xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision 9516a85c44490b3406aa9974ddbba09e424672ec)
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 #include <petsctime.h>
12 
13 #define PTAP_PROFILE
14 
15 extern PetscErrorCode MatDestroy_MPIAIJ(Mat);
16 #undef __FUNCT__
17 #define __FUNCT__ "MatDestroy_MPIAIJ_PtAP"
18 PetscErrorCode MatDestroy_MPIAIJ_PtAP(Mat A)
19 {
20   PetscErrorCode ierr;
21   Mat_MPIAIJ     *a   =(Mat_MPIAIJ*)A->data;
22   Mat_PtAPMPI    *ptap=a->ptap;
23 
24   PetscFunctionBegin;
25   if (ptap) {
26     Mat_Merge_SeqsToMPI *merge=ptap->merge;
27     ierr = PetscFree2(ptap->startsj_s,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 = MatDestroy(&ptap->A_loc);CHKERRQ(ierr); /* used by MatTransposeMatMult() */
32     ierr = MatDestroy(&ptap->R);CHKERRQ(ierr);
33     if (ptap->api) {ierr = PetscFree(ptap->api);CHKERRQ(ierr);}
34     if (ptap->apj) {ierr = PetscFree(ptap->apj);CHKERRQ(ierr);}
35     if (ptap->apa) {ierr = PetscFree(ptap->apa);CHKERRQ(ierr);}
36     if (merge) {
37       ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
38       ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
39       ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
40       ierr = PetscFree(merge->bi);CHKERRQ(ierr);
41       ierr = PetscFree(merge->bj);CHKERRQ(ierr);
42       ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
43       ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
44       ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
45       ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
46       ierr = PetscFree(merge->coi);CHKERRQ(ierr);
47       ierr = PetscFree(merge->coj);CHKERRQ(ierr);
48       ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
49       ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
50       ierr = merge->destroy(A);CHKERRQ(ierr);
51       ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
52     }
53     ierr = PetscFree(ptap);CHKERRQ(ierr);
54   }
55   PetscFunctionReturn(0);
56 }
57 
58 #undef __FUNCT__
59 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatPtAP"
60 PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat A, MatDuplicateOption op, Mat *M)
61 {
62   PetscErrorCode      ierr;
63   Mat_MPIAIJ          *a     = (Mat_MPIAIJ*)A->data;
64   Mat_PtAPMPI         *ptap  = a->ptap;
65   Mat_Merge_SeqsToMPI *merge = ptap->merge;
66 
67   PetscFunctionBegin;
68   ierr = (*merge->duplicate)(A,op,M);CHKERRQ(ierr);
69 
70   (*M)->ops->destroy   = merge->destroy;
71   (*M)->ops->duplicate = merge->duplicate;
72   PetscFunctionReturn(0);
73 }
74 
75 #undef __FUNCT__
76 #define __FUNCT__ "MatPtAP_MPIAIJ_MPIAIJ"
77 PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
78 {
79   PetscErrorCode ierr;
80 
81   PetscFunctionBegin;
82   if (scall == MAT_INITIAL_MATRIX) {
83     ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
84     ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
85     ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
86   }
87   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
88   ierr = MatPtAPNumeric_MPIAIJ_MPIAIJ(A,P,*C);CHKERRQ(ierr);
89   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
90   PetscFunctionReturn(0);
91 }
92 
93 #undef __FUNCT__
94 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ_MPIAIJ"
95 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
96 {
97   PetscErrorCode      ierr;
98   Mat                 Cmpi;
99   Mat_PtAPMPI         *ptap;
100   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
101   Mat_MPIAIJ          *a        =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
102   Mat_SeqAIJ          *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
103   Mat_SeqAIJ          *p_loc,*p_oth;
104   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ;
105   PetscInt            *adi=ad->i,*aj,*aoi=ao->i,nnz;
106   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
107   PetscInt            am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n;
108   PetscBT             lnkbt;
109   MPI_Comm            comm;
110   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0;
111   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
112   PetscInt            len,proc,*dnz,*onz,*owners;
113   PetscInt            nzi,*pti,*ptj;
114   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
115   MPI_Request         *swaits,*rwaits;
116   MPI_Status          *sstatus,rstatus;
117   Mat_Merge_SeqsToMPI *merge;
118   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0;
119   PetscReal           afill=1.0,afill_tmp;
120   PetscInt            rmax;
121 
122   PetscFunctionBegin;
123   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
124 
125   /* check if matrix local sizes are compatible */
126   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
127     SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
128   }
129   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) {
130     SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
131   }
132 
133   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
134   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
135 
136   /* create struct Mat_PtAPMPI and attached it to C later */
137   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
138   ierr        = PetscNew(&merge);CHKERRQ(ierr);
139   ptap->merge = merge;
140   ptap->reuse = MAT_INITIAL_MATRIX;
141 
142   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
143   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
144 
145   /* get P_loc by taking all local rows of P */
146   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
147 
148   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
149   p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
150   pi_loc = p_loc->i; pj_loc = p_loc->j;
151   pi_oth = p_oth->i; pj_oth = p_oth->j;
152 
153   /* (1) compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth (api,apj) */
154   /*--------------------------------------------------------------------------*/
155   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
156   api[0] = 0;
157 
158   /* create and initialize a linked list */
159   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
160 
161   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) -OOM for ex56, np=8k on Intrepid! */
162   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
163 
164   current_space = free_space;
165 
166   for (i=0; i<am; i++) {
167     /* diagonal portion of A */
168     nzi = adi[i+1] - adi[i];
169     aj  = ad->j + adi[i];
170     for (j=0; j<nzi; j++) {
171       row  = aj[j];
172       pnz  = pi_loc[row+1] - pi_loc[row];
173       Jptr = pj_loc + pi_loc[row];
174       /* add non-zero cols of P into the sorted linked list lnk */
175       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
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 = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
185     }
186     apnz     = lnk[0];
187     api[i+1] = api[i] + apnz;
188     if (ap_rmax < apnz) ap_rmax = apnz;
189 
190     /* if free space is not available, double the total space in the list */
191     if (current_space->local_remaining<apnz) {
192       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
193       nspacedouble++;
194     }
195 
196     /* Copy data into free space, then initialize lnk */
197     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
198 
199     current_space->array           += apnz;
200     current_space->local_used      += apnz;
201     current_space->local_remaining -= apnz;
202   }
203 
204   /* Allocate space for apj, initialize apj, and */
205   /* destroy list of free space and other temporary array(s) */
206   ierr      = PetscMalloc1(api[am]+1,&apj);CHKERRQ(ierr);
207   ierr      = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
208   afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1);
209   if (afill_tmp > afill) afill = afill_tmp;
210 
211   /* (2) determine symbolic Co=(p->B)^T*AP - send to others (coi,coj)*/
212   /*-----------------------------------------------------------------*/
213   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
214 
215   /* then, compute symbolic Co = (p->B)^T*AP */
216   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors
217                          >= (num of nonzero rows of C_seq) - pn */
218   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
219   coi[0] = 0;
220 
221   /* set initial free space to be fill*(nnz(p->B) + nnz(AP)) */
222   nnz           = fill*(poti[pon] + api[am]);
223   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
224   current_space = free_space;
225 
226   for (i=0; i<pon; i++) {
227     pnz = poti[i+1] - poti[i];
228     ptJ = potj + poti[i];
229     for (j=0; j<pnz; j++) {
230       row  = ptJ[j]; /* row of AP == col of Pot */
231       apnz = api[row+1] - api[row];
232       Jptr = apj + api[row];
233       /* add non-zero cols of AP into the sorted linked list lnk */
234       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
235     }
236     nnz = lnk[0];
237 
238     /* If free space is not available, double the total space in the list */
239     if (current_space->local_remaining<nnz) {
240       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
241       nspacedouble++;
242     }
243 
244     /* Copy data into free space, and zero out denserows */
245     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
246 
247     current_space->array           += nnz;
248     current_space->local_used      += nnz;
249     current_space->local_remaining -= nnz;
250 
251     coi[i+1] = coi[i] + nnz;
252   }
253 
254   ierr      = PetscMalloc1(coi[pon],&coj);CHKERRQ(ierr);
255   ierr      = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
256   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]+1);
257   if (afill_tmp > afill) afill = afill_tmp;
258   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
259 
260   /* (3) send j-array (coj) of Co to other processors */
261   /*--------------------------------------------------*/
262   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
263   len_s        = merge->len_s;
264   merge->nsend = 0;
265 
266 
267   /* determine row ownership */
268   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
269   merge->rowmap->n  = pn;
270   merge->rowmap->bs = 1;
271 
272   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
273   owners = merge->rowmap->range;
274 
275   /* determine the number of messages to send, their lengths */
276   ierr = PetscMalloc2(size,&len_si,size,&sstatus);CHKERRQ(ierr);
277   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
278   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
279 
280   proc = 0;
281   for (i=0; i<pon; i++) {
282     while (prmap[i] >= owners[proc+1]) proc++;
283     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
284     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
285   }
286 
287   len          = 0; /* max length of buf_si[], see (4) */
288   owners_co[0] = 0;
289   for (proc=0; proc<size; proc++) {
290     owners_co[proc+1] = owners_co[proc] + len_si[proc];
291     if (len_s[proc]) {
292       merge->nsend++;
293       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
294       len         += len_si[proc];
295     }
296   }
297 
298   /* determine the number and length of messages to receive for coi and coj  */
299   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
300   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
301 
302   /* post the Irecv and Isend of coj */
303   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
304   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
305   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
306   for (proc=0, k=0; proc<size; proc++) {
307     if (!len_s[proc]) continue;
308     i    = owners_co[proc];
309     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
310     k++;
311   }
312 
313   /* receives and sends of coj are complete */
314   for (i=0; i<merge->nrecv; i++) {
315     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
316   }
317   ierr = PetscFree(rwaits);CHKERRQ(ierr);
318   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
319 
320   /* (4) send and recv coi */
321   /*-----------------------*/
322   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
323   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
324   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
325   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
326   for (proc=0,k=0; proc<size; proc++) {
327     if (!len_s[proc]) continue;
328     /* form outgoing message for i-structure:
329          buf_si[0]:                 nrows to be sent
330                [1:nrows]:           row index (global)
331                [nrows+1:2*nrows+1]: i-structure index
332     */
333     /*-------------------------------------------*/
334     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
335     buf_si_i    = buf_si + nrows+1;
336     buf_si[0]   = nrows;
337     buf_si_i[0] = 0;
338     nrows       = 0;
339     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
340       nzi = coi[i+1] - coi[i];
341       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
342       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
343       nrows++;
344     }
345     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
346     k++;
347     buf_si += len_si[proc];
348   }
349   i = merge->nrecv;
350   while (i--) {
351     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
352   }
353   ierr = PetscFree(rwaits);CHKERRQ(ierr);
354   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
355 
356   ierr = PetscFree2(len_si,sstatus);CHKERRQ(ierr);
357   ierr = PetscFree(len_ri);CHKERRQ(ierr);
358   ierr = PetscFree(swaits);CHKERRQ(ierr);
359   ierr = PetscFree(buf_s);CHKERRQ(ierr);
360 
361   /* (5) compute the local portion of C (mpi mat) */
362   /*----------------------------------------------*/
363   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
364 
365   /* allocate pti array and free space for accumulating nonzero column info */
366   ierr   = PetscMalloc1(pn+1,&pti);CHKERRQ(ierr);
367   pti[0] = 0;
368 
369   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
370   nnz           = fill*(pi_loc[pm] + api[am]);
371   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
372   current_space = free_space;
373 
374   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
375   for (k=0; k<merge->nrecv; k++) {
376     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
377     nrows       = *buf_ri_k[k];
378     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
379     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
380   }
381   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
382   rmax = 0;
383   for (i=0; i<pn; i++) {
384     /* add pdt[i,:]*AP into lnk */
385     pnz = pdti[i+1] - pdti[i];
386     ptJ = pdtj + pdti[i];
387     for (j=0; j<pnz; j++) {
388       row  = ptJ[j];  /* row of AP == col of Pt */
389       apnz = api[row+1] - api[row];
390       Jptr = apj + api[row];
391       /* add non-zero cols of AP into the sorted linked list lnk */
392       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
393     }
394 
395     /* add received col data into lnk */
396     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
397       if (i == *nextrow[k]) { /* i-th row */
398         nzi  = *(nextci[k]+1) - *nextci[k];
399         Jptr = buf_rj[k] + *nextci[k];
400         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
401         nextrow[k]++; nextci[k]++;
402       }
403     }
404     nnz = lnk[0];
405 
406     /* if free space is not available, make more free space */
407     if (current_space->local_remaining<nnz) {
408       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
409       nspacedouble++;
410     }
411     /* copy data into free space, then initialize lnk */
412     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
413     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
414 
415     current_space->array           += nnz;
416     current_space->local_used      += nnz;
417     current_space->local_remaining -= nnz;
418 
419     pti[i+1] = pti[i] + nnz;
420     if (nnz > rmax) rmax = nnz;
421   }
422   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
423   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
424 
425   ierr      = PetscMalloc1(pti[pn]+1,&ptj);CHKERRQ(ierr);
426   ierr      = PetscFreeSpaceContiguous(&free_space,ptj);CHKERRQ(ierr);
427   afill_tmp = (PetscReal)pti[pn]/(pi_loc[pm] + api[am]+1);
428   if (afill_tmp > afill) afill = afill_tmp;
429   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
430 
431   /* (6) create symbolic parallel matrix Cmpi */
432   /*------------------------------------------*/
433   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
434   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
435   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
436   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
437   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
438   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
439 
440   merge->bi        = pti;      /* Cseq->i */
441   merge->bj        = ptj;      /* Cseq->j */
442   merge->coi       = coi;      /* Co->i   */
443   merge->coj       = coj;      /* Co->j   */
444   merge->buf_ri    = buf_ri;
445   merge->buf_rj    = buf_rj;
446   merge->owners_co = owners_co;
447   merge->destroy   = Cmpi->ops->destroy;
448   merge->duplicate = Cmpi->ops->duplicate;
449 
450   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
451   Cmpi->assembled      = PETSC_FALSE;
452   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_PtAP;
453   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatPtAP;
454 
455   /* attach the supporting struct to Cmpi for reuse */
456   c           = (Mat_MPIAIJ*)Cmpi->data;
457   c->ptap     = ptap;
458   ptap->api   = api;
459   ptap->apj   = apj;
460   ptap->rmax  = ap_rmax;
461   *C          = Cmpi;
462 
463   /* flag 'scalable' determines which implementations to be used:
464        0: do dense axpy in MatPtAPNumeric() - fast, but requires storage of a nonscalable dense array apa;
465        1: do sparse axpy in MatPtAPNumeric() - might slow, uses a sparse array apa */
466   /* set default scalable */
467   ptap->scalable = PETSC_FALSE; //PETSC_TRUE;
468 
469   ierr = PetscOptionsGetBool(((PetscObject)Cmpi)->prefix,"-matptap_scalable",&ptap->scalable,NULL);CHKERRQ(ierr);
470   if (!ptap->scalable) {  /* Do dense axpy */
471     ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
472     ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->R);CHKERRQ(ierr);
473   } else {
474     ierr = PetscCalloc1(ap_rmax+1,&ptap->apa);CHKERRQ(ierr);
475   }
476 
477 #if defined(PETSC_USE_INFO)
478   if (pti[pn] != 0) {
479     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
480     ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
481   } else {
482     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
483   }
484 #endif
485   PetscFunctionReturn(0);
486 }
487 
488 #undef __FUNCT__
489 #define __FUNCT__ "MatPtAPNumeric_MPIAIJ_MPIAIJ"
490 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
491 {
492   PetscErrorCode      ierr;
493   Mat_MPIAIJ          *a =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
494   Mat_SeqAIJ          *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
495   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
496   Mat_SeqAIJ          *p_loc,*p_oth;
497   Mat_PtAPMPI         *ptap;
498   Mat_Merge_SeqsToMPI *merge;
499   PetscInt            *adi=ad->i,*aoi=ao->i,*adj,*aoj,*apJ,nextp;
500   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pJ,*pj;
501   PetscInt            i,j,k,anz,pnz,apnz,nextap,row,*cj;
502   MatScalar           *ada,*aoa,*apa,*pa,*ca,*pa_loc,*pa_oth,valtmp;
503   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
504   MPI_Comm            comm;
505   PetscMPIInt         size,rank,taga,*len_s;
506   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
507   PetscInt            **buf_ri,**buf_rj;
508   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
509   MPI_Request         *s_waits,*r_waits;
510   MPI_Status          *status;
511   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
512   PetscInt            *api,*apj,*coi,*coj;
513   PetscInt            *poJ=po->j,*pdJ=pd->j,pcstart=P->cmap->rstart,pcend=P->cmap->rend;
514   PetscBool           scalable;
515 #if defined(PTAP_PROFILE)
516   PetscLogDouble t0,t1,t2,t3,t4,et2_AP=0.0,et2_PtAP=0.0,t2_0,t2_1,t2_2,t_tran0,t_tran1;
517 #endif
518 
519   PetscFunctionBegin;
520   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
521 #if defined(PTAP_PROFILE)
522   ierr = PetscTime(&t0);CHKERRQ(ierr);
523 #endif
524   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
525   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
526 
527   ptap = c->ptap;
528   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_INCOMP,"MatPtAP() has not been called to create matrix C yet, cannot use MAT_REUSE_MATRIX");
529   merge    = ptap->merge;
530   apa      = ptap->apa;
531   scalable = ptap->scalable;
532 
533   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
534   /*-----------------------------------------------------*/
535   if (ptap->reuse == MAT_INITIAL_MATRIX) {
536     /* P_oth and P_loc are obtained in MatPtASymbolic(), skip calling MatGetBrowsOfAoCols() and MatMPIAIJGetLocalMat() */
537     ptap->reuse = MAT_REUSE_MATRIX;
538   } else { /* update numerical values of P_oth and P_loc */
539     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
540     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
541   }
542 #if defined(PTAP_PROFILE)
543   ierr = PetscTime(&t1);CHKERRQ(ierr);
544 #endif
545 
546   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
547   /*--------------------------------------------------------------*/
548   /* get data from symbolic products */
549   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
550   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
551   pi_loc=p_loc->i; pj_loc=p_loc->j; pJ=pj_loc; pa_loc=p_loc->a;
552   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
553 
554   coi  = merge->coi; coj = merge->coj;
555   ierr = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
556 
557   bi     = merge->bi; bj = merge->bj;
558   owners = merge->rowmap->range;
559   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);  /* ba: Cseq->a */
560 
561   api = ptap->api; apj = ptap->apj;
562 
563   if (!scalable) { /* Do dense axpy on apa (length of pN, stores A[i,:]*P) - nonscalable, but faster (could take 1/3 scalable time) */
564     ierr = PetscInfo(C,"Using non-scalable dense axpy\n");CHKERRQ(ierr);
565     /*-----------------------------------------------------------------------------------------------------*/
566     ierr = PetscTime(&t_tran0);CHKERRQ(ierr);
567     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->R);CHKERRQ(ierr);
568     ierr = PetscTime(&t_tran1);CHKERRQ(ierr);
569 
570     Mat         R = ptap->R;
571     Mat_SeqAIJ  *r = (Mat_SeqAIJ*)R->data;
572     PetscInt    *ri=r->i,*rj=r->j,rnz,arow,l,prow,pcol,pN=P->cmap->N;
573     PetscScalar *ra=r->a,tmp,cdense[pN];
574 
575     ierr = PetscMemzero(cdense,pN*sizeof(PetscScalar));CHKERRQ(ierr);
576     for (i=0; i<cm; i++) { /* each row of C or R */
577       rnz = ri[i+1] - ri[i];
578 
579       for (j=0; j<rnz; j++) { /* each nz of R */
580         arow = rj[ri[i] + j];
581 
582         /* diagonal portion of A */
583         anz  = ad->i[arow+1] - ad->i[arow];
584         for (k=0; k<anz; k++) { /* each nz of Ad */
585           tmp  = ra[ri[i] + j]*ad->a[ad->i[arow] + k];
586           prow = ad->j[ad->i[arow] + k];
587           pnz  = pi_loc[prow+1] - pi_loc[prow];
588 
589           for (l=0; l<pnz; l++) { /* each nz of P_loc */
590             pcol = pj_loc[pi_loc[prow] + l];
591             cdense[pcol] += tmp*pa_loc[pi_loc[prow] + l];
592           }
593         }
594 
595         /* off-diagonal portion of A */
596         anz  = ao->i[arow+1] - ao->i[arow];
597         for (k=0; k<anz; k++) { /* each nz of Ao */
598           tmp  = ra[ri[i] + j]*ao->a[ao->i[arow] + k];
599           prow = ao->j[ao->i[arow] + k];
600           pnz  = pi_oth[prow+1] - pi_oth[prow];
601 
602           for (l=0; l<pnz; l++) { /* each nz of P_oth */
603             pcol = pj_oth[pi_oth[prow] + l];
604             cdense[pcol] += tmp*pa_oth[pi_oth[prow] + l];
605           }
606         }
607 
608       } //for (j=0; j<rnz; j++)
609 
610       /* copy cdense[] into ca; zero cdense[] */
611       cnz = bi[i+1] - bi[i];
612       cj  = bj + bi[i];
613       ca  = ba + bi[i];
614       for (j=0; j<cnz; j++) {
615         ca[j] += cdense[cj[j]];
616         cdense[cj[j]] = 0.0;
617       }
618 #if 0
619       if (rank == 0) {
620         printf("[%d] row %d: ",rank,i);
621         for (j=0; j<pN; j++) printf(" %g,",cdense[j]);
622         printf("\n");
623       }
624       for (j=0; j<pN; j++) cdense[j]=0.0; // zero cdnese[]
625 #endif
626     } //for (i=0; i<cm; i++) {
627 
628     //==========================================
629 
630 
631     for (i=0; i<am; i++) {
632 #if defined(PTAP_PROFILE)
633       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
634 #endif
635       /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */
636       /*------------------------------------------------------------*/
637       apJ = apj + api[i];
638 
639       /* diagonal portion of A */
640       anz = adi[i+1] - adi[i];
641       adj = ad->j + adi[i];
642       ada = ad->a + adi[i];
643       for (j=0; j<anz; j++) {
644         row = adj[j];
645         pnz = pi_loc[row+1] - pi_loc[row];
646         pj  = pj_loc + pi_loc[row];
647         pa  = pa_loc + pi_loc[row];
648 
649         /* perform dense axpy */
650         valtmp = ada[j];
651         for (k=0; k<pnz; k++) {
652           apa[pj[k]] += valtmp*pa[k];
653         }
654         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
655       }
656 
657       /* off-diagonal portion of A */
658       anz = aoi[i+1] - aoi[i];
659       aoj = ao->j + aoi[i];
660       aoa = ao->a + aoi[i];
661       for (j=0; j<anz; j++) {
662         row = aoj[j];
663         pnz = pi_oth[row+1] - pi_oth[row];
664         pj  = pj_oth + pi_oth[row];
665         pa  = pa_oth + pi_oth[row];
666 
667         /* perform dense axpy */
668         valtmp = aoa[j];
669         for (k=0; k<pnz; k++) {
670           apa[pj[k]] += valtmp*pa[k];
671         }
672         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
673       }
674 #if defined(PTAP_PROFILE)
675       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
676       et2_AP += t2_1 - t2_0;
677 #endif
678 
679       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
680       /*--------------------------------------------------------------*/
681       apnz = api[i+1] - api[i];
682       /* put the value into Co=(p->B)^T*AP (off-diagonal part, send to others) */
683       pnz = po->i[i+1] - po->i[i];
684       poJ = po->j + po->i[i];
685       pA  = po->a + po->i[i];
686       for (j=0; j<pnz; j++) {
687         row = poJ[j];
688         cnz = coi[row+1] - coi[row];
689         cj  = coj + coi[row];
690         ca  = coa + coi[row];
691         /* perform dense axpy */
692         valtmp = pA[j];
693         for (k=0; k<cnz; k++) {
694           ca[k] += valtmp*apa[cj[k]];
695         }
696         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
697       }
698 #if 0
699       /* put the value into Cd (diagonal part) */
700       pnz = pd->i[i+1] - pd->i[i];
701       pdJ = pd->j + pd->i[i];
702       pA  = pd->a + pd->i[i];
703       for (j=0; j<pnz; j++) {
704         row = pdJ[j];
705         cnz = bi[row+1] - bi[row];
706         cj  = bj + bi[row];
707         ca  = ba + bi[row];
708         /* perform dense axpy */
709         valtmp = pA[j];
710         for (k=0; k<cnz; k++) {
711           ca[k] += valtmp*apa[cj[k]];
712         }
713         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
714       }
715 #endif
716       /* zero the current row of A*P */
717       for (k=0; k<apnz; k++) apa[apJ[k]] = 0.0;
718 #if defined(PTAP_PROFILE)
719       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
720       et2_PtAP += t2_2 - t2_1;
721 #endif
722     }
723 
724     if (rank == 100) {
725     for (row=0; row<cm; row++) {
726       printf("[%d] row %d: ",rank,row);
727       cnz = bi[row+1] - bi[row];
728       for (j=0; j<cnz; j++) printf(" %g,",ba[bi[row]+j]);
729       printf("\n");
730     }
731     }
732 
733   } else { /* Do sparse axpy on apa (length of ap_rmax, stores A[i,:]*P) - scalable, but slower */
734     ierr = PetscInfo(C,"Using scalable sparse axpy\n");CHKERRQ(ierr);
735     /*-----------------------------------------------------------------------------------------*/
736     pA=pa_loc;
737     for (i=0; i<am; i++) {
738 #if defined(PTAP_PROFILE)
739       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
740 #endif
741       /* form i-th sparse row of A*P */
742       apnz = api[i+1] - api[i];
743       apJ  = apj + api[i];
744       /* diagonal portion of A */
745       anz = adi[i+1] - adi[i];
746       adj = ad->j + adi[i];
747       ada = ad->a + adi[i];
748       for (j=0; j<anz; j++) {
749         row    = adj[j];
750         pnz    = pi_loc[row+1] - pi_loc[row];
751         pj     = pj_loc + pi_loc[row];
752         pa     = pa_loc + pi_loc[row];
753         valtmp = ada[j];
754         nextp  = 0;
755         for (k=0; nextp<pnz; k++) {
756           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
757             apa[k] += valtmp*pa[nextp++];
758           }
759         }
760         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
761       }
762       /* off-diagonal portion of A */
763       anz = aoi[i+1] - aoi[i];
764       aoj = ao->j + aoi[i];
765       aoa = ao->a + aoi[i];
766       for (j=0; j<anz; j++) {
767         row    = aoj[j];
768         pnz    = pi_oth[row+1] - pi_oth[row];
769         pj     = pj_oth + pi_oth[row];
770         pa     = pa_oth + pi_oth[row];
771         valtmp = aoa[j];
772         nextp  = 0;
773         for (k=0; nextp<pnz; k++) {
774           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
775             apa[k] += valtmp*pa[nextp++];
776           }
777         }
778         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
779       }
780 #if defined(PTAP_PROFILE)
781       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
782       et2_AP += t2_1 - t2_0;
783 #endif
784 
785       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
786       /*--------------------------------------------------------------*/
787       pnz = pi_loc[i+1] - pi_loc[i];
788       pJ  = pj_loc + pi_loc[i];
789       for (j=0; j<pnz; j++) {
790         nextap = 0;
791         row    = pJ[j]; /* global index */
792         if (row < pcstart || row >=pcend) { /* put the value into Co */
793           row = *poJ;
794           cj  = coj + coi[row];
795           ca  = coa + coi[row]; poJ++;
796         } else {                            /* put the value into Cd */
797           row = *pdJ;
798           cj  = bj + bi[row];
799           ca  = ba + bi[row]; pdJ++;
800         }
801         valtmp = pA[j];
802         for (k=0; nextap<apnz; k++) {
803           if (cj[k]==apJ[nextap]) ca[k] += valtmp*apa[nextap++];
804         }
805         ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
806       }
807       pA += pnz;
808       /* zero the current row info for A*P */
809       ierr = PetscMemzero(apa,apnz*sizeof(MatScalar));CHKERRQ(ierr);
810 #if defined(PTAP_PROFILE)
811       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
812       et2_PtAP += t2_2 - t2_1;
813 #endif
814     }
815   }
816 #if defined(PTAP_PROFILE)
817   ierr = PetscTime(&t2);CHKERRQ(ierr);
818 #endif
819 
820   /* 3) send and recv matrix values coa */
821   /*------------------------------------*/
822   buf_ri = merge->buf_ri;
823   buf_rj = merge->buf_rj;
824   len_s  = merge->len_s;
825   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
826   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
827 
828   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
829   for (proc=0,k=0; proc<size; proc++) {
830     if (!len_s[proc]) continue;
831     i    = merge->owners_co[proc];
832     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
833     k++;
834   }
835   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
836   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
837 
838   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
839   ierr = PetscFree(r_waits);CHKERRQ(ierr);
840   ierr = PetscFree(coa);CHKERRQ(ierr);
841 #if defined(PTAP_PROFILE)
842   ierr = PetscTime(&t3);CHKERRQ(ierr);
843 #endif
844 
845   /* 4) insert local Cseq and received values into Cmpi */
846   /*------------------------------------------------------*/
847   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
848   for (k=0; k<merge->nrecv; k++) {
849     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
850     nrows       = *(buf_ri_k[k]);
851     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
852     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
853   }
854 
855   for (i=0; i<cm; i++) {
856     row  = owners[rank] + i; /* global row index of C_seq */
857     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
858     ba_i = ba + bi[i];
859     bnz  = bi[i+1] - bi[i];
860     /* add received vals into ba */
861     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
862       /* i-th row */
863       if (i == *nextrow[k]) {
864         cnz    = *(nextci[k]+1) - *nextci[k];
865         cj     = buf_rj[k] + *(nextci[k]);
866         ca     = abuf_r[k] + *(nextci[k]);
867         nextcj = 0;
868         for (j=0; nextcj<cnz; j++) {
869           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
870             ba_i[j] += ca[nextcj++];
871           }
872         }
873         nextrow[k]++; nextci[k]++;
874         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
875       }
876     }
877     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
878   }
879   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
880   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
881 
882   ierr = PetscFree(ba);CHKERRQ(ierr);
883   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
884   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
885   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
886 #if defined(PTAP_PROFILE)
887   ierr = PetscTime(&t4);CHKERRQ(ierr);
888   if (rank==1) {
889     ierr = PetscPrintf(MPI_COMM_SELF," R=Pd^T %g\n", t_tran1 - t_tran0);CHKERRQ(ierr);
890     ierr = PetscPrintf(MPI_COMM_SELF,"  [%d] PtAPNum %g/P + %g/PtAP( %g/A*P + %g/Pt*AP ) + %g/comm + %g/Cloc = %g\n\n",rank,t1-t0,t2-t1,et2_AP,et2_PtAP,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr);
891   }
892 #endif
893   PetscFunctionReturn(0);
894 }
895