(nz);CHKERRQ(ierr);
3050     }
3051 
3052     ierr  = PetscLayoutGetRange(C->rmap,&rstart,&rend);CHKERRQ(ierr);
3053     shift = rend-rstart;
3054     count = 0;
3055     rowindices = NULL;
3056     colindices = NULL;
3057     if (rowemb) {
3058       ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
3059     }
3060     if (ocolemb) {
3061       ierr = ISGetIndices(ocolemb,&colindices);CHKERRQ(ierr);
3062     }
3063     for (i=0; i<B->rmap->n; i++) {
3064       PetscInt row;
3065       row = i;
3066       if (rowindices) row = rowindices[i];
3067       for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
3068 	col  = Baij->j[count];
3069 	if (colindices) col = colindices[col];
3070 	if (Bdisassembled && col>=rstart) col += shift;
3071 	v    = Baij->a[count];
3072 	ierr = MatSetValues(aij->B,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
3073 	++count;
3074       }
3075     }
3076     /* No assembly for aij->B is necessary. */
3077     /* FIXME: set aij->B's nonzerostate correctly. */
3078   } else {
3079     ierr = MatSetUp(aij->B);CHKERRQ(ierr);
3080   }
3081   C->preallocated  = PETSC_TRUE;
3082   C->was_assembled = PETSC_FALSE;
3083   C->assembled     = PETSC_FALSE;
3084    /*
3085       C will need to be assembled so that aij->B can be compressed into local form in MatSetUpMultiply_MPIAIJ().
3086       Furthermore, its nonzerostate will need to be based on that of aij->A's and aij->B's.
3087    */
3088   PetscFunctionReturn(0);
3089 }
3090 
3091 /*
3092   B uses local indices with column indices ranging between 0 and N-n; they  must be interpreted using garray.
3093  */
3094 PetscErrorCode MatGetSeqMats_MPIAIJ(Mat C,Mat *A,Mat *B)
3095 {
3096   Mat_MPIAIJ *aij = (Mat_MPIAIJ*) (C->data);
3097 
3098   PetscFunctionBegin;
3099   PetscValidPointer(A,2);
3100   PetscValidPointer(B,3);
3101   /* FIXME: make sure C is assembled */
3102   *A = aij->A;
3103   *B = aij->B;
3104   /* Note that we don't incref *A and *B, so be careful! */
3105   PetscFunctionReturn(0);
3106 }
3107 
3108 /*
3109   Extract MPI submatrices encoded by pairs of IS that may live on subcomms of C.
3110   NOT SCALABLE due to the use of ISGetNonlocalIS() (see below).
3111 */
3112 PetscErrorCode MatGetSubMatricesMPI_MPIXAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[],
3113                                                  PetscErrorCode(*getsubmats_seq)(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat**),
3114 					         PetscErrorCode(*getlocalmats)(Mat,Mat*,Mat*),
3115 					         PetscErrorCode(*setseqmat)(Mat,IS,IS,MatStructure,Mat),
3116 					         PetscErrorCode(*setseqmats)(Mat,IS,IS,IS,MatStructure,Mat,Mat))
3117 {
3118   PetscErrorCode ierr;
3119   PetscMPIInt    isize,flag;
3120   PetscInt       i,ii,cismax,ispar;
3121   Mat            *A,*B;
3122   IS             *isrow_p,*iscol_p,*cisrow,*ciscol,*ciscol_p;
3123 
3124   PetscFunctionBegin;
3125   if (!ismax) PetscFunctionReturn(0);
3126 
3127   for (i = 0, cismax = 0; i < ismax; ++i) {
3128     PetscMPIInt isize;
3129     ierr = MPI_Comm_compare(((PetscObject)isrow[i])->comm,((PetscObject)iscol[i])->comm,&flag);CHKERRQ(ierr);
3130     if (flag != MPI_IDENT) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Row and column index sets must have the same communicator");
3131     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm, &isize);CHKERRQ(ierr);
3132     if (isize > 1) ++cismax;
3133   }
3134 
3135   /*
3136      If cismax is zero on all C's ranks, then and only then can we use purely sequential matrix extraction.
3137      ispar counts the number of parallel ISs across C's comm.
3138   */
3139   ierr = MPIU_Allreduce(&cismax,&ispar,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)C));CHKERRQ(ierr);
3140   if (!ispar) { /* Sequential ISs only across C's comm, so can call the sequential matrix extraction subroutine. */
3141     ierr = (*getsubmats_seq)(C,ismax,isrow,iscol,scall,submat);CHKERRQ(ierr);
3142     PetscFunctionReturn(0);
3143   }
3144 
3145   /* if (ispar) */
3146   /*
3147     Construct the "complements" -- the off-processor indices -- of the iscol ISs for parallel ISs only.
3148     These are used to extract the off-diag portion of the resulting parallel matrix.
3149     The row IS for the off-diag portion is the same as for the diag portion,
3150     so we merely alias (without increfing) the row IS, while skipping those that are sequential.
3151   */
3152   ierr = PetscMalloc2(cismax,&cisrow,cismax,&ciscol);CHKERRQ(ierr);
3153   ierr = PetscMalloc1(cismax,&ciscol_p);CHKERRQ(ierr);
3154   for (i = 0, ii = 0; i < ismax; ++i) {
3155     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3156     if (isize > 1) {
3157       /*
3158 	 TODO: This is the part that's ***NOT SCALABLE***.
3159 	 To fix this we need to extract just the indices of C's nonzero columns
3160 	 that lie on the intersection of isrow[i] and ciscol[ii] -- the nonlocal
3161 	 part of iscol[i] -- without actually computing ciscol[ii]. This also has
3162 	 to be done without serializing on the IS list, so, most likely, it is best
3163 	 done by rewriting MatGetSubMatrices_MPIAIJ() directly.
3164       */
3165       ierr = ISGetNonlocalIS(iscol[i],&(ciscol[ii]));CHKERRQ(ierr);
3166       /* Now we have to
3167 	 (a) make sure ciscol[ii] is sorted, since, even if the off-proc indices
3168 	     were sorted on each rank, concatenated they might no longer be sorted;
3169 	 (b) Use ISSortPermutation() to construct ciscol_p, the mapping from the
3170 	     indices in the nondecreasing order to the original index positions.
3171 	 If ciscol[ii] is strictly increasing, the permutation IS is NULL.
3172       */
3173       ierr = ISSortPermutation(ciscol[ii],PETSC_FALSE,ciscol_p+ii);CHKERRQ(ierr);
3174       ierr = ISSort(ciscol[ii]);CHKERRQ(ierr);
3175       ++ii;
3176     }
3177   }
3178   ierr = PetscMalloc2(ismax,&isrow_p,ismax,&iscol_p);CHKERRQ(ierr);
3179   for (i = 0, ii = 0; i < ismax; ++i) {
3180     PetscInt       j,issize;
3181     const PetscInt *indices;
3182 
3183     /*
3184        Permute the indices into a nondecreasing order. Reject row and col indices with duplicates.
3185      */
3186     ierr = ISSortPermutation(isrow[i],PETSC_FALSE,isrow_p+i);CHKERRQ(ierr);
3187     ierr = ISSort(isrow[i]);CHKERRQ(ierr);
3188     ierr = ISGetLocalSize(isrow[i],&issize);CHKERRQ(ierr);
3189     ierr = ISGetIndices(isrow[i],&indices);CHKERRQ(ierr);
3190     for (j = 1; j < issize; ++j) {
3191       if (indices[j] == indices[j-1]) {
3192 	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]);
3193       }
3194     }
3195     ierr = ISRestoreIndices(isrow[i],&indices);CHKERRQ(ierr);
3196 
3197 
3198     ierr = ISSortPermutation(iscol[i],PETSC_FALSE,iscol_p+i);CHKERRQ(ierr);
3199     ierr = ISSort(iscol[i]);CHKERRQ(ierr);
3200     ierr = ISGetLocalSize(iscol[i],&issize);CHKERRQ(ierr);
3201     ierr = ISGetIndices(iscol[i],&indices);CHKERRQ(ierr);
3202     for (j = 1; j < issize; ++j) {
3203       if (indices[j-1] == indices[j]) {
3204 	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]);
3205       }
3206     }
3207     ierr = ISRestoreIndices(iscol[i],&indices);CHKERRQ(ierr);
3208     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3209     if (isize > 1) {
3210       cisrow[ii] = isrow[i];
3211       ++ii;
3212     }
3213   }
3214   /*
3215     Allocate the necessary arrays to hold the resulting parallel matrices as well as the intermediate
3216     array of sequential matrices underlying the resulting parallel matrices.
3217     Which arrays to allocate is based on the value of MatReuse scall and whether ISs are sorted and/or
3218     contain duplicates.
3219 
3220     There are as many diag matrices as there are original index sets. There are only as many parallel
3221     and off-diag matrices, as there are parallel (comm size > 1) index sets.
3222 
3223     ARRAYS that can hold Seq matrices get allocated in any event -- either here or by getsubmats_seq():
3224     - If the array of MPI matrices already exists and is being reused, we need to allocate the array
3225       and extract the underlying seq matrices into it to serve as placeholders, into which getsubmats_seq
3226       will deposite the extracted diag and off-diag parts. Thus, we allocate the A&B arrays and fill them
3227       with A[i] and B[ii] extracted from the corresponding MPI submat.
3228     - However, if the rows, A's column indices or B's column indices are not sorted, the extracted A[i] & B[ii]
3229       will have a different order from what getsubmats_seq expects.  To handle this case -- indicated
3230       by a nonzero isrow_p[i], iscol_p[i], or ciscol_p[ii] -- we duplicate A[i] --> AA[i], B[ii] --> BB[ii]
3231       (retrieve composed AA[i] or BB[ii]) and reuse them here. AA[i] and BB[ii] are then used to permute its
3232       values into A[i] and B[ii] sitting inside the corresponding submat.
3233     - If no reuse is taking place then getsubmats_seq will allocate the A&B arrays and create the corresponding
3234       A[i], B[ii], AA[i] or BB[ii] matrices.
3235   */
3236   /* Parallel matrix array is allocated here only if no reuse is taking place. If reused, it is passed in by the caller. */
3237   if (scall == MAT_INITIAL_MATRIX) {
3238     ierr = PetscMalloc1(ismax,submat);CHKERRQ(ierr);
3239   }
3240 
3241   /* Now obtain the sequential A and B submatrices separately. */
3242   /* scall=MAT_REUSE_MATRIX is not handled yet, because getsubmats_seq() requires reuse of A and B */
3243   ierr = (*getsubmats_seq)(C,ismax,isrow,iscol,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
3244   ierr = (*getsubmats_seq)(C,cismax,cisrow,ciscol,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
3245 
3246   /*
3247     If scall == MAT_REUSE_MATRIX AND the permutations are NULL, we are done, since the sequential
3248     matrices A & B have been extracted directly into the parallel matrices containing them, or
3249     simply into the sequential matrix identical with the corresponding A (if isize == 1).
3250     Note that in that case colmap doesn't need to be rebuilt, since the matrices are expected
3251     to have the same sparsity pattern.
3252     Otherwise, A and/or B have to be properly embedded into C's index spaces and the correct colmap
3253     must be constructed for C. This is done by setseqmat(s).
3254   */
3255   for (i = 0, ii = 0; i < ismax; ++i) {
3256     /*
3257        TODO: cache ciscol, permutation ISs and maybe cisrow? What about isrow & iscol?
3258        That way we can avoid sorting and computing permutations when reusing.
3259        To this end:
3260         - remove the old cache, if it exists, when extracting submatrices with MAT_INITIAL_MATRIX
3261 	- if caching arrays to hold the ISs, make and compose a container for them so that it can
3262 	  be destroyed upon destruction of C (use PetscContainerUserDestroy() to clear out the contents).
3263     */
3264     MatStructure pattern;
3265     pattern = DIFFERENT_NONZERO_PATTERN;
3266 
3267     ierr = MPI_Comm_size(((PetscObject)isrow[i])->comm,&isize);CHKERRQ(ierr);
3268     /* Construct submat[i] from the Seq pieces A (and B, if necessary). */
3269     if (isize > 1) {
3270       if (scall == MAT_INITIAL_MATRIX) {
3271 	ierr = MatCreate(((PetscObject)isrow[i])->comm,(*submat)+i);CHKERRQ(ierr);
3272 	ierr = MatSetSizes((*submat)[i],A[i]->rmap->n,A[i]->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3273 	ierr = MatSetType((*submat)[i],MATMPIAIJ);CHKERRQ(ierr);
3274 	ierr = PetscLayoutSetUp((*submat)[i]->rmap);CHKERRQ(ierr);
3275 	ierr = PetscLayoutSetUp((*submat)[i]->cmap);CHKERRQ(ierr);
3276       }
3277       /*
3278 	For each parallel isrow[i], insert the extracted sequential matrices into the parallel matrix.
3279       */
3280       {
3281 	Mat AA,BB;
3282         AA = A[i];
3283         BB = B[ii];
3284 	if (AA || BB) {
3285 	  ierr = setseqmats((*submat)[i],isrow_p[i],iscol_p[i],ciscol_p[ii],pattern,AA,BB);CHKERRQ(ierr);
3286 	  ierr = MatAssemblyBegin((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3287 	  ierr = MatAssemblyEnd((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3288 	}
3289 
3290         ierr = MatDestroy(&AA);CHKERRQ(ierr);
3291         ierr = MatDestroy(&BB);CHKERRQ(ierr);
3292       }
3293       ierr = ISDestroy(ciscol+ii);CHKERRQ(ierr);
3294       ierr = ISDestroy(ciscol_p+ii);CHKERRQ(ierr);
3295       ++ii;
3296     } else { /* if (isize == 1) */
3297       if (scall == MAT_REUSE_MATRIX) {
3298         ierr = MatDestroy(&(*submat)[i]);CHKERRQ(ierr);
3299       }
3300       if (isrow_p[i] || iscol_p[i]) {
3301         ierr = MatDuplicate(A[i],MAT_DO_NOT_COPY_VALUES,(*submat)+i);CHKERRQ(ierr);
3302         ierr = setseqmat((*submat)[i],isrow_p[i],iscol_p[i],pattern,A[i]);CHKERRQ(ierr);
3303 	/* Otherwise A is extracted straight into (*submats)[i]. */
3304 	/* TODO: Compose A[i] on (*submat([i] for future use, if ((isrow_p[i] || iscol_p[i]) && MAT_INITIAL_MATRIX). */
3305 	ierr = MatDestroy(A+i);CHKERRQ(ierr);
3306       } else (*submat)[i] = A[i];
3307     }
3308     ierr = ISDestroy(&isrow_p[i]);CHKERRQ(ierr);
3309     ierr = ISDestroy(&iscol_p[i]);CHKERRQ(ierr);
3310   }
3311   ierr = PetscFree2(cisrow,ciscol);CHKERRQ(ierr);
3312   ierr = PetscFree2(isrow_p,iscol_p);CHKERRQ(ierr);
3313   ierr = PetscFree(ciscol_p);CHKERRQ(ierr);
3314   ierr = PetscFree(A);CHKERRQ(ierr);
3315   ierr = PetscFree(B);CHKERRQ(ierr);
3316   PetscFunctionReturn(0);
3317 }
3318 
3319 PetscErrorCode MatGetSubMatricesMPI_MPIAIJ(Mat C,PetscInt ismax,const IS isrow[],const IS iscol[],MatReuse scall,Mat *submat[])
3320 {
3321   PetscErrorCode ierr;
3322 
3323   PetscFunctionBegin;
3324   ierr = MatGetSubMatricesMPI_MPIXAIJ(C,ismax,isrow,iscol,scall,submat,MatGetSubMatrices_MPIAIJ,MatGetSeqMats_MPIAIJ,MatSetSeqMat_SeqAIJ,MatSetSeqMats_MPIAIJ);CHKERRQ(ierr);
3325   PetscFunctionReturn(0);
3326 }
3327