xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision 1c2f57072f0347b6d0fda06db40e0a8eb3c8b659)
1 
2 /*
3   Defines projective product routines where A is a MPIAIJ matrix
4           C = P^T * A * P
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h>   /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <../src/mat/impls/aij/mpi/mpiaij.h>
10 #include <petscbt.h>
11 
12 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
13 #undef __FUNCT__
14 #define __FUNCT__ "MatDestroy_MPIAIJ_PtAP"
15 PetscErrorCode MatDestroy_MPIAIJ_PtAP(Mat A)
16 {
17   PetscErrorCode       ierr;
18   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data;
19   Mat_PtAPMPI          *ptap=a->ptap;
20 
21   PetscFunctionBegin;
22   if (ptap){
23     ierr = PetscFree2(ptap->startsj,ptap->startsj_r);CHKERRQ(ierr);
24     ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
25     ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
26     ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
27     ierr = PetscFree(ptap->api);CHKERRQ(ierr);
28     ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
29   }
30   if (ptap->merge) {
31     Mat_Merge_SeqsToMPI  *merge=ptap->merge;
32     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
33     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
34     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
35     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
36     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
37     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
38     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
39     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
40     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
41     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
42     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
43     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
44     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
45     ierr = merge->destroy(A);CHKERRQ(ierr);
46     ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
47   }
48   ierr = PetscFree(ptap);CHKERRQ(ierr);
49   PetscFunctionReturn(0);
50 }
51 
52 #undef __FUNCT__
53 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatPtAP"
54 PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat A, MatDuplicateOption op, Mat *M)
55 {
56   PetscErrorCode       ierr;
57   Mat_Merge_SeqsToMPI  *merge;
58   PetscContainer       container;
59 
60   PetscFunctionBegin;
61   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
62   if (container) {
63     ierr  = PetscContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
64   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
65   ierr = (*merge->duplicate)(A,op,M);CHKERRQ(ierr);
66   (*M)->ops->destroy   = merge->destroy;   /* =MatDestroy_MPIAIJ, *M doesn't duplicate A's container! */
67   (*M)->ops->duplicate = merge->duplicate; /* =MatDuplicate_ MPIAIJ */
68   PetscFunctionReturn(0);
69 }
70 
71 #undef __FUNCT__
72 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ"
73 PetscErrorCode MatPtAPSymbolic_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
74 {
75   PetscErrorCode ierr;
76 
77   PetscFunctionBegin;
78   if (!P->ops->ptapsymbolic_mpiaij) SETERRQ2(((PetscObject)A)->comm,PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",((PetscObject)A)->type_name,((PetscObject)P)->type_name);
79   ierr = (*P->ops->ptapsymbolic_mpiaij)(A,P,fill,C);CHKERRQ(ierr);
80   PetscFunctionReturn(0);
81 }
82 
83 #undef __FUNCT__
84 #define __FUNCT__ "MatPtAPNumeric_MPIAIJ"
85 PetscErrorCode MatPtAPNumeric_MPIAIJ(Mat A,Mat P,Mat C)
86 {
87   PetscErrorCode ierr;
88 
89   PetscFunctionBegin;
90   if (!P->ops->ptapnumeric_mpiaij) SETERRQ2(((PetscObject)A)->comm,PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",((PetscObject)A)->type_name,((PetscObject)P)->type_name);
91   ierr = (*P->ops->ptapnumeric_mpiaij)(A,P,C);CHKERRQ(ierr);
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ_MPIAIJ"
97 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
98 {
99   PetscErrorCode       ierr;
100   Mat                  Cmpi;
101   Mat_PtAPMPI          *ptap;
102   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
103   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
104   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
105   Mat_SeqAIJ           *p_loc,*p_oth;
106   PetscInt             *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ;
107   PetscInt             *adi=ad->i,*aj,*aoi=ao->i,nnz;
108   PetscInt             nlnk,*lnk,*owners_co,*coi,*coj,i,k,pnz,row;
109   PetscInt             am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n;
110   PetscBT              lnkbt;
111   MPI_Comm             comm=((PetscObject)A)->comm;
112   PetscMPIInt          size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
113   PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
114   PetscInt             len,proc,*dnz,*onz,*owners;
115   PetscInt             nzi,*bi,*bj;
116   PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
117   MPI_Request          *swaits,*rwaits;
118   MPI_Status           *sstatus,rstatus;
119   Mat_Merge_SeqsToMPI  *merge;
120   PetscInt             *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0;
121   PetscReal            afill=1.0,afill_tmp;
122   PetscLogDouble       t0,tf,etime=0.0,t00,tff,time_matupdate=0.0,time_Cd=0.0,time_AP=0.0,time_Co=0.0;
123   PetscInt             rstart = P->cmap->rstart,rmax;
124   PetscScalar          *vals;
125 
126   PetscFunctionBegin;
127   ierr = PetscGetTime(&t00);CHKERRQ(ierr);
128   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
129   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
130 
131   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
132   /* create struct Mat_PtAPMPI and attached it to C later */
133   ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
134   ptap->reuse    = MAT_INITIAL_MATRIX;
135 
136 
137   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
138   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
139   /* get P_loc by taking all local rows of P */
140   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
141 
142   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
143   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
144   pi_loc = p_loc->i; pj_loc = p_loc->j;
145   pi_oth = p_oth->i; pj_oth = p_oth->j;
146 
147   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
148   time_matupdate += tf-t0;
149 
150   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
151   /*-------------------------------------------------------------------*/
152   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
153   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&api);CHKERRQ(ierr);
154   api[0] = 0;
155 
156   /* create and initialize a linked list */
157   nlnk = pN+1;
158   ierr = PetscLLCreate(pN,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
159 
160   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
161   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
162   current_space = free_space;
163 
164   for (i=0; i<am; i++) {
165     apnz = 0;
166     /* diagonal portion of A */
167     nzi = adi[i+1] - adi[i];
168     aj  = ad->j + adi[i];
169     for (j=0; j<nzi; j++){
170       row  = aj[j];
171       pnz  = pi_loc[row+1] - pi_loc[row];
172       Jptr = pj_loc + pi_loc[row];
173       /* add non-zero cols of P into the sorted linked list lnk */
174       ierr = PetscLLAddSorted(pnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
175       apnz += nlnk;
176     }
177     /* off-diagonal portion of A */
178     nzi = aoi[i+1] - aoi[i];
179     aj  = ao->j + aoi[i];
180     for (j=0; j<nzi; j++){
181       row = aj[j];
182       pnz = pi_oth[row+1] - pi_oth[row];
183       Jptr  = pj_oth + pi_oth[row];
184       ierr = PetscLLAddSorted(pnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
185       apnz += nlnk;
186     }
187 
188     api[i+1] = api[i] + apnz;
189     if (ap_rmax < apnz) ap_rmax = apnz;
190 
191     /* if free space is not available, double the total space in the list */
192     if (current_space->local_remaining<apnz) {
193       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
194       nspacedouble++;
195     }
196 
197     /* Copy data into free space, then initialize lnk */
198     ierr = PetscLLClean(pN,pN,apnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
199     current_space->array           += apnz;
200     current_space->local_used      += apnz;
201     current_space->local_remaining -= apnz;
202   }
203   /* Allocate space for apj, initialize apj, and */
204   /* destroy list of free space and other temporary array(s) */
205   ierr = PetscMalloc((api[am]+1)*sizeof(PetscInt),&apj);CHKERRQ(ierr);
206   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
207   afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]);
208   if (afill_tmp > afill) afill = afill_tmp;
209 
210   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
211   time_AP += tf-t0;
212 
213   /* determine symbolic Co=(p->B)^T*AP - send to others */
214   /*----------------------------------------------------*/
215   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
216   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
217 
218   /* then, compute symbolic Co = (p->B)^T*AP */
219   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
220                          >= (num of nonzero rows of C_seq) - pn */
221   ierr = PetscMalloc((pon+1)*sizeof(PetscInt),&coi);CHKERRQ(ierr);
222   coi[0] = 0;
223 
224   /* set initial free space to be fill*(nnz(p->B) + nnz(AP)) */
225   nnz           = fill*(poti[pon] + api[am]);
226   ierr          = PetscFreeSpaceGet(nnz,&free_space);
227   current_space = free_space;
228 
229   for (i=0; i<pon; i++) {
230     nnz = 0;
231     pnz = poti[i+1] - poti[i];
232     ptJ = potj + poti[i];
233     for (j=0; j<pnz; j++){
234       row  = ptJ[j]; /* row of AP == col of Pot */
235       apnz = api[row+1] - api[row];
236       Jptr = apj + api[row];
237       /* add non-zero cols of AP into the sorted linked list lnk */
238       ierr = PetscLLAddSorted(apnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
239       nnz += nlnk;
240     }
241 
242     /* If free space is not available, double the total space in the list */
243     if (current_space->local_remaining<nnz) {
244       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
245       nspacedouble++;
246     }
247 
248     /* Copy data into free space, and zero out denserows */
249     ierr = PetscLLClean(pN,pN,nnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
250     current_space->array           += nnz;
251     current_space->local_used      += nnz;
252     current_space->local_remaining -= nnz;
253     coi[i+1] = coi[i] + nnz;
254   }
255   ierr = PetscMalloc((coi[pon]+1)*sizeof(PetscInt),&coj);CHKERRQ(ierr);
256   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
257   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]);
258   if (afill_tmp > afill) afill = afill_tmp;
259   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
260 
261   /* send j-array (coj) of Co to other processors */
262   /*----------------------------------------------*/
263   /* determine row ownership */
264   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
265   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
266   merge->rowmap->n = pn;
267   merge->rowmap->bs = 1;
268   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
269   owners = merge->rowmap->range;
270 
271   /* determine the number of messages to send, their lengths */
272   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
273   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
274   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
275   len_s = merge->len_s;
276   merge->nsend = 0;
277 
278   ierr = PetscMalloc((size+2)*sizeof(PetscInt),&owners_co);CHKERRQ(ierr);
279   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
280 
281   proc = 0;
282   for (i=0; i<pon; i++){
283     while (prmap[i] >= owners[proc+1]) proc++;
284     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
285     len_s[proc] += coi[i+1] - coi[i];
286   }
287 
288   len   = 0;  /* max length of buf_si[] */
289   owners_co[0] = 0;
290   for (proc=0; proc<size; proc++){
291     owners_co[proc+1] = owners_co[proc] + len_si[proc];
292     if (len_si[proc]){
293       merge->nsend++;
294       len_si[proc] = 2*(len_si[proc] + 1);
295       len += len_si[proc];
296     }
297   }
298 
299   /* determine the number and length of messages to receive for coi and coj  */
300   ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
301   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
302 
303   /* post the Irecv and Isend of coj */
304   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
305   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
306   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&swaits);CHKERRQ(ierr);
307   for (proc=0, k=0; proc<size; proc++){
308     if (!len_s[proc]) continue;
309     i = owners_co[proc];
310     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
311     k++;
312   }
313 
314   /* receives and sends of coj are complete */
315   ierr = PetscMalloc(size*sizeof(MPI_Status),&sstatus);CHKERRQ(ierr);
316   for (i=0; i<merge->nrecv; i++){
317     ierr = MPI_Waitany(merge->nrecv,rwaits,&j,&rstatus);CHKERRQ(ierr);
318   }
319   ierr = PetscFree(rwaits);CHKERRQ(ierr);
320   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
321 
322   /* send and recv coi */
323   /*-------------------*/
324   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
325   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
326   ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
327   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
328   for (proc=0,k=0; proc<size; proc++){
329     if (!len_s[proc]) continue;
330     /* form outgoing message for i-structure:
331          buf_si[0]:                 nrows to be sent
332                [1:nrows]:           row index (global)
333                [nrows+1:2*nrows+1]: i-structure index
334     */
335     /*-------------------------------------------*/
336     nrows = len_si[proc]/2 - 1;
337     buf_si_i    = buf_si + nrows+1;
338     buf_si[0]   = nrows;
339     buf_si_i[0] = 0;
340     nrows = 0;
341     for (i=owners_co[proc]; i<owners_co[proc+1]; i++){
342       nzi = coi[i+1] - coi[i];
343       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
344       buf_si[nrows+1] =prmap[i] -owners[proc]; /* local row index */
345       nrows++;
346     }
347     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
348     k++;
349     buf_si += len_si[proc];
350   }
351   i = merge->nrecv;
352   while (i--) {
353     ierr = MPI_Waitany(merge->nrecv,rwaits,&j,&rstatus);CHKERRQ(ierr);
354   }
355   ierr = PetscFree(rwaits);CHKERRQ(ierr);
356   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
357   /*
358   ierr = PetscInfo2(A,"nsend: %d, nrecv: %d\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
359   for (i=0; i<merge->nrecv; i++){
360     ierr = PetscInfo3(A,"recv len_ri=%d, len_rj=%d from [%d]\n",len_ri[i],merge->len_r[i],merge->id_r[i]);CHKERRQ(ierr);
361   }
362   */
363   ierr = PetscFree(len_si);CHKERRQ(ierr);
364   ierr = PetscFree(len_ri);CHKERRQ(ierr);
365   ierr = PetscFree(swaits);CHKERRQ(ierr);
366   ierr = PetscFree(sstatus);CHKERRQ(ierr);
367   ierr = PetscFree(buf_s);CHKERRQ(ierr);
368 
369   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
370   time_Co += tf-t0;
371 
372   /* compute the local portion of C (mpi mat) */
373   /*------------------------------------------*/
374   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
375   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
376 
377   /* allocate bi array and free space for accumulating nonzero column info */
378   ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
379   bi[0] = 0;
380 
381   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
382   nnz           = fill*(pi_loc[pm] + api[am]);
383   ierr          = PetscFreeSpaceGet(nnz,&free_space);
384   current_space = free_space;
385 
386   ierr = PetscMalloc3(merge->nrecv,PetscInt**,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextci);CHKERRQ(ierr);
387   for (k=0; k<merge->nrecv; k++){
388     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
389     nrows       = *buf_ri_k[k];
390     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
391     nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
392   }
393   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
394   rmax = 0;
395   for (i=0; i<pn; i++) {
396     /* add pdt[i,:]*AP into lnk */
397     nnz = 0;
398     pnz = pdti[i+1] - pdti[i];
399     ptJ = pdtj + pdti[i];
400     for (j=0; j<pnz; j++){
401       row  = ptJ[j];  /* row of AP == col of Pt */
402       apnz = api[row+1] - api[row];
403       Jptr = apj + api[row];
404       /* add non-zero cols of AP into the sorted linked list lnk */
405       ierr = PetscLLAddSorted(apnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
406       nnz += nlnk;
407     }
408     /* add received col data into lnk */
409     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
410       if (i == *nextrow[k]) { /* i-th row */
411         nzi = *(nextci[k]+1) - *nextci[k];
412         Jptr  = buf_rj[k] + *nextci[k];
413         ierr = PetscLLAddSorted(nzi,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
414         nnz += nlnk;
415         nextrow[k]++; nextci[k]++;
416       }
417     }
418 
419     /* if free space is not available, make more free space */
420     if (current_space->local_remaining<nnz) {
421       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
422       nspacedouble++;
423     }
424     /* copy data into free space, then initialize lnk */
425     ierr = PetscLLClean(pN,pN,nnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
426     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
427     current_space->array           += nnz;
428     current_space->local_used      += nnz;
429     current_space->local_remaining -= nnz;
430     bi[i+1] = bi[i] + nnz;
431     if (nnz > rmax) rmax = nnz;
432   }
433   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
434   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
435 
436   ierr = PetscMalloc((bi[pn]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
437   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
438   afill_tmp = (PetscReal)bi[pn]/(pi_loc[pm] + api[am]);
439   if (afill_tmp > afill) afill = afill_tmp;
440   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
441 
442   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
443   time_Cd += tf-t0;
444 
445   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part - check runex55_SA ?  */
446   /*------------------------------------------------------------------------------------------------------*/
447   ierr = PetscMalloc((rmax+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
448   ierr = PetscMemzero(vals,rmax*sizeof(PetscScalar));CHKERRQ(ierr);
449   /*
450   ierr = PetscSynchronizedPrintf(comm, "[%d] pn %D, pN %D, cstart %D, rmax %D\n", rank,pn,pN,rstart,rmax);CHKERRQ(ierr);
451   ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
452    */
453 
454   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
455   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
456   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
457   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
458   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
459   ierr = MatSetBlockSize(Cmpi,1);CHKERRQ(ierr);
460   for (i=0; i<pn; i++){
461     row = i + rstart;
462     nnz = bi[i+1] - bi[i];
463     Jptr = bj + bi[i];
464     ierr = MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);CHKERRQ(ierr);
465   }
466   ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
467   ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
468   ierr = PetscFree(vals);CHKERRQ(ierr);
469 
470   merge->bi            = bi;
471   merge->bj            = bj;
472   merge->coi           = coi;
473   merge->coj           = coj;
474   merge->buf_ri        = buf_ri;
475   merge->buf_rj        = buf_rj;
476   merge->owners_co     = owners_co;
477   merge->destroy       = Cmpi->ops->destroy;
478   merge->duplicate     = Cmpi->ops->duplicate;
479 
480   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
481   /* Cmpi->assembled      = PETSC_FALSE; */
482   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_PtAP;
483   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatPtAP;
484 
485   /* attach the supporting struct to Cmpi for reuse */
486   c = (Mat_MPIAIJ*)Cmpi->data;
487   c->ptap        = ptap;
488   ptap->api      = api;
489   ptap->apj      = apj;
490   ptap->merge    = merge;
491   ptap->abnz_max = ap_rmax;
492 
493   *C = Cmpi;
494 #if defined(PETSC_USE_INFO)
495   if (bi[pn] != 0) {
496     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
497     ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr);
498   } else {
499     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
500   }
501 #endif
502   ierr = PetscGetTime(&tff);CHKERRQ(ierr);
503   etime += tff - t00;
504   /*
505   PetscInt prid=0;
506   if (rank == prid){
507     ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] PtAPSym time %g = matsetup %g + AP %g + Co %g + Cd %g\n",rank,etime,time_matupdate,time_AP,time_Co,time_Cd);
508   }
509    */
510   PetscFunctionReturn(0);
511 }
512 
513 #undef __FUNCT__
514 #define __FUNCT__ "MatPtAPNumeric_MPIAIJ_MPIAIJ"
515 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
516 {
517   PetscErrorCode       ierr;
518   Mat_Merge_SeqsToMPI  *merge;
519   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
520   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
521   Mat_SeqAIJ           *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
522   Mat_SeqAIJ           *p_loc,*p_oth;
523   Mat_PtAPMPI          *ptap;
524   PetscInt             *adi=ad->i,*aoi=ao->i,*adj,*aoj,*apJ,nextp;
525   PetscInt             *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pJ,*pj;
526   PetscInt             i,j,k,anz,pnz,apnz,nextap,row,*cj;
527   MatScalar            *ada,*aoa,*apa,*pa,*ca,*pa_loc,*pa_oth,valtmp;
528   PetscInt             am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
529   MPI_Comm             comm=((PetscObject)C)->comm;
530   PetscMPIInt          size,rank,taga,*len_s;
531   PetscInt             *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
532   PetscInt             **buf_ri,**buf_rj;
533   PetscInt             cnz=0,*bj_i,*bi,*bj,bnz,nextcj; /* bi,bj,ba: local array of C(mpi mat) */
534   MPI_Request          *s_waits,*r_waits;
535   MPI_Status           *status;
536   MatScalar            **abuf_r,*ba_i,*pA,*coa,*ba;
537   PetscInt             *api,*apj,*coi,*coj;
538   PetscInt             *poJ=po->j,*pdJ=pd->j,pcstart=P->cmap->rstart,pcend=P->cmap->rend;
539   PetscInt             sparse_axpy;
540   PetscLogDouble       t0,tf,etime=0.0,t00,tff,time_matupdate=0.0,time_malloc=0.0,time_Cseq0=0.0,time_Cseq1=0.0,time_setvals=0.0;
541 
542   PetscFunctionBegin;
543   /* ierr = MPI_Barrier(comm);CHKERRQ(ierr); */
544   ierr = PetscGetTime(&t00);CHKERRQ(ierr);
545   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
546   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
547 
548   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
549   ptap  = c->ptap;
550   merge = ptap->merge;
551 
552   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
553   /*--------------------------------------------------*/
554   if (ptap->reuse == MAT_INITIAL_MATRIX){
555     ptap->reuse = MAT_REUSE_MATRIX;
556   } else { /* update numerical values of P_oth and P_loc */
557     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
558     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
559   }
560 
561   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
562   time_matupdate += tf-t0;
563 
564   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
565   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
566   /*--------------------------------------------------------------*/
567   /* get data from symbolic products */
568   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
569   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
570   pi_loc=p_loc->i; pj_loc=p_loc->j; pJ=pj_loc; pa_loc=p_loc->a;
571   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
572 
573   coi = merge->coi; coj = merge->coj;
574   ierr = PetscMalloc((coi[pon]+1)*sizeof(MatScalar),&coa);CHKERRQ(ierr);
575   ierr = PetscMemzero(coa,coi[pon]*sizeof(MatScalar));CHKERRQ(ierr);
576 
577   bi     = merge->bi; bj = merge->bj;
578   owners = merge->rowmap->range;
579   ierr   = PetscMalloc((bi[cm]+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
580   ierr   = PetscMemzero(ba,bi[cm]*sizeof(MatScalar));CHKERRQ(ierr);
581   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
582   time_malloc += tf-t0;
583 
584   api = ptap->api; apj = ptap->apj;
585   /* flag 'sparse_axpy' determines which implementations to be used:
586        0: do dense axpy in MatPtAPNumeric() - fastest, but requires storage of a dense array apa; (default)
587        1: do one sparse axpy - uses same memory as sparse_axpy=0 and might execute less flops
588           (apnz vs. cnz in the outerproduct), slower than case '0' when cnz is not too large than apnz;
589        2: do two sparse axpy in MatPtAPNumeric() - slowest, uses a sparse array apa */
590   /* set default sparse_axpy */
591   sparse_axpy = 0;
592   ierr = PetscOptionsGetInt(PETSC_NULL,"-matptap_sparseaxpy",&sparse_axpy,PETSC_NULL);CHKERRQ(ierr);
593   if (sparse_axpy == 0){  /* Do not perform sparse axpy */
594     /*--------------------------------------------------*/
595     /* malloc apa to store dense row A[i,:]*P */
596     ierr = PetscMalloc((P->cmap->N)*sizeof(PetscScalar),&apa);CHKERRQ(ierr);
597     ierr = PetscMemzero(apa,P->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
598 
599     for (i=0; i<am; i++) {
600       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
601       /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */
602       /*------------------------------------------------------------*/
603       apJ = apj + api[i];
604 
605       /* diagonal portion of A */
606       anz = adi[i+1] - adi[i];
607       adj = ad->j + adi[i];
608       ada = ad->a + adi[i];
609       for (j=0; j<anz; j++) {
610         row = adj[j];
611         pnz = pi_loc[row+1] - pi_loc[row];
612         pj  = pj_loc + pi_loc[row];
613         pa  = pa_loc + pi_loc[row];
614 
615         /* perform dense axpy */
616         valtmp = ada[j];
617         for (k=0; k<pnz; k++){
618           apa[pj[k]] += valtmp*pa[k];
619         }
620         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
621       }
622 
623       /* off-diagonal portion of A */
624       anz = aoi[i+1] - aoi[i];
625       aoj = ao->j + aoi[i];
626       aoa = ao->a + aoi[i];
627       for (j=0; j<anz; j++) {
628         row = aoj[j];
629         pnz = pi_oth[row+1] - pi_oth[row];
630         pj  = pj_oth + pi_oth[row];
631         pa  = pa_oth + pi_oth[row];
632 
633         /* perform dense axpy */
634         valtmp = aoa[j];
635         for (k=0; k<pnz; k++){
636           apa[pj[k]] += valtmp*pa[k];
637         }
638         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
639       }
640       ierr = PetscGetTime(&tf);CHKERRQ(ierr);
641       time_Cseq0 += tf - t0;
642 
643       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
644       /*--------------------------------------------------------------*/
645       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
646       apnz = api[i+1] - api[i];
647       /* put the value into Co=(p->B)^T*AP (off-diagonal part, send to others) */
648       pnz = po->i[i+1] - po->i[i];
649       poJ = po->j + po->i[i];
650       pA  = po->a + po->i[i];
651       for (j=0; j<pnz; j++){
652         row = poJ[j];
653         cnz = coi[row+1] - coi[row];
654         cj  = coj + coi[row];
655         ca  = coa + coi[row];
656         /* perform dense axpy */
657         valtmp = pA[j];
658         for (k=0; k<cnz; k++) {
659           ca[k] += valtmp*apa[cj[k]];
660         }
661         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
662       }
663 
664       /* put the value into Cd (diagonal part) */
665       pnz = pd->i[i+1] - pd->i[i];
666       pdJ = pd->j + pd->i[i];
667       pA  = pd->a + pd->i[i];
668       for (j=0; j<pnz; j++){
669         row = pdJ[j];
670         cnz = bi[row+1] - bi[row];
671         cj  = bj + bi[row];
672         ca  = ba + bi[row];
673         /* perform dense axpy */
674         valtmp = pA[j];
675         for (k=0; k<cnz; k++) {
676           ca[k] += valtmp*apa[cj[k]];
677         }
678         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
679       }
680 
681       /* zero the current row of A*P */
682       for (k=0; k<apnz; k++) apa[apJ[k]] = 0.0;
683       ierr = PetscGetTime(&tf);CHKERRQ(ierr);
684       time_Cseq1 += tf - t0;
685     }
686   } else if (sparse_axpy == 1){  /* Perform one sparse axpy */
687     /*------------------------------------------------------*/
688     /* malloc apa to store dense row A[i,:]*P */
689     ierr = PetscMalloc((P->cmap->N)*sizeof(PetscScalar),&apa);CHKERRQ(ierr);
690     ierr = PetscMemzero(apa,P->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
691 
692     for (i=0; i<am; i++) {
693       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
694       /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */
695       /*------------------------------------------------------------*/
696       apJ = apj + api[i];
697 
698       /* diagonal portion of A */
699       anz = adi[i+1] - adi[i];
700       adj = ad->j + adi[i];
701       ada = ad->a + adi[i];
702       for (j=0; j<anz; j++) {
703         row = adj[j];
704         pnz = pi_loc[row+1] - pi_loc[row];
705         pj  = pj_loc + pi_loc[row];
706         pa  = pa_loc + pi_loc[row];
707 
708         /* perform dense axpy */
709         valtmp = ada[j];
710         for (k=0; k<pnz; k++){
711           apa[pj[k]] += valtmp*pa[k];
712         }
713         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
714       }
715 
716       /* off-diagonal portion of A */
717       anz = aoi[i+1] - aoi[i];
718       aoj = ao->j + aoi[i];
719       aoa = ao->a + aoi[i];
720       for (j=0; j<anz; j++) {
721         row = aoj[j];
722         pnz = pi_oth[row+1] - pi_oth[row];
723         pj  = pj_oth + pi_oth[row];
724         pa  = pa_oth + pi_oth[row];
725 
726         /* perform dense axpy */
727         valtmp = aoa[j];
728         for (k=0; k<pnz; k++){
729           apa[pj[k]] += valtmp*pa[k];
730         }
731         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
732       }
733       ierr = PetscGetTime(&tf);CHKERRQ(ierr);
734       time_Cseq0 += tf - t0;
735 
736       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
737       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
738       /*--------------------------------------------------------------*/
739       apnz = api[i+1] - api[i];
740       /* put the value into Co=(p->B)^T*AP (off-diagonal part, send to others) */
741       pnz = po->i[i+1] - po->i[i];
742       poJ = po->j + po->i[i];
743       pA  = po->a + po->i[i];
744       for (j=0; j<pnz; j++){
745         row    = poJ[j];
746         cj     = coj + coi[row];
747         ca     = coa + coi[row];
748         valtmp = pA[j];
749         /* perform sparse axpy */
750         nextap = 0;
751         for (k=0; nextap<apnz; k++) {
752           if (cj[k]==apJ[nextap]) { /* global column index */
753             ca[k] += valtmp*apa[cj[k]]; nextap++;
754           }
755         }
756         ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
757       }
758 
759       /* put the value into Cd (diagonal part) */
760       pnz = pd->i[i+1] - pd->i[i];
761       pdJ = pd->j + pd->i[i];
762       pA  = pd->a + pd->i[i];
763       for (j=0; j<pnz; j++){
764         row    = pdJ[j];
765         cj     = bj + bi[row];
766         ca     = ba + bi[row];
767         valtmp = pA[j];
768         /* perform sparse axpy */
769         nextap = 0;
770         for (k=0; nextap<apnz; k++) {
771           if (cj[k]==apJ[nextap]) { /* global column index */
772             ca[k] += valtmp*apa[cj[k]];
773             nextap++;
774           }
775         }
776         ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
777       }
778 
779       /* zero the current row of A*P */
780       for (k=0; k<apnz; k++) apa[apJ[k]] = 0.0;
781       ierr = PetscGetTime(&tf);CHKERRQ(ierr);
782       time_Cseq1 += tf - t0;
783     }
784   } else if (sparse_axpy == 2){/* Perform two sparse axpy */
785     /*----------------------------------------------------*/
786     /* malloc apa to store sparse row A[i,:]*P */
787     ierr = PetscMalloc((ptap->abnz_max+1)*sizeof(MatScalar),&apa);CHKERRQ(ierr);
788     ierr = PetscMemzero(apa,ptap->abnz_max*sizeof(MatScalar));CHKERRQ(ierr);
789 
790     pA=pa_loc;
791     for (i=0; i<am; i++) {
792       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
793       /* form i-th sparse row of A*P */
794       apnz = api[i+1] - api[i];
795       apJ  = apj + api[i];
796       /* diagonal portion of A */
797       anz = adi[i+1] - adi[i];
798       adj = ad->j + adi[i];
799       ada = ad->a + adi[i];
800       for (j=0; j<anz; j++) {
801         row = adj[j];
802         pnz = pi_loc[row+1] - pi_loc[row];
803         pj  = pj_loc + pi_loc[row];
804         pa  = pa_loc + pi_loc[row];
805         valtmp = ada[j];
806         nextp  = 0;
807         for (k=0; nextp<pnz; k++) {
808           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
809             apa[k] += valtmp*pa[nextp++];
810           }
811         }
812         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
813       }
814       /* off-diagonal portion of A */
815       anz = aoi[i+1] - aoi[i];
816       aoj = ao->j + aoi[i];
817       aoa = ao->a + aoi[i];
818       for (j=0; j<anz; j++) {
819         row = aoj[j];
820         pnz = pi_oth[row+1] - pi_oth[row];
821         pj  = pj_oth + pi_oth[row];
822         pa  = pa_oth + pi_oth[row];
823         valtmp = aoa[j];
824         nextp  = 0;
825         for (k=0; nextp<pnz; k++) {
826           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
827             apa[k] += valtmp*pa[nextp++];
828           }
829         }
830         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
831       }
832       ierr = PetscGetTime(&tf);CHKERRQ(ierr);
833       time_Cseq0 += tf - t0;
834 
835       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
836       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
837       /*--------------------------------------------------------------*/
838       pnz = pi_loc[i+1] - pi_loc[i];
839       pJ  = pj_loc + pi_loc[i];
840       for (j=0; j<pnz; j++) {
841         nextap = 0;
842         row    = pJ[j]; /* global index */
843         if (row < pcstart || row >=pcend) { /* put the value into Co */
844           row = *poJ;
845           cj  = coj + coi[row];
846           ca  = coa + coi[row]; poJ++;
847         } else {                            /* put the value into Cd */
848           row  = *pdJ;
849           cj   = bj + bi[row];
850           ca   = ba + bi[row]; pdJ++;
851         }
852         valtmp = pA[j];
853         for (k=0; nextap<apnz; k++) {
854           if (cj[k]==apJ[nextap]) ca[k] += valtmp*apa[nextap++];
855         }
856         ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
857       }
858       pA += pnz;
859       /* zero the current row info for A*P */
860       ierr = PetscMemzero(apa,apnz*sizeof(MatScalar));CHKERRQ(ierr);
861       ierr = PetscGetTime(&tf);CHKERRQ(ierr);
862       time_Cseq1 += tf - t0;
863     }
864   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"sparse_axpy only takes values 0, 1 and 2");
865   ierr = PetscFree(apa);CHKERRQ(ierr);
866 
867   /* 3) send and recv matrix values coa */
868   /*------------------------------------*/
869   buf_ri = merge->buf_ri;
870   buf_rj = merge->buf_rj;
871   len_s  = merge->len_s;
872   ierr = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
873   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
874 
875   ierr = PetscMalloc2(merge->nsend+1,MPI_Request,&s_waits,size,MPI_Status,&status);CHKERRQ(ierr);
876   for (proc=0,k=0; proc<size; proc++){
877     if (!len_s[proc]) continue;
878     i = merge->owners_co[proc];
879     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
880     k++;
881   }
882   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
883   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
884 
885   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
886   ierr = PetscFree(r_waits);CHKERRQ(ierr);
887   ierr = PetscFree(coa);CHKERRQ(ierr);
888 
889   /* 4) insert local Cseq and received values into Cmpi */
890   /*------------------------------------------------------*/
891   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
892   ierr = PetscMalloc3(merge->nrecv,PetscInt**,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextci);CHKERRQ(ierr);
893 
894   for (k=0; k<merge->nrecv; k++){
895     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
896     nrows       = *(buf_ri_k[k]);
897     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
898     nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
899   }
900 
901   for (i=0; i<cm; i++) {
902     row = owners[rank] + i; /* global row index of C_seq */
903     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
904     ba_i = ba + bi[i];
905     bnz  = bi[i+1] - bi[i];
906     /* add received vals into ba */
907     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
908       /* i-th row */
909       if (i == *nextrow[k]) {
910         cnz = *(nextci[k]+1) - *nextci[k];
911         cj  = buf_rj[k] + *(nextci[k]);
912         ca  = abuf_r[k] + *(nextci[k]);
913         nextcj = 0;
914         for (j=0; nextcj<cnz; j++){
915           if (bj_i[j] == cj[nextcj]){ /* bcol == ccol */
916             ba_i[j] += ca[nextcj++];
917           }
918         }
919         nextrow[k]++; nextci[k]++;
920       }
921     }
922     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
923     ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
924   }
925   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
926   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
927   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
928   time_setvals += tf-t0;
929 
930   ierr = PetscFree(ba);CHKERRQ(ierr);
931   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
932   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
933   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
934 
935   ierr = PetscGetTime(&tff);CHKERRQ(ierr);
936   etime += tff - t00;
937   /*
938   PetscInt prid=0;
939   if (rank == prid){
940    ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] PtAPNum time %g = matupdate %g + malloc %g + Cseq %g + %g + setvals %g\n",rank,etime,time_matupdate,time_malloc,time_Cseq0,time_Cseq1,time_setvals);
941   }
942    */
943   PetscFunctionReturn(0);
944 }
945