xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision a63bb30eff8b1dff6ddce5531d6230e04f6fd10b) !
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 /*
13 #define DEBUG_MATPTAP
14  */
15 
16 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
17 #undef __FUNCT__
18 #define __FUNCT__ "MatDestroy_MPIAIJ_PtAP"
19 PetscErrorCode MatDestroy_MPIAIJ_PtAP(Mat A)
20 {
21   PetscErrorCode       ierr;
22   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data;
23   Mat_PtAPMPI          *ptap=a->ptap;
24 
25   PetscFunctionBegin;
26   if (ptap){
27     ierr = PetscFree2(ptap->startsj,ptap->startsj_r);CHKERRQ(ierr);
28     ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
29     ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
30     ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
31     ierr = PetscFree(ptap->api);CHKERRQ(ierr);
32     ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
33   }
34   if (ptap->merge) {
35     Mat_Merge_SeqsToMPI  *merge=ptap->merge;
36     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
37     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
38     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
39     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
40     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
41     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
42     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
43     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
44     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
45     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
46     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
47     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
48     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
49     ierr = merge->destroy(A);CHKERRQ(ierr);
50     ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
51   }
52   ierr = PetscFree(ptap);CHKERRQ(ierr);
53   PetscFunctionReturn(0);
54 }
55 
56 #undef __FUNCT__
57 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatPtAP"
58 PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat A, MatDuplicateOption op, Mat *M)
59 {
60   PetscErrorCode       ierr;
61   Mat_Merge_SeqsToMPI  *merge;
62   PetscContainer       container;
63 
64   PetscFunctionBegin;
65   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject *)&container);CHKERRQ(ierr);
66   if (container) {
67     ierr  = PetscContainerGetPointer(container,(void **)&merge);CHKERRQ(ierr);
68   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
69   ierr = (*merge->duplicate)(A,op,M);CHKERRQ(ierr);
70   (*M)->ops->destroy   = merge->destroy;   /* =MatDestroy_MPIAIJ, *M doesn't duplicate A's container! */
71   (*M)->ops->duplicate = merge->duplicate; /* =MatDuplicate_ MPIAIJ */
72   PetscFunctionReturn(0);
73 }
74 
75 #undef __FUNCT__
76 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ"
77 PetscErrorCode MatPtAPSymbolic_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
78 {
79   PetscErrorCode ierr;
80 
81   PetscFunctionBegin;
82   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);
83   ierr = (*P->ops->ptapsymbolic_mpiaij)(A,P,fill,C);CHKERRQ(ierr);
84   PetscFunctionReturn(0);
85 }
86 
87 #undef __FUNCT__
88 #define __FUNCT__ "MatPtAPNumeric_MPIAIJ"
89 PetscErrorCode MatPtAPNumeric_MPIAIJ(Mat A,Mat P,Mat C)
90 {
91   PetscErrorCode ierr;
92 
93   PetscFunctionBegin;
94   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);
95   ierr = (*P->ops->ptapnumeric_mpiaij)(A,P,C);CHKERRQ(ierr);
96   PetscFunctionReturn(0);
97 }
98 
99 #undef __FUNCT__
100 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ_MPIAIJ"
101 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
102 {
103   PetscErrorCode       ierr;
104   Mat                  Cmpi;
105   Mat_PtAPMPI          *ptap;
106   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
107   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
108   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
109   Mat_SeqAIJ           *p_loc,*p_oth;
110   PetscInt             *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ;
111   PetscInt             *adi=ad->i,*aj,*aoi=ao->i,nnz;
112   PetscInt             nlnk,*lnk,*owners_co,*coi,*coj,i,k,pnz,row;
113   PetscInt             am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n;
114   PetscBT              lnkbt;
115   MPI_Comm             comm=((PetscObject)A)->comm;
116   PetscMPIInt          size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
117   PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
118   PetscInt             len,proc,*dnz,*onz,*owners;
119   PetscInt             nzi,*bi,*bj;
120   PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
121   MPI_Request          *swaits,*rwaits;
122   MPI_Status           *sstatus,rstatus;
123   Mat_Merge_SeqsToMPI  *merge;
124   PetscInt             *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0;
125   PetscReal            afill=1.0,afill_tmp;
126   PetscInt             rstart = P->cmap->rstart,rmax;
127   PetscScalar          *vals;
128 
129   PetscFunctionBegin;
130   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
131   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
132 
133   /* create struct Mat_PtAPMPI and attached it to C later */
134   ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
135   ptap->reuse    = MAT_INITIAL_MATRIX;
136 
137 
138   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
139   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
140 #if defined(DEBUG_MATPTAP)
141    if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] P_oth is done...\n",rank);
142 #endif
143 
144   /* get P_loc by taking all local rows of P */
145   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
146 #if defined(DEBUG_MATPTAP)
147   ierr = MPI_Barrier(comm);CHKERRQ(ierr);
148   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] P_loc is done...\n",rank);
149 #endif
150 
151   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
152   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
153   pi_loc = p_loc->i; pj_loc = p_loc->j;
154   pi_oth = p_oth->i; pj_oth = p_oth->j;
155 
156   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
157   /*-------------------------------------------------------------------*/
158   ierr = PetscMalloc((am+1)*sizeof(PetscInt),&api);CHKERRQ(ierr);
159   api[0] = 0;
160 
161   /* create and initialize a linked list */
162   nlnk = pN+1;
163 #if defined(DEBUG_MATPTAP)
164   ierr = MPI_Barrier(comm);CHKERRQ(ierr);
165   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call PetscLLCreate(), pN %D, P_rmax %D %D; Annz %D\n",rank,pN,p_loc->rmax,p_oth->rmax,adi[am]+aoi[am]);
166 #endif
167   ierr = PetscLLCreate(pN,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
168 #if defined(DEBUG_MATPTAP)
169   ierr = MPI_Barrier(comm);CHKERRQ(ierr);
170   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call PetscLLCreate() is done\n",rank);
171 #endif
172 
173   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
174   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
175   current_space = free_space;
176 
177   for (i=0; i<am; i++) {
178     apnz = 0;
179     /* diagonal portion of A */
180     nzi = adi[i+1] - adi[i];
181     aj  = ad->j + adi[i];
182     for (j=0; j<nzi; j++){
183       row  = aj[j];
184       pnz  = pi_loc[row+1] - pi_loc[row];
185       Jptr = pj_loc + pi_loc[row];
186       /* add non-zero cols of P into the sorted linked list lnk */
187       ierr = PetscLLAddSorted(pnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
188       apnz += nlnk;
189     }
190     /* off-diagonal portion of A */
191     nzi = aoi[i+1] - aoi[i];
192     aj  = ao->j + aoi[i];
193     for (j=0; j<nzi; j++){
194       row = aj[j];
195       pnz = pi_oth[row+1] - pi_oth[row];
196       Jptr  = pj_oth + pi_oth[row];
197       ierr = PetscLLAddSorted(pnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
198       apnz += nlnk;
199     }
200 
201     api[i+1] = api[i] + apnz;
202     if (ap_rmax < apnz) ap_rmax = apnz;
203 
204     /* if free space is not available, double the total space in the list */
205     if (current_space->local_remaining<apnz) {
206       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
207       nspacedouble++;
208     }
209 
210     /* Copy data into free space, then initialize lnk */
211     ierr = PetscLLClean(pN,pN,apnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
212     current_space->array           += apnz;
213     current_space->local_used      += apnz;
214     current_space->local_remaining -= apnz;
215   }
216   /* Allocate space for apj, initialize apj, and */
217   /* destroy list of free space and other temporary array(s) */
218   ierr = PetscMalloc((api[am]+1)*sizeof(PetscInt),&apj);CHKERRQ(ierr);
219   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
220   afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]);
221   if (afill_tmp > afill) afill = afill_tmp;
222 
223   /* determine symbolic Co=(p->B)^T*AP - send to others */
224   /*----------------------------------------------------*/
225   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
226 
227   /* then, compute symbolic Co = (p->B)^T*AP */
228   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
229                          >= (num of nonzero rows of C_seq) - pn */
230   ierr = PetscMalloc((pon+1)*sizeof(PetscInt),&coi);CHKERRQ(ierr);
231   coi[0] = 0;
232 
233   /* set initial free space to be fill*(nnz(p->B) + nnz(AP)) */
234   nnz           = fill*(poti[pon] + api[am]);
235   ierr          = PetscFreeSpaceGet(nnz,&free_space);
236   current_space = free_space;
237 
238   for (i=0; i<pon; i++) {
239     nnz = 0;
240     pnz = poti[i+1] - poti[i];
241     ptJ = potj + poti[i];
242     for (j=0; j<pnz; j++){
243       row  = ptJ[j]; /* row of AP == col of Pot */
244       apnz = api[row+1] - api[row];
245       Jptr = apj + api[row];
246       /* add non-zero cols of AP into the sorted linked list lnk */
247       ierr = PetscLLAddSorted(apnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
248       nnz += nlnk;
249     }
250 
251     /* If free space is not available, double the total space in the list */
252     if (current_space->local_remaining<nnz) {
253       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
254       nspacedouble++;
255     }
256 
257     /* Copy data into free space, and zero out denserows */
258     ierr = PetscLLClean(pN,pN,nnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
259     current_space->array           += nnz;
260     current_space->local_used      += nnz;
261     current_space->local_remaining -= nnz;
262     coi[i+1] = coi[i] + nnz;
263   }
264   ierr = PetscMalloc((coi[pon]+1)*sizeof(PetscInt),&coj);CHKERRQ(ierr);
265   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
266   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]);
267   if (afill_tmp > afill) afill = afill_tmp;
268   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
269 
270 #if defined(DEBUG_MATPTAP)
271   ierr = MPI_Barrier(comm);CHKERRQ(ierr);
272   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] local Co is done\n",rank);
273 #endif
274 
275   /* send j-array (coj) of Co to other processors */
276   /*----------------------------------------------*/
277   /* determine row ownership */
278   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
279   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
280   merge->rowmap->n = pn;
281   merge->rowmap->bs = 1;
282   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
283   owners = merge->rowmap->range;
284 
285   /* determine the number of messages to send, their lengths */
286   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
287   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
288   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
289   len_s = merge->len_s;
290   merge->nsend = 0;
291 
292   ierr = PetscMalloc((size+2)*sizeof(PetscInt),&owners_co);CHKERRQ(ierr);
293   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
294 
295   proc = 0;
296   for (i=0; i<pon; i++){
297     while (prmap[i] >= owners[proc+1]) proc++;
298     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
299     len_s[proc] += coi[i+1] - coi[i];
300   }
301 
302   len   = 0;  /* max length of buf_si[] */
303   owners_co[0] = 0;
304   for (proc=0; proc<size; proc++){
305     owners_co[proc+1] = owners_co[proc] + len_si[proc];
306     if (len_si[proc]){
307       merge->nsend++;
308       len_si[proc] = 2*(len_si[proc] + 1);
309       len += len_si[proc];
310     }
311   }
312 
313   /* determine the number and length of messages to receive for coi and coj  */
314   ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
315   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
316 
317   /* post the Irecv and Isend of coj */
318   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
319   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
320   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&swaits);CHKERRQ(ierr);
321   for (proc=0, k=0; proc<size; proc++){
322     if (!len_s[proc]) continue;
323     i = owners_co[proc];
324     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
325     k++;
326   }
327 
328   /* receives and sends of coj are complete */
329   ierr = PetscMalloc(size*sizeof(MPI_Status),&sstatus);CHKERRQ(ierr);
330   for (i=0; i<merge->nrecv; i++){
331     ierr = MPI_Waitany(merge->nrecv,rwaits,&j,&rstatus);CHKERRQ(ierr);
332   }
333   ierr = PetscFree(rwaits);CHKERRQ(ierr);
334   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
335 
336   /* send and recv coi */
337   /*-------------------*/
338   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
339   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
340   ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
341   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
342   for (proc=0,k=0; proc<size; proc++){
343     if (!len_s[proc]) continue;
344     /* form outgoing message for i-structure:
345          buf_si[0]:                 nrows to be sent
346                [1:nrows]:           row index (global)
347                [nrows+1:2*nrows+1]: i-structure index
348     */
349     /*-------------------------------------------*/
350     nrows = len_si[proc]/2 - 1;
351     buf_si_i    = buf_si + nrows+1;
352     buf_si[0]   = nrows;
353     buf_si_i[0] = 0;
354     nrows = 0;
355     for (i=owners_co[proc]; i<owners_co[proc+1]; i++){
356       nzi = coi[i+1] - coi[i];
357       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
358       buf_si[nrows+1] =prmap[i] -owners[proc]; /* local row index */
359       nrows++;
360     }
361     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
362     k++;
363     buf_si += len_si[proc];
364   }
365   i = merge->nrecv;
366   while (i--) {
367     ierr = MPI_Waitany(merge->nrecv,rwaits,&j,&rstatus);CHKERRQ(ierr);
368   }
369   ierr = PetscFree(rwaits);CHKERRQ(ierr);
370   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
371   /*
372   ierr = PetscInfo2(A,"nsend: %d, nrecv: %d\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
373   for (i=0; i<merge->nrecv; i++){
374     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);
375   }
376   */
377   ierr = PetscFree(len_si);CHKERRQ(ierr);
378   ierr = PetscFree(len_ri);CHKERRQ(ierr);
379   ierr = PetscFree(swaits);CHKERRQ(ierr);
380   ierr = PetscFree(sstatus);CHKERRQ(ierr);
381   ierr = PetscFree(buf_s);CHKERRQ(ierr);
382 
383 #if defined(DEBUG_MATPTAP)
384   ierr = MPI_Barrier(comm);CHKERRQ(ierr);
385   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] Co is done\n",rank);
386 #endif
387 
388   /* compute the local portion of C (mpi mat) */
389   /*------------------------------------------*/
390   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
391 
392   /* allocate bi array and free space for accumulating nonzero column info */
393   ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
394   bi[0] = 0;
395 
396   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
397   nnz           = fill*(pi_loc[pm] + api[am]);
398   ierr          = PetscFreeSpaceGet(nnz,&free_space);
399   current_space = free_space;
400 
401   ierr = PetscMalloc3(merge->nrecv,PetscInt**,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextci);CHKERRQ(ierr);
402   for (k=0; k<merge->nrecv; k++){
403     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
404     nrows       = *buf_ri_k[k];
405     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
406     nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
407   }
408   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
409   rmax = 0;
410   for (i=0; i<pn; i++) {
411     /* add pdt[i,:]*AP into lnk */
412     nnz = 0;
413     pnz = pdti[i+1] - pdti[i];
414     ptJ = pdtj + pdti[i];
415     for (j=0; j<pnz; j++){
416       row  = ptJ[j];  /* row of AP == col of Pt */
417       apnz = api[row+1] - api[row];
418       Jptr = apj + api[row];
419       /* add non-zero cols of AP into the sorted linked list lnk */
420       ierr = PetscLLAddSorted(apnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
421       nnz += nlnk;
422     }
423     /* add received col data into lnk */
424     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
425       if (i == *nextrow[k]) { /* i-th row */
426         nzi = *(nextci[k]+1) - *nextci[k];
427         Jptr  = buf_rj[k] + *nextci[k];
428         ierr = PetscLLAddSorted(nzi,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
429         nnz += nlnk;
430         nextrow[k]++; nextci[k]++;
431       }
432     }
433 
434     /* if free space is not available, make more free space */
435     if (current_space->local_remaining<nnz) {
436       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
437       nspacedouble++;
438     }
439     /* copy data into free space, then initialize lnk */
440     ierr = PetscLLClean(pN,pN,nnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
441     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
442     current_space->array           += nnz;
443     current_space->local_used      += nnz;
444     current_space->local_remaining -= nnz;
445     bi[i+1] = bi[i] + nnz;
446     if (nnz > rmax) rmax = nnz;
447   }
448   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
449   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
450 
451   ierr = PetscMalloc((bi[pn]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
452   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
453   afill_tmp = (PetscReal)bi[pn]/(pi_loc[pm] + api[am]);
454   if (afill_tmp > afill) afill = afill_tmp;
455   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
456 
457   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part - check runex55_SA ?  */
458   /*------------------------------------------------------------------------------------------------------*/
459   ierr = PetscMalloc((rmax+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
460   ierr = PetscMemzero(vals,rmax*sizeof(PetscScalar));CHKERRQ(ierr);
461 
462   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
463   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
464   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
465   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
466   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
467   ierr = MatSetBlockSize(Cmpi,1);CHKERRQ(ierr);
468   for (i=0; i<pn; i++){
469     row = i + rstart;
470     nnz = bi[i+1] - bi[i];
471     Jptr = bj + bi[i];
472     ierr = MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);CHKERRQ(ierr);
473   }
474   ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
475   ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
476   ierr = PetscFree(vals);CHKERRQ(ierr);
477 
478   merge->bi            = bi;
479   merge->bj            = bj;
480   merge->coi           = coi;
481   merge->coj           = coj;
482   merge->buf_ri        = buf_ri;
483   merge->buf_rj        = buf_rj;
484   merge->owners_co     = owners_co;
485   merge->destroy       = Cmpi->ops->destroy;
486   merge->duplicate     = Cmpi->ops->duplicate;
487 
488   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
489   /* Cmpi->assembled      = PETSC_FALSE; */
490   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_PtAP;
491   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatPtAP;
492 
493   /* attach the supporting struct to Cmpi for reuse */
494   c = (Mat_MPIAIJ*)Cmpi->data;
495   c->ptap        = ptap;
496   ptap->api      = api;
497   ptap->apj      = apj;
498   ptap->merge    = merge;
499   ptap->apnz_max = ap_rmax;
500 
501   *C = Cmpi;
502 #if defined(PETSC_USE_INFO)
503   if (bi[pn] != 0) {
504     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
505     ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr);
506   } else {
507     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
508   }
509 #endif
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->apnz_max+1)*sizeof(MatScalar),&apa);CHKERRQ(ierr);
788     ierr = PetscMemzero(apa,ptap->apnz_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