xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision 7c8652dd9fb051dfaf30896d504f41ba028df3ea)
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     if (ptap->api) {ierr = PetscFree(ptap->api);CHKERRQ(ierr);}
33     if (ptap->apj) {ierr = PetscFree(ptap->apj);CHKERRQ(ierr);}
34     if (ptap->apa) {ierr = PetscFree(ptap->apa);CHKERRQ(ierr);}
35     if (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   }
54   PetscFunctionReturn(0);
55 }
56 
57 #undef __FUNCT__
58 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatPtAP"
59 PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat A, MatDuplicateOption op, Mat *M)
60 {
61   PetscErrorCode      ierr;
62   Mat_MPIAIJ          *a     = (Mat_MPIAIJ*)A->data;
63   Mat_PtAPMPI         *ptap  = a->ptap;
64   Mat_Merge_SeqsToMPI *merge = ptap->merge;
65 
66   PetscFunctionBegin;
67   ierr = (*merge->duplicate)(A,op,M);CHKERRQ(ierr);
68 
69   (*M)->ops->destroy   = merge->destroy;
70   (*M)->ops->duplicate = merge->duplicate;
71   PetscFunctionReturn(0);
72 }
73 
74 #undef __FUNCT__
75 #define __FUNCT__ "MatPtAP_MPIAIJ_MPIAIJ"
76 PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
77 {
78   PetscErrorCode ierr;
79 
80   PetscFunctionBegin;
81   if (scall == MAT_INITIAL_MATRIX) {
82     ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
83     ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
84     ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
85   }
86   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
87   ierr = MatPtAPNumeric_MPIAIJ_MPIAIJ(A,P,*C);CHKERRQ(ierr);
88   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
89   PetscFunctionReturn(0);
90 }
91 
92 #undef __FUNCT__
93 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ_MPIAIJ"
94 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
95 {
96   PetscErrorCode      ierr;
97   Mat                 Cmpi;
98   Mat_PtAPMPI         *ptap;
99   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
100   Mat_MPIAIJ          *a        =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
101   Mat_SeqAIJ          *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
102   Mat_SeqAIJ          *p_loc,*p_oth;
103   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ;
104   PetscInt            *adi=ad->i,*aj,*aoi=ao->i,nnz;
105   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
106   PetscInt            am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n;
107   PetscBT             lnkbt;
108   MPI_Comm            comm;
109   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0;
110   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
111   PetscInt            len,proc,*dnz,*onz,*owners;
112   PetscInt            nzi,*pti,*ptj;
113   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
114   MPI_Request         *swaits,*rwaits;
115   MPI_Status          *sstatus,rstatus;
116   Mat_Merge_SeqsToMPI *merge;
117   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0;
118   PetscReal           afill=1.0,afill_tmp;
119   PetscInt            rmax;
120 #if defined(PTAP_PROFILE)
121   PetscLogDouble t0,t1,t2,t3,t4;
122 #endif
123 
124   PetscFunctionBegin;
125   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
126 #if defined(PTAP_PROFILE)
127   ierr = PetscTime(&t0);CHKERRQ(ierr);
128 #endif
129 
130   /* check if matrix local sizes are compatible */
131   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
132     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);
133   }
134   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) {
135     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);
136   }
137 
138   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
139   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
140 
141   /* create struct Mat_PtAPMPI and attached it to C later */
142   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
143   ierr        = PetscNew(&merge);CHKERRQ(ierr);
144   ptap->merge = merge;
145   ptap->reuse = MAT_INITIAL_MATRIX;
146 
147   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
148   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
149 
150   /* get P_loc by taking all local rows of P */
151   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
152 
153   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
154   p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
155   pi_loc = p_loc->i; pj_loc = p_loc->j;
156   pi_oth = p_oth->i; pj_oth = p_oth->j;
157 #if defined(PTAP_PROFILE)
158   ierr = PetscTime(&t1);CHKERRQ(ierr);
159 #endif
160 
161   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
162   /*-------------------------------------------------------------------*/
163   ierr   = PetscMalloc1((am+1),&api);CHKERRQ(ierr);
164   api[0] = 0;
165 
166   /* create and initialize a linked list */
167   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
168 
169   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) -OOM for ex56, np=8k on Intrepid! */
170   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
171 
172   current_space = free_space;
173 
174   for (i=0; i<am; i++) {
175     /* diagonal portion of A */
176     nzi = adi[i+1] - adi[i];
177     aj  = ad->j + adi[i];
178     for (j=0; j<nzi; j++) {
179       row  = aj[j];
180       pnz  = pi_loc[row+1] - pi_loc[row];
181       Jptr = pj_loc + pi_loc[row];
182       /* add non-zero cols of P into the sorted linked list lnk */
183       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
184     }
185     /* off-diagonal portion of A */
186     nzi = aoi[i+1] - aoi[i];
187     aj  = ao->j + aoi[i];
188     for (j=0; j<nzi; j++) {
189       row  = aj[j];
190       pnz  = pi_oth[row+1] - pi_oth[row];
191       Jptr = pj_oth + pi_oth[row];
192       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
193     }
194     apnz     = lnk[0];
195     api[i+1] = api[i] + apnz;
196     if (ap_rmax < apnz) ap_rmax = apnz;
197 
198     /* if free space is not available, double the total space in the list */
199     if (current_space->local_remaining<apnz) {
200       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
201       nspacedouble++;
202     }
203 
204     /* Copy data into free space, then initialize lnk */
205     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
206 
207     current_space->array           += apnz;
208     current_space->local_used      += apnz;
209     current_space->local_remaining -= apnz;
210   }
211 
212   /* Allocate space for apj, initialize apj, and */
213   /* destroy list of free space and other temporary array(s) */
214   ierr      = PetscMalloc1((api[am]+1),&apj);CHKERRQ(ierr);
215   ierr      = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
216   afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1);
217   if (afill_tmp > afill) afill = afill_tmp;
218 
219 #if defined(PTAP_PROFILE)
220   ierr = PetscTime(&t2);CHKERRQ(ierr);
221 #endif
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   = PetscMalloc1((pon+1),&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);CHKERRQ(ierr);
236   current_space = free_space;
237 
238   for (i=0; i<pon; i++) {
239     pnz = poti[i+1] - poti[i];
240     ptJ = potj + poti[i];
241     for (j=0; j<pnz; j++) {
242       row  = ptJ[j]; /* row of AP == col of Pot */
243       apnz = api[row+1] - api[row];
244       Jptr = apj + api[row];
245       /* add non-zero cols of AP into the sorted linked list lnk */
246       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
247     }
248     nnz = lnk[0];
249 
250     /* If free space is not available, double the total space in the list */
251     if (current_space->local_remaining<nnz) {
252       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
253       nspacedouble++;
254     }
255 
256     /* Copy data into free space, and zero out denserows */
257     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
258 
259     current_space->array           += nnz;
260     current_space->local_used      += nnz;
261     current_space->local_remaining -= nnz;
262 
263     coi[i+1] = coi[i] + nnz;
264   }
265   ierr      = PetscMalloc1((coi[pon]+1),&coj);CHKERRQ(ierr);
266   ierr      = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
267   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]+1);
268   if (afill_tmp > afill) afill = afill_tmp;
269   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
270 
271   /* send j-array (coj) of Co to other processors */
272   /*----------------------------------------------*/
273   /* determine row ownership */
274   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
275   merge->rowmap->n  = pn;
276   merge->rowmap->bs = 1;
277 
278   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
279   owners = merge->rowmap->range;
280 
281   /* determine the number of messages to send, their lengths */
282   ierr = PetscMalloc2(size,&len_si,size,&sstatus);CHKERRQ(ierr);
283   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
284   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
285 
286   len_s        = merge->len_s;
287   merge->nsend = 0;
288 
289   ierr = PetscMalloc1((size+2),&owners_co);CHKERRQ(ierr);
290 
291   proc = 0;
292   for (i=0; i<pon; i++) {
293     while (prmap[i] >= owners[proc+1]) proc++;
294     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
295     len_s[proc] += coi[i+1] - coi[i];
296   }
297 
298   len          = 0; /* max length of buf_si[] */
299   owners_co[0] = 0;
300   for (proc=0; proc<size; proc++) {
301     owners_co[proc+1] = owners_co[proc] + len_si[proc];
302     if (len_si[proc]) {
303       merge->nsend++;
304       len_si[proc] = 2*(len_si[proc] + 1);
305       len         += len_si[proc];
306     }
307   }
308 
309   /* determine the number and length of messages to receive for coi and coj  */
310   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
311   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
312 
313   /* post the Irecv and Isend of coj */
314   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
315   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
316   ierr = PetscMalloc1((merge->nsend+1),&swaits);CHKERRQ(ierr);
317   for (proc=0, k=0; proc<size; proc++) {
318     if (!len_s[proc]) continue;
319     i    = owners_co[proc];
320     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
321     k++;
322   }
323 
324   /* receives and sends of coj are complete */
325   for (i=0; i<merge->nrecv; i++) {
326     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
327   }
328   ierr = PetscFree(rwaits);CHKERRQ(ierr);
329   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
330 
331   /* send and recv coi */
332   /*-------------------*/
333   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
334   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
335   ierr   = PetscMalloc1((len+1),&buf_s);CHKERRQ(ierr);
336   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
337   for (proc=0,k=0; proc<size; proc++) {
338     if (!len_s[proc]) continue;
339     /* form outgoing message for i-structure:
340          buf_si[0]:                 nrows to be sent
341                [1:nrows]:           row index (global)
342                [nrows+1:2*nrows+1]: i-structure index
343     */
344     /*-------------------------------------------*/
345     nrows       = len_si[proc]/2 - 1;
346     buf_si_i    = buf_si + nrows+1;
347     buf_si[0]   = nrows;
348     buf_si_i[0] = 0;
349     nrows       = 0;
350     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
351       nzi = coi[i+1] - coi[i];
352 
353       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
354       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
355       nrows++;
356     }
357     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
358     k++;
359     buf_si += len_si[proc];
360   }
361   i = merge->nrecv;
362   while (i--) {
363     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
364   }
365   ierr = PetscFree(rwaits);CHKERRQ(ierr);
366   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
367 
368   ierr = PetscFree2(len_si,sstatus);CHKERRQ(ierr);
369   ierr = PetscFree(len_ri);CHKERRQ(ierr);
370   ierr = PetscFree(swaits);CHKERRQ(ierr);
371   ierr = PetscFree(buf_s);CHKERRQ(ierr);
372 
373 #if defined(PTAP_PROFILE)
374   ierr = PetscTime(&t3);CHKERRQ(ierr);
375 #endif
376 
377   /* compute the local portion of C (mpi mat) */
378   /*------------------------------------------*/
379   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
380 
381   /* allocate pti array and free space for accumulating nonzero column info */
382   ierr   = PetscMalloc1((pn+1),&pti);CHKERRQ(ierr);
383   pti[0] = 0;
384 
385   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
386   nnz           = fill*(pi_loc[pm] + api[am]);
387   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
388   current_space = free_space;
389 
390   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
391   for (k=0; k<merge->nrecv; k++) {
392     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
393     nrows       = *buf_ri_k[k];
394     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
395     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
396   }
397   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
398   rmax = 0;
399   for (i=0; i<pn; i++) {
400     /* add pdt[i,:]*AP into lnk */
401     pnz = pdti[i+1] - pdti[i];
402     ptJ = pdtj + pdti[i];
403     for (j=0; j<pnz; j++) {
404       row  = ptJ[j];  /* row of AP == col of Pt */
405       apnz = api[row+1] - api[row];
406       Jptr = apj + api[row];
407       /* add non-zero cols of AP into the sorted linked list lnk */
408       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
409     }
410 
411     /* add received col data into lnk */
412     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
413       if (i == *nextrow[k]) { /* i-th row */
414         nzi  = *(nextci[k]+1) - *nextci[k];
415         Jptr = buf_rj[k] + *nextci[k];
416         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
417         nextrow[k]++; nextci[k]++;
418       }
419     }
420     nnz = lnk[0];
421 
422     /* if free space is not available, make more free space */
423     if (current_space->local_remaining<nnz) {
424       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
425       nspacedouble++;
426     }
427     /* copy data into free space, then initialize lnk */
428     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
429     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
430 
431     current_space->array           += nnz;
432     current_space->local_used      += nnz;
433     current_space->local_remaining -= nnz;
434 
435     pti[i+1] = pti[i] + nnz;
436     if (nnz > rmax) rmax = nnz;
437   }
438   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
439   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
440 
441   ierr      = PetscMalloc1((pti[pn]+1),&ptj);CHKERRQ(ierr);
442   ierr      = PetscFreeSpaceContiguous(&free_space,ptj);CHKERRQ(ierr);
443   afill_tmp = (PetscReal)pti[pn]/(pi_loc[pm] + api[am]+1);
444   if (afill_tmp > afill) afill = afill_tmp;
445   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
446 
447   /* create symbolic parallel matrix Cmpi */
448   /*--------------------------------------*/
449   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
450   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
451   ierr = MatSetBlockSizes(Cmpi,P->cmap->bs,P->cmap->bs);CHKERRQ(ierr);
452   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
453   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
454   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
455 
456   merge->bi        = pti;      /* Cseq->i */
457   merge->bj        = ptj;      /* Cseq->j */
458   merge->coi       = coi;      /* Co->i   */
459   merge->coj       = coj;      /* Co->j   */
460   merge->buf_ri    = buf_ri;
461   merge->buf_rj    = buf_rj;
462   merge->owners_co = owners_co;
463   merge->destroy   = Cmpi->ops->destroy;
464   merge->duplicate = Cmpi->ops->duplicate;
465 
466   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
467   Cmpi->assembled      = PETSC_FALSE;
468   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_PtAP;
469   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatPtAP;
470 
471   /* attach the supporting struct to Cmpi for reuse */
472   c           = (Mat_MPIAIJ*)Cmpi->data;
473   c->ptap     = ptap;
474   ptap->api   = api;
475   ptap->apj   = apj;
476   ptap->rmax  = ap_rmax;
477   *C          = Cmpi;
478 
479   /* flag 'scalable' determines which implementations to be used:
480        0: do dense axpy in MatPtAPNumeric() - fast, but requires storage of a nonscalable dense array apa;
481        1: do sparse axpy in MatPtAPNumeric() - might slow, uses a sparse array apa */
482   /* set default scalable */
483   ptap->scalable = PETSC_TRUE;
484 
485   ierr = PetscOptionsGetBool(((PetscObject)Cmpi)->prefix,"-matptap_scalable",&ptap->scalable,NULL);CHKERRQ(ierr);
486   if (!ptap->scalable) {  /* Do dense axpy */
487     ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
488   } else {
489     ierr = PetscCalloc1(ap_rmax+1,&ptap->apa);CHKERRQ(ierr);
490   }
491 
492 #if defined(PTAP_PROFILE)
493   ierr = PetscTime(&t4);CHKERRQ(ierr);
494   if (rank==1) PetscPrintf(MPI_COMM_SELF,"  [%d] PtAPSymbolic %g/P + %g/AP + %g/comm + %g/PtAP = %g\n",rank,t1-t0,t2-t1,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr);
495 #endif
496 
497 #if defined(PETSC_USE_INFO)
498   if (pti[pn] != 0) {
499     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
500     ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
501   } else {
502     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
503   }
504 #endif
505   PetscFunctionReturn(0);
506 }
507 
508 #undef __FUNCT__
509 #define __FUNCT__ "MatPtAPNumeric_MPIAIJ_MPIAIJ"
510 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
511 {
512   PetscErrorCode      ierr;
513   Mat_MPIAIJ          *a =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
514   Mat_SeqAIJ          *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
515   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
516   Mat_SeqAIJ          *p_loc,*p_oth;
517   Mat_PtAPMPI         *ptap;
518   Mat_Merge_SeqsToMPI *merge;
519   PetscInt            *adi=ad->i,*aoi=ao->i,*adj,*aoj,*apJ,nextp;
520   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pJ,*pj;
521   PetscInt            i,j,k,anz,pnz,apnz,nextap,row,*cj;
522   MatScalar           *ada,*aoa,*apa,*pa,*ca,*pa_loc,*pa_oth,valtmp;
523   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
524   MPI_Comm            comm;
525   PetscMPIInt         size,rank,taga,*len_s;
526   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
527   PetscInt            **buf_ri,**buf_rj;
528   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
529   MPI_Request         *s_waits,*r_waits;
530   MPI_Status          *status;
531   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
532   PetscInt            *api,*apj,*coi,*coj;
533   PetscInt            *poJ=po->j,*pdJ=pd->j,pcstart=P->cmap->rstart,pcend=P->cmap->rend;
534   PetscBool           scalable;
535 #if defined(PTAP_PROFILE)
536   PetscLogDouble t0,t1,t2,t3,t4,et2_AP=0.0,et2_PtAP=0.0,t2_0,t2_1,t2_2;
537 #endif
538 
539   PetscFunctionBegin;
540   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
541 #if defined(PTAP_PROFILE)
542   ierr = PetscTime(&t0);CHKERRQ(ierr);
543 #endif
544   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
545   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
546 
547   ptap = c->ptap;
548   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");
549   merge    = ptap->merge;
550   apa      = ptap->apa;
551   scalable = ptap->scalable;
552 
553   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
554   /*--------------------------------------------------*/
555   if (ptap->reuse == MAT_INITIAL_MATRIX) {
556     /* P_oth and P_loc are obtained in MatPtASymbolic(), skip calling MatGetBrowsOfAoCols() and MatMPIAIJGetLocalMat() */
557     ptap->reuse = MAT_REUSE_MATRIX;
558   } else { /* update numerical values of P_oth and P_loc */
559     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
560     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
561   }
562 #if defined(PTAP_PROFILE)
563   ierr = PetscTime(&t1);CHKERRQ(ierr);
564 #endif
565 
566   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
567   /*--------------------------------------------------------------*/
568   /* get data from symbolic products */
569   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
570   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
571   pi_loc=p_loc->i; pj_loc=p_loc->j; pJ=pj_loc; pa_loc=p_loc->a;
572   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
573 
574   coi  = merge->coi; coj = merge->coj;
575   ierr = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
576 
577   bi     = merge->bi; bj = merge->bj;
578   owners = merge->rowmap->range;
579   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);  /* ba: Cseq->a */
580 
581   api = ptap->api; apj = ptap->apj;
582 
583   if (!scalable) { /* Do dense axpy on apa (length of pN, stores A[i,:]*P) - nonscalable, but fast */
584     ierr = PetscInfo(C,"Using non-scalable dense axpy\n");CHKERRQ(ierr);
585     /*-----------------------------------------------------------------------------------------------------*/
586     for (i=0; i<am; i++) {
587 #if defined(PTAP_PROFILE)
588       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
589 #endif
590       /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */
591       /*------------------------------------------------------------*/
592       apJ = apj + api[i];
593 
594       /* diagonal portion of A */
595       anz = adi[i+1] - adi[i];
596       adj = ad->j + adi[i];
597       ada = ad->a + adi[i];
598       for (j=0; j<anz; j++) {
599         row = adj[j];
600         pnz = pi_loc[row+1] - pi_loc[row];
601         pj  = pj_loc + pi_loc[row];
602         pa  = pa_loc + pi_loc[row];
603 
604         /* perform dense axpy */
605         valtmp = ada[j];
606         for (k=0; k<pnz; k++) {
607           apa[pj[k]] += valtmp*pa[k];
608         }
609         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
610       }
611 
612       /* off-diagonal portion of A */
613       anz = aoi[i+1] - aoi[i];
614       aoj = ao->j + aoi[i];
615       aoa = ao->a + aoi[i];
616       for (j=0; j<anz; j++) {
617         row = aoj[j];
618         pnz = pi_oth[row+1] - pi_oth[row];
619         pj  = pj_oth + pi_oth[row];
620         pa  = pa_oth + pi_oth[row];
621 
622         /* perform dense axpy */
623         valtmp = aoa[j];
624         for (k=0; k<pnz; k++) {
625           apa[pj[k]] += valtmp*pa[k];
626         }
627         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
628       }
629 #if defined(PTAP_PROFILE)
630       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
631       et2_AP += t2_1 - t2_0;
632 #endif
633 
634       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
635       /*--------------------------------------------------------------*/
636       apnz = api[i+1] - api[i];
637       /* put the value into Co=(p->B)^T*AP (off-diagonal part, send to others) */
638       pnz = po->i[i+1] - po->i[i];
639       poJ = po->j + po->i[i];
640       pA  = po->a + po->i[i];
641       for (j=0; j<pnz; j++) {
642         row = poJ[j];
643         cnz = coi[row+1] - coi[row];
644         cj  = coj + coi[row];
645         ca  = coa + coi[row];
646         /* perform dense axpy */
647         valtmp = pA[j];
648         for (k=0; k<cnz; k++) {
649           ca[k] += valtmp*apa[cj[k]];
650         }
651         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
652       }
653 
654       /* put the value into Cd (diagonal part) */
655       pnz = pd->i[i+1] - pd->i[i];
656       pdJ = pd->j + pd->i[i];
657       pA  = pd->a + pd->i[i];
658       for (j=0; j<pnz; j++) {
659         row = pdJ[j];
660         cnz = bi[row+1] - bi[row];
661         cj  = bj + bi[row];
662         ca  = ba + bi[row];
663         /* perform dense axpy */
664         valtmp = pA[j];
665         for (k=0; k<cnz; k++) {
666           ca[k] += valtmp*apa[cj[k]];
667         }
668         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
669       }
670 
671       /* zero the current row of A*P */
672       for (k=0; k<apnz; k++) apa[apJ[k]] = 0.0;
673 #if defined(PTAP_PROFILE)
674       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
675       et2_PtAP += t2_2 - t2_1;
676 #endif
677     }
678   } else { /* Do sparse axpy on apa (length of ap_rmax, stores A[i,:]*P) - scalable, but slower */
679     ierr = PetscInfo(C,"Using scalable sparse axpy\n");CHKERRQ(ierr);
680     /*-----------------------------------------------------------------------------------------*/
681     pA=pa_loc;
682     for (i=0; i<am; i++) {
683 #if defined(PTAP_PROFILE)
684       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
685 #endif
686       /* form i-th sparse row of A*P */
687       apnz = api[i+1] - api[i];
688       apJ  = apj + api[i];
689       /* diagonal portion of A */
690       anz = adi[i+1] - adi[i];
691       adj = ad->j + adi[i];
692       ada = ad->a + adi[i];
693       for (j=0; j<anz; j++) {
694         row    = adj[j];
695         pnz    = pi_loc[row+1] - pi_loc[row];
696         pj     = pj_loc + pi_loc[row];
697         pa     = pa_loc + pi_loc[row];
698         valtmp = ada[j];
699         nextp  = 0;
700         for (k=0; nextp<pnz; k++) {
701           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
702             apa[k] += valtmp*pa[nextp++];
703           }
704         }
705         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
706       }
707       /* off-diagonal portion of A */
708       anz = aoi[i+1] - aoi[i];
709       aoj = ao->j + aoi[i];
710       aoa = ao->a + aoi[i];
711       for (j=0; j<anz; j++) {
712         row    = aoj[j];
713         pnz    = pi_oth[row+1] - pi_oth[row];
714         pj     = pj_oth + pi_oth[row];
715         pa     = pa_oth + pi_oth[row];
716         valtmp = aoa[j];
717         nextp  = 0;
718         for (k=0; nextp<pnz; k++) {
719           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
720             apa[k] += valtmp*pa[nextp++];
721           }
722         }
723         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
724       }
725 #if defined(PTAP_PROFILE)
726       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
727       et2_AP += t2_1 - t2_0;
728 #endif
729 
730       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
731       /*--------------------------------------------------------------*/
732       pnz = pi_loc[i+1] - pi_loc[i];
733       pJ  = pj_loc + pi_loc[i];
734       for (j=0; j<pnz; j++) {
735         nextap = 0;
736         row    = pJ[j]; /* global index */
737         if (row < pcstart || row >=pcend) { /* put the value into Co */
738           row = *poJ;
739           cj  = coj + coi[row];
740           ca  = coa + coi[row]; poJ++;
741         } else {                            /* put the value into Cd */
742           row = *pdJ;
743           cj  = bj + bi[row];
744           ca  = ba + bi[row]; pdJ++;
745         }
746         valtmp = pA[j];
747         for (k=0; nextap<apnz; k++) {
748           if (cj[k]==apJ[nextap]) ca[k] += valtmp*apa[nextap++];
749         }
750         ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
751       }
752       pA += pnz;
753       /* zero the current row info for A*P */
754       ierr = PetscMemzero(apa,apnz*sizeof(MatScalar));CHKERRQ(ierr);
755 #if defined(PTAP_PROFILE)
756       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
757       et2_PtAP += t2_2 - t2_1;
758 #endif
759     }
760   }
761 #if defined(PTAP_PROFILE)
762   ierr = PetscTime(&t2);CHKERRQ(ierr);
763 #endif
764 
765   /* 3) send and recv matrix values coa */
766   /*------------------------------------*/
767   buf_ri = merge->buf_ri;
768   buf_rj = merge->buf_rj;
769   len_s  = merge->len_s;
770   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
771   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
772 
773   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
774   for (proc=0,k=0; proc<size; proc++) {
775     if (!len_s[proc]) continue;
776     i    = merge->owners_co[proc];
777     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
778     k++;
779   }
780   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
781   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
782 
783   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
784   ierr = PetscFree(r_waits);CHKERRQ(ierr);
785   ierr = PetscFree(coa);CHKERRQ(ierr);
786 #if defined(PTAP_PROFILE)
787   ierr = PetscTime(&t3);CHKERRQ(ierr);
788 #endif
789 
790   /* 4) insert local Cseq and received values into Cmpi */
791   /*------------------------------------------------------*/
792   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
793   for (k=0; k<merge->nrecv; k++) {
794     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
795     nrows       = *(buf_ri_k[k]);
796     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
797     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
798   }
799 
800   for (i=0; i<cm; i++) {
801     row  = owners[rank] + i; /* global row index of C_seq */
802     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
803     ba_i = ba + bi[i];
804     bnz  = bi[i+1] - bi[i];
805     /* add received vals into ba */
806     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
807       /* i-th row */
808       if (i == *nextrow[k]) {
809         cnz    = *(nextci[k]+1) - *nextci[k];
810         cj     = buf_rj[k] + *(nextci[k]);
811         ca     = abuf_r[k] + *(nextci[k]);
812         nextcj = 0;
813         for (j=0; nextcj<cnz; j++) {
814           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
815             ba_i[j] += ca[nextcj++];
816           }
817         }
818         nextrow[k]++; nextci[k]++;
819         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
820       }
821     }
822     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
823   }
824   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
825   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
826 
827   ierr = PetscFree(ba);CHKERRQ(ierr);
828   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
829   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
830   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
831 #if defined(PTAP_PROFILE)
832   ierr = PetscTime(&t4);CHKERRQ(ierr);
833   if (rank==1) PetscPrintf(MPI_COMM_SELF,"  [%d] PtAPNum %g/P + %g/PtAP( %g + %g ) + %g/comm + %g/Cloc = %g\n\n",rank,t1-t0,t2-t1,et2_AP,et2_PtAP,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr);
834 #endif
835   PetscFunctionReturn(0);
836 }
837