xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision 0d3441ae8a080c728abf17e90308c510e39e951b)
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 
33     ierr = MatDestroy(&ptap->Rd);CHKERRQ(ierr);
34     ierr = MatDestroy(&ptap->Ro);CHKERRQ(ierr);
35     ierr = MatDestroy(&ptap->AP);CHKERRQ(ierr);
36     ierr = MatDestroy(&ptap->AP_loc);CHKERRQ(ierr);
37 
38     if (ptap->api) {ierr = PetscFree(ptap->api);CHKERRQ(ierr);}
39     if (ptap->apj) {ierr = PetscFree(ptap->apj);CHKERRQ(ierr);}
40     if (ptap->apa) {ierr = PetscFree(ptap->apa);CHKERRQ(ierr);}
41     if (merge) {
42       ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
43       ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
44       ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
45       ierr = PetscFree(merge->bi);CHKERRQ(ierr);
46       ierr = PetscFree(merge->bj);CHKERRQ(ierr);
47       ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
48       ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
49       ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
50       ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
51       ierr = PetscFree(merge->coi);CHKERRQ(ierr);
52       ierr = PetscFree(merge->coj);CHKERRQ(ierr);
53       ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
54       ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
55       ierr = merge->destroy(A);CHKERRQ(ierr);
56       ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
57     }
58     ierr = PetscFree(ptap);CHKERRQ(ierr);
59   }
60   PetscFunctionReturn(0);
61 }
62 
63 #undef __FUNCT__
64 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatPtAP"
65 PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat A, MatDuplicateOption op, Mat *M)
66 {
67   PetscErrorCode      ierr;
68   Mat_MPIAIJ          *a     = (Mat_MPIAIJ*)A->data;
69   Mat_PtAPMPI         *ptap  = a->ptap;
70   Mat_Merge_SeqsToMPI *merge = ptap->merge;
71 
72   PetscFunctionBegin;
73   ierr = (*merge->duplicate)(A,op,M);CHKERRQ(ierr);
74 
75   (*M)->ops->destroy   = merge->destroy;
76   (*M)->ops->duplicate = merge->duplicate;
77   PetscFunctionReturn(0);
78 }
79 
80 #undef __FUNCT__
81 #define __FUNCT__ "MatPtAP_MPIAIJ_MPIAIJ"
82 PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
83 {
84   PetscErrorCode ierr;
85   PetscBool      newalg=PETSC_FALSE;
86 
87   PetscFunctionBegin;
88   ierr = PetscOptionsGetBool(NULL,"-matptap_new",&newalg,NULL);CHKERRQ(ierr);
89   if (scall == MAT_INITIAL_MATRIX) {
90     ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
91     if (newalg) {
92       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_new(A,P,fill,C);CHKERRQ(ierr);
93     } else {
94       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
95     }
96     ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
97   }
98   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
99   if (newalg) {
100     ierr = MatPtAPNumeric_MPIAIJ_MPIAIJ_new(A,P,*C);CHKERRQ(ierr);
101   } else {
102     ierr = MatPtAPNumeric_MPIAIJ_MPIAIJ(A,P,*C);CHKERRQ(ierr);
103   }
104   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
105   PetscFunctionReturn(0);
106 }
107 
108 #undef __FUNCT__
109 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ_MPIAIJ_new"
110 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_new(Mat A,Mat P,PetscReal fill,Mat *C)
111 {
112   PetscErrorCode ierr;
113   Mat_PtAPMPI    *ptap;
114   Mat_MPIAIJ     *c,*p=(Mat_MPIAIJ*)P->data;
115 
116   PetscFunctionBegin;
117   ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
118   c    = (Mat_MPIAIJ*)(*C)->data;
119   ptap = c->ptap;
120   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
121   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
122   ierr = MatMatMult(A,P,MAT_INITIAL_MATRIX,2.0,&ptap->AP);CHKERRQ(ierr);
123   ierr = MatMPIAIJGetLocalMat(ptap->AP,MAT_INITIAL_MATRIX,&ptap->AP_loc);CHKERRQ(ierr);
124   PetscFunctionReturn(0);
125 }
126 
127 #undef __FUNCT__
128 #define __FUNCT__ "MatPtAPNumeric_MPIAIJ_MPIAIJ_new"
129 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_new(Mat A,Mat P,Mat C)
130 {
131   PetscErrorCode    ierr;
132   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
133   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
134   //Mat_SeqAIJ        *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
135 
136   Mat_PtAPMPI       *ptap = c->ptap;
137   Mat               AP_loc,C_loc,Co;
138   PetscInt          i,rstart,rend,cm,ncols,row;
139   PetscMPIInt       rank;
140   MPI_Comm          comm;
141   const PetscInt    *cols;
142   const PetscScalar *vals;
143   PetscLogDouble t0,t1,t2,t3,t4,eR,eAP,eCseq,eCmpi;
144 
145   PetscFunctionBegin;
146   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
147   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
148 
149   ierr = MatZeroEntries(C);CHKERRQ(ierr);
150 
151   /* get R = Pd^T,Ro = Po^T */
152   ierr = PetscTime(&t0);CHKERRQ(ierr);
153   ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
154   ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
155   ierr = PetscTime(&t1);CHKERRQ(ierr);
156   eR = t1 - t0;
157 
158   /* get AP = A*P, AP_loc */
159   ierr = MatMatMult(A,P,MAT_REUSE_MATRIX,2.0,&ptap->AP);CHKERRQ(ierr);
160   ierr = MatMPIAIJGetLocalMat(ptap->AP,MAT_REUSE_MATRIX,&ptap->AP_loc);CHKERRQ(ierr);
161   AP_loc = ptap->AP_loc;
162 
163 #if 0
164   //============ new get AP = A*P, AP_loc
165 
166   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
167   /*-----------------------------------------------------*/
168   //if (ptap->reuse == MAT_INITIAL_MATRIX) {
169     /* P_oth and P_loc are obtained in MatPtASymbolic(), skip calling MatGetBrowsOfAoCols() and MatMPIAIJGetLocalMat() */
170   //ptap->reuse = MAT_REUSE_MATRIX;
171   //} else { /* update numerical values of P_oth and P_loc */
172     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
173     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
174     //}
175 
176   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
177   /*--------------------------------------------------------------*/
178   /* get data from symbolic products */
179   Mat_SeqAIJ  *p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
180   Mat_SeqAIJ  *p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
181 
182   PetscInt    *pi_loc,*pj_loc,*pJ,*pi_oth,*pj_oth,*apJ,*api,*apj,anz;
183   PetscInt    *adi=ad->i,*adj,j,k,*pi,*pj,pnz;
184   PetscInt    *aoi=ao->i,*aoj;
185   PetscScalar *pa_loc,*pa_oth;
186   PetscScalar *ada,*aoa,*apa,*pa,*ca,valtmp;
187 
188   pi_loc=p_loc->i; pj_loc=p_loc->j; pJ=pj_loc; pa_loc=p_loc->a;
189   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
190 
191   PetscInt am = A->rmap->n;
192   apa = ptap->apa;
193   api = ptap->api; apj = ptap->apj;
194   //printf("scalable %d\n",ptap->scalable);
195   for (i=0; i<am; i++) { /* !scalable */
196 
197     /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */
198     /*------------------------------------------------------------*/
199     apJ = apj + api[i];
200 
201     /* diagonal portion of A */
202     anz = adi[i+1] - adi[i];
203     adj = ad->j + adi[i];
204     ada = ad->a + adi[i];
205     for (j=0; j<anz; j++) {
206       row = adj[j];
207       pnz = pi_loc[row+1] - pi_loc[row];
208       pj  = pj_loc + pi_loc[row];
209       pa  = pa_loc + pi_loc[row];
210 
211       /* perform dense axpy */
212       valtmp = ada[j];
213       for (k=0; k<pnz; k++) {
214         apa[pj[k]] += valtmp*pa[k];
215       }
216       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
217     }
218 
219     /* off-diagonal portion of A */
220     anz = aoi[i+1] - aoi[i];
221     aoj = ao->j + aoi[i];
222     aoa = ao->a + aoi[i];
223     for (j=0; j<anz; j++) {
224       row = aoj[j];
225       pnz = pi_oth[row+1] - pi_oth[row];
226       pj  = pj_oth + pi_oth[row];
227       pa  = pa_oth + pi_oth[row];
228 
229       /* perform dense axpy */
230       valtmp = aoa[j];
231       for (k=0; k<pnz; k++) {
232         apa[pj[k]] += valtmp*pa[k];
233       }
234       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
235     }
236 
237 
238   }
239 #endif
240 
241   //================================
242   ierr = PetscTime(&t2);CHKERRQ(ierr);
243   eAP = t2 - t1;
244 
245   /* C_loc = R*AP_loc, Co = Ro*AP_loc */
246   ierr = MatMatMult(ptap->Rd,AP_loc,MAT_INITIAL_MATRIX,2.0,&C_loc);CHKERRQ(ierr);
247   ierr = MatMatMult(ptap->Ro,AP_loc,MAT_INITIAL_MATRIX,2.0,&Co);CHKERRQ(ierr);
248   //printf("[%d] Co %d, %d\n", rank,Co->rmap->N,Co->cmap->N);
249   ierr = PetscTime(&t3);CHKERRQ(ierr);
250   eCseq = t3 - t2;
251 
252   /* add C_loc and Co to to C */
253   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
254 
255   /* C_loc -> C */
256   cm = C_loc->rmap->N;
257   for (i=0; i<cm; i++) {
258     ierr = MatGetRow(C_loc,i,&ncols,&cols,&vals);CHKERRQ(ierr);
259     row = rstart + i;
260     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
261     ierr = MatRestoreRow(C_loc,i,&ncols,&cols,&vals);CHKERRQ(ierr);
262   }
263 
264   /* Co -> C, off-processor part */
265   //printf("[%d] p->B %d, %d\n",rank,p->B->rmap->N,p->B->cmap->N);
266   for (i=0; i<Co->rmap->N; i++) {
267     ierr = MatGetRow(Co,i,&ncols,&cols,&vals);CHKERRQ(ierr);
268     row = p->garray[i];
269     //printf("[%d] row[%d] = %d\n",rank,i,row);
270     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
271     ierr = MatRestoreRow(Co,i,&ncols,&cols,&vals);CHKERRQ(ierr);
272   }
273   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
274   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
275   ierr = PetscTime(&t4);CHKERRQ(ierr);
276   eCmpi = t4 - t3;
277 
278   ierr = MatDestroy(&C_loc);CHKERRQ(ierr);
279   ierr = MatDestroy(&Co);CHKERRQ(ierr);
280 
281   if (rank==1) {
282     ierr = PetscPrintf(MPI_COMM_SELF," R %g, AP %g, Cseq %g, Cmpi %g = %g\n", eR,eAP,eCseq,eCmpi,eR+eAP+eCseq+eCmpi);CHKERRQ(ierr);
283   }
284   PetscFunctionReturn(0);
285 }
286 
287 #undef __FUNCT__
288 #define __FUNCT__ "MatPtAPSymbolic_MPIAIJ_MPIAIJ"
289 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
290 {
291   PetscErrorCode      ierr;
292   Mat                 Cmpi;
293   Mat_PtAPMPI         *ptap;
294   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
295   Mat_MPIAIJ          *a        =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
296   Mat_SeqAIJ          *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
297   Mat_SeqAIJ          *p_loc,*p_oth;
298   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ;
299   PetscInt            *adi=ad->i,*aj,*aoi=ao->i,nnz;
300   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
301   PetscInt            am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n;
302   PetscBT             lnkbt;
303   MPI_Comm            comm;
304   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0;
305   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
306   PetscInt            len,proc,*dnz,*onz,*owners;
307   PetscInt            nzi,*pti,*ptj;
308   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
309   MPI_Request         *swaits,*rwaits;
310   MPI_Status          *sstatus,rstatus;
311   Mat_Merge_SeqsToMPI *merge;
312   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0;
313   PetscReal           afill=1.0,afill_tmp;
314   PetscInt            rmax;
315 
316   PetscFunctionBegin;
317   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
318 
319   /* check if matrix local sizes are compatible */
320   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
321     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);
322   }
323   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) {
324     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);
325   }
326 
327   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
328   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
329 
330   /* create struct Mat_PtAPMPI and attached it to C later */
331   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
332   ierr        = PetscNew(&merge);CHKERRQ(ierr);
333   ptap->merge = merge;
334   ptap->reuse = MAT_INITIAL_MATRIX;
335 
336   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
337   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
338 
339   /* get P_loc by taking all local rows of P */
340   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
341 
342   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
343   p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
344   pi_loc = p_loc->i; pj_loc = p_loc->j;
345   pi_oth = p_oth->i; pj_oth = p_oth->j;
346 
347   /* (1) compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth (api,apj) */
348   /*--------------------------------------------------------------------------*/
349   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
350   api[0] = 0;
351 
352   /* create and initialize a linked list */
353   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
354 
355   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) -OOM for ex56, np=8k on Intrepid! */
356   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
357 
358   current_space = free_space;
359 
360   for (i=0; i<am; i++) {
361     /* diagonal portion of A */
362     nzi = adi[i+1] - adi[i];
363     aj  = ad->j + adi[i];
364     for (j=0; j<nzi; j++) {
365       row  = aj[j];
366       pnz  = pi_loc[row+1] - pi_loc[row];
367       Jptr = pj_loc + pi_loc[row];
368       /* add non-zero cols of P into the sorted linked list lnk */
369       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
370     }
371     /* off-diagonal portion of A */
372     nzi = aoi[i+1] - aoi[i];
373     aj  = ao->j + aoi[i];
374     for (j=0; j<nzi; j++) {
375       row  = aj[j];
376       pnz  = pi_oth[row+1] - pi_oth[row];
377       Jptr = pj_oth + pi_oth[row];
378       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
379     }
380     apnz     = lnk[0];
381     api[i+1] = api[i] + apnz;
382     if (ap_rmax < apnz) ap_rmax = apnz;
383 
384     /* if free space is not available, double the total space in the list */
385     if (current_space->local_remaining<apnz) {
386       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
387       nspacedouble++;
388     }
389 
390     /* Copy data into free space, then initialize lnk */
391     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
392 
393     current_space->array           += apnz;
394     current_space->local_used      += apnz;
395     current_space->local_remaining -= apnz;
396   }
397 
398   /* Allocate space for apj, initialize apj, and */
399   /* destroy list of free space and other temporary array(s) */
400   ierr      = PetscMalloc1(api[am]+1,&apj);CHKERRQ(ierr);
401   ierr      = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
402   afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1);
403   if (afill_tmp > afill) afill = afill_tmp;
404 
405   /* (2) determine symbolic Co=(p->B)^T*AP - send to others (coi,coj)*/
406   /*-----------------------------------------------------------------*/
407   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
408 
409   /* then, compute symbolic Co = (p->B)^T*AP */
410   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors
411                          >= (num of nonzero rows of C_seq) - pn */
412   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
413   coi[0] = 0;
414 
415   /* set initial free space to be fill*(nnz(p->B) + nnz(AP)) */
416   nnz           = fill*(poti[pon] + api[am]);
417   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
418   current_space = free_space;
419 
420   for (i=0; i<pon; i++) {
421     pnz = poti[i+1] - poti[i];
422     ptJ = potj + poti[i];
423     for (j=0; j<pnz; j++) {
424       row  = ptJ[j]; /* row of AP == col of Pot */
425       apnz = api[row+1] - api[row];
426       Jptr = apj + api[row];
427       /* add non-zero cols of AP into the sorted linked list lnk */
428       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
429     }
430     nnz = lnk[0];
431 
432     /* If free space is not available, double the total space in the list */
433     if (current_space->local_remaining<nnz) {
434       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
435       nspacedouble++;
436     }
437 
438     /* Copy data into free space, and zero out denserows */
439     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
440 
441     current_space->array           += nnz;
442     current_space->local_used      += nnz;
443     current_space->local_remaining -= nnz;
444 
445     coi[i+1] = coi[i] + nnz;
446   }
447 
448   ierr      = PetscMalloc1(coi[pon],&coj);CHKERRQ(ierr);
449   ierr      = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
450   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]+1);
451   if (afill_tmp > afill) afill = afill_tmp;
452   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
453 
454   /* (3) send j-array (coj) of Co to other processors */
455   /*--------------------------------------------------*/
456   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
457   len_s        = merge->len_s;
458   merge->nsend = 0;
459 
460 
461   /* determine row ownership */
462   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
463   merge->rowmap->n  = pn;
464   merge->rowmap->bs = 1;
465 
466   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
467   owners = merge->rowmap->range;
468 
469   /* determine the number of messages to send, their lengths */
470   ierr = PetscMalloc2(size,&len_si,size,&sstatus);CHKERRQ(ierr);
471   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
472   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
473 
474   proc = 0;
475   for (i=0; i<pon; i++) {
476     while (prmap[i] >= owners[proc+1]) proc++;
477     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
478     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
479   }
480 
481   len          = 0; /* max length of buf_si[], see (4) */
482   owners_co[0] = 0;
483   for (proc=0; proc<size; proc++) {
484     owners_co[proc+1] = owners_co[proc] + len_si[proc];
485     if (len_s[proc]) {
486       merge->nsend++;
487       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
488       len         += len_si[proc];
489     }
490   }
491 
492   /* determine the number and length of messages to receive for coi and coj  */
493   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
494   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
495 
496   /* post the Irecv and Isend of coj */
497   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
498   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
499   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
500   for (proc=0, k=0; proc<size; proc++) {
501     if (!len_s[proc]) continue;
502     i    = owners_co[proc];
503     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
504     k++;
505   }
506 
507   /* receives and sends of coj are complete */
508   for (i=0; i<merge->nrecv; i++) {
509     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
510   }
511   ierr = PetscFree(rwaits);CHKERRQ(ierr);
512   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
513 
514   /* (4) send and recv coi */
515   /*-----------------------*/
516   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
517   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
518   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
519   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
520   for (proc=0,k=0; proc<size; proc++) {
521     if (!len_s[proc]) continue;
522     /* form outgoing message for i-structure:
523          buf_si[0]:                 nrows to be sent
524                [1:nrows]:           row index (global)
525                [nrows+1:2*nrows+1]: i-structure index
526     */
527     /*-------------------------------------------*/
528     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
529     buf_si_i    = buf_si + nrows+1;
530     buf_si[0]   = nrows;
531     buf_si_i[0] = 0;
532     nrows       = 0;
533     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
534       nzi = coi[i+1] - coi[i];
535       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
536       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
537       nrows++;
538     }
539     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
540     k++;
541     buf_si += len_si[proc];
542   }
543   i = merge->nrecv;
544   while (i--) {
545     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
546   }
547   ierr = PetscFree(rwaits);CHKERRQ(ierr);
548   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
549 
550   ierr = PetscFree2(len_si,sstatus);CHKERRQ(ierr);
551   ierr = PetscFree(len_ri);CHKERRQ(ierr);
552   ierr = PetscFree(swaits);CHKERRQ(ierr);
553   ierr = PetscFree(buf_s);CHKERRQ(ierr);
554 
555   /* (5) compute the local portion of C (mpi mat) */
556   /*----------------------------------------------*/
557   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
558 
559   /* allocate pti array and free space for accumulating nonzero column info */
560   ierr   = PetscMalloc1(pn+1,&pti);CHKERRQ(ierr);
561   pti[0] = 0;
562 
563   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
564   nnz           = fill*(pi_loc[pm] + api[am]);
565   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
566   current_space = free_space;
567 
568   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
569   for (k=0; k<merge->nrecv; k++) {
570     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
571     nrows       = *buf_ri_k[k];
572     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
573     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
574   }
575   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
576   rmax = 0;
577   for (i=0; i<pn; i++) {
578     /* add pdt[i,:]*AP into lnk */
579     pnz = pdti[i+1] - pdti[i];
580     ptJ = pdtj + pdti[i];
581     for (j=0; j<pnz; j++) {
582       row  = ptJ[j];  /* row of AP == col of Pt */
583       apnz = api[row+1] - api[row];
584       Jptr = apj + api[row];
585       /* add non-zero cols of AP into the sorted linked list lnk */
586       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
587     }
588 
589     /* add received col data into lnk */
590     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
591       if (i == *nextrow[k]) { /* i-th row */
592         nzi  = *(nextci[k]+1) - *nextci[k];
593         Jptr = buf_rj[k] + *nextci[k];
594         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
595         nextrow[k]++; nextci[k]++;
596       }
597     }
598     nnz = lnk[0];
599 
600     /* if free space is not available, make more free space */
601     if (current_space->local_remaining<nnz) {
602       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
603       nspacedouble++;
604     }
605     /* copy data into free space, then initialize lnk */
606     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
607     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
608 
609     current_space->array           += nnz;
610     current_space->local_used      += nnz;
611     current_space->local_remaining -= nnz;
612 
613     pti[i+1] = pti[i] + nnz;
614     if (nnz > rmax) rmax = nnz;
615   }
616   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
617   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
618 
619   ierr      = PetscMalloc1(pti[pn]+1,&ptj);CHKERRQ(ierr);
620   ierr      = PetscFreeSpaceContiguous(&free_space,ptj);CHKERRQ(ierr);
621   afill_tmp = (PetscReal)pti[pn]/(pi_loc[pm] + api[am]+1);
622   if (afill_tmp > afill) afill = afill_tmp;
623   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
624 
625   /* (6) create symbolic parallel matrix Cmpi */
626   /*------------------------------------------*/
627   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
628   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
629   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
630   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
631   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
632   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
633 
634   merge->bi        = pti;      /* Cseq->i */
635   merge->bj        = ptj;      /* Cseq->j */
636   merge->coi       = coi;      /* Co->i   */
637   merge->coj       = coj;      /* Co->j   */
638   merge->buf_ri    = buf_ri;
639   merge->buf_rj    = buf_rj;
640   merge->owners_co = owners_co;
641   merge->destroy   = Cmpi->ops->destroy;
642   merge->duplicate = Cmpi->ops->duplicate;
643 
644   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
645   Cmpi->assembled      = PETSC_FALSE;
646   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_PtAP;
647   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatPtAP;
648 
649   /* attach the supporting struct to Cmpi for reuse */
650   c           = (Mat_MPIAIJ*)Cmpi->data;
651   c->ptap     = ptap;
652   ptap->api   = api;
653   ptap->apj   = apj;
654   ptap->rmax  = ap_rmax;
655   *C          = Cmpi;
656 
657   /* flag 'scalable' determines which implementations to be used:
658        0: do dense axpy in MatPtAPNumeric() - fast, but requires storage of a nonscalable dense array apa;
659        1: do sparse axpy in MatPtAPNumeric() - might slow, uses a sparse array apa */
660   /* set default scalable */
661   ptap->scalable = PETSC_FALSE; //PETSC_TRUE;
662 
663   ierr = PetscOptionsGetBool(((PetscObject)Cmpi)->prefix,"-matptap_scalable",&ptap->scalable,NULL);CHKERRQ(ierr);
664   if (!ptap->scalable) {  /* Do dense axpy */
665     ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
666   } else {
667     ierr = PetscCalloc1(ap_rmax+1,&ptap->apa);CHKERRQ(ierr);
668   }
669 
670 #if defined(PETSC_USE_INFO)
671   if (pti[pn] != 0) {
672     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
673     ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
674   } else {
675     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
676   }
677 #endif
678   PetscFunctionReturn(0);
679 }
680 
681 #undef __FUNCT__
682 #define __FUNCT__ "MatPtAPNumeric_MPIAIJ_MPIAIJ"
683 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
684 {
685   PetscErrorCode      ierr;
686   Mat_MPIAIJ          *a =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
687   Mat_SeqAIJ          *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
688   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
689   Mat_SeqAIJ          *p_loc,*p_oth;
690   Mat_PtAPMPI         *ptap;
691   Mat_Merge_SeqsToMPI *merge;
692   PetscInt            *adi=ad->i,*aoi=ao->i,*adj,*aoj,*apJ,nextp;
693   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pJ,*pj;
694   PetscInt            i,j,k,anz,pnz,apnz,nextap,row,*cj;
695   MatScalar           *ada,*aoa,*apa,*pa,*ca,*pa_loc,*pa_oth,valtmp;
696   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
697   MPI_Comm            comm;
698   PetscMPIInt         size,rank,taga,*len_s;
699   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
700   PetscInt            **buf_ri,**buf_rj;
701   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
702   MPI_Request         *s_waits,*r_waits;
703   MPI_Status          *status;
704   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
705   PetscInt            *api,*apj,*coi,*coj;
706   PetscInt            *poJ=po->j,*pdJ=pd->j,pcstart=P->cmap->rstart,pcend=P->cmap->rend;
707   PetscBool           scalable;
708 #if defined(PTAP_PROFILE)
709   PetscLogDouble t0,t1,t2,eP,t3,t4,et2_AP=0.0,ePtAP=0.0,t2_0,t2_1,t2_2,t_tran0,t_tran1,t_tran2,t_tran3;
710 #endif
711 
712   PetscFunctionBegin;
713   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
714 #if defined(PTAP_PROFILE)
715   ierr = PetscTime(&t0);CHKERRQ(ierr);
716 #endif
717   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
718   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
719 
720   ptap = c->ptap;
721   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");
722   merge    = ptap->merge;
723   apa      = ptap->apa;
724   scalable = ptap->scalable;
725 
726   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
727   /*-----------------------------------------------------*/
728   if (ptap->reuse == MAT_INITIAL_MATRIX) {
729     /* P_oth and P_loc are obtained in MatPtASymbolic(), skip calling MatGetBrowsOfAoCols() and MatMPIAIJGetLocalMat() */
730     ptap->reuse = MAT_REUSE_MATRIX;
731   } else { /* update numerical values of P_oth and P_loc */
732     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
733     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
734   }
735 #if defined(PTAP_PROFILE)
736   ierr = PetscTime(&t1);CHKERRQ(ierr);
737   eP = t1-t0;
738 #endif
739   /*
740   printf("[%d] Ad: %d, %d; Ao: %d, %d; P_loc: %d, %d; P_oth %d, %d;\n",rank,
741          a->A->rmap->N,a->A->cmap->N,a->B->rmap->N,a->B->cmap->N,
742          ptap->P_loc->rmap->N,ptap->P_loc->cmap->N,
743          ptap->P_oth->rmap->N,ptap->P_oth->cmap->N);
744    */
745 
746   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
747   /*--------------------------------------------------------------*/
748   /* get data from symbolic products */
749   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
750   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
751   pi_loc=p_loc->i; pj_loc=p_loc->j; pJ=pj_loc; pa_loc=p_loc->a;
752   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
753 
754   coi  = merge->coi; coj = merge->coj;
755   ierr = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
756 
757   bi     = merge->bi; bj = merge->bj;
758   owners = merge->rowmap->range;
759   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);  /* ba: Cseq->a */
760 
761   api = ptap->api; apj = ptap->apj;
762 
763   if (!scalable) { /* Do dense axpy on apa (length of pN, stores A[i,:]*P) - nonscalable, but faster (could take 1/3 scalable time) */
764     ierr = PetscInfo(C,"Using non-scalable dense axpy\n");CHKERRQ(ierr);
765 #if 0
766     /* ------ 10x slower -------------- */
767     /*==================================*/
768     Mat         R = ptap->R;
769     Mat_SeqAIJ  *r = (Mat_SeqAIJ*)R->data;
770     PetscInt    *ri=r->i,*rj=r->j,rnz,arow,l,prow,pcol,pN=P->cmap->N;
771     PetscScalar *ra=r->a,tmp,cdense[pN];
772 
773     ierr = PetscMemzero(cdense,pN*sizeof(PetscScalar));CHKERRQ(ierr);
774     for (i=0; i<cm; i++) { /* each row of C or R */
775       rnz = ri[i+1] - ri[i];
776 
777       for (j=0; j<rnz; j++) { /* each nz of R */
778         arow = rj[ri[i] + j];
779 
780         /* diagonal portion of A */
781         anz  = ad->i[arow+1] - ad->i[arow];
782         for (k=0; k<anz; k++) { /* each nz of Ad */
783           tmp  = ra[ri[i] + j]*ad->a[ad->i[arow] + k];
784           prow = ad->j[ad->i[arow] + k];
785           pnz  = pi_loc[prow+1] - pi_loc[prow];
786 
787           for (l=0; l<pnz; l++) { /* each nz of P_loc */
788             pcol = pj_loc[pi_loc[prow] + l];
789             cdense[pcol] += tmp*pa_loc[pi_loc[prow] + l];
790           }
791         }
792 
793         /* off-diagonal portion of A */
794         anz  = ao->i[arow+1] - ao->i[arow];
795         for (k=0; k<anz; k++) { /* each nz of Ao */
796           tmp  = ra[ri[i] + j]*ao->a[ao->i[arow] + k];
797           prow = ao->j[ao->i[arow] + k];
798           pnz  = pi_oth[prow+1] - pi_oth[prow];
799 
800           for (l=0; l<pnz; l++) { /* each nz of P_oth */
801             pcol = pj_oth[pi_oth[prow] + l];
802             cdense[pcol] += tmp*pa_oth[pi_oth[prow] + l];
803           }
804         }
805 
806       } //for (j=0; j<rnz; j++)
807 
808       /* copy cdense[] into ca; zero cdense[] */
809       cnz = bi[i+1] - bi[i];
810       cj  = bj + bi[i];
811       ca  = ba + bi[i];
812       for (j=0; j<cnz; j++) {
813         ca[j] += cdense[cj[j]];
814         cdense[cj[j]] = 0.0;
815       }
816 #if 0
817       if (rank == 0) {
818         printf("[%d] row %d: ",rank,i);
819         for (j=0; j<pN; j++) printf(" %g,",cdense[j]);
820         printf("\n");
821       }
822       for (j=0; j<pN; j++) cdense[j]=0.0; // zero cdnese[]
823 #endif
824     } //for (i=0; i<cm; i++) {
825 #endif
826     ierr = PetscTime(&t_tran3);CHKERRQ(ierr);
827 
828     //==========================================
829 
830     ierr = PetscTime(&t1);CHKERRQ(ierr);
831     for (i=0; i<am; i++) {
832 #if defined(PTAP_PROFILE)
833       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
834 #endif
835       /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */
836       /*------------------------------------------------------------*/
837       apJ = apj + api[i];
838 
839       /* diagonal portion of A */
840       anz = adi[i+1] - adi[i];
841       adj = ad->j + adi[i];
842       ada = ad->a + adi[i];
843       for (j=0; j<anz; j++) {
844         row = adj[j];
845         pnz = pi_loc[row+1] - pi_loc[row];
846         pj  = pj_loc + pi_loc[row];
847         pa  = pa_loc + pi_loc[row];
848 
849         /* perform dense axpy */
850         valtmp = ada[j];
851         for (k=0; k<pnz; k++) {
852           apa[pj[k]] += valtmp*pa[k];
853         }
854         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
855       }
856 
857       /* off-diagonal portion of A */
858       anz = aoi[i+1] - aoi[i];
859       aoj = ao->j + aoi[i];
860       aoa = ao->a + aoi[i];
861       for (j=0; j<anz; j++) {
862         row = aoj[j];
863         pnz = pi_oth[row+1] - pi_oth[row];
864         pj  = pj_oth + pi_oth[row];
865         pa  = pa_oth + pi_oth[row];
866 
867         /* perform dense axpy */
868         valtmp = aoa[j];
869         for (k=0; k<pnz; k++) {
870           apa[pj[k]] += valtmp*pa[k];
871         }
872         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
873       }
874 #if defined(PTAP_PROFILE)
875       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
876       et2_AP += t2_1 - t2_0;
877 #endif
878 
879       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
880       /*--------------------------------------------------------------*/
881       apnz = api[i+1] - api[i];
882       /* put the value into Co=(p->B)^T*AP (off-diagonal part, send to others) */
883       pnz = po->i[i+1] - po->i[i];
884       poJ = po->j + po->i[i];
885       pA  = po->a + po->i[i];
886       for (j=0; j<pnz; j++) {
887         row = poJ[j];
888         cnz = coi[row+1] - coi[row];
889         cj  = coj + coi[row];
890         ca  = coa + coi[row];
891         /* perform dense axpy */
892         valtmp = pA[j];
893         for (k=0; k<cnz; k++) {
894           ca[k] += valtmp*apa[cj[k]];
895         }
896         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
897       }
898 #if 1
899       /* put the value into Cd (diagonal part) */
900       pnz = pd->i[i+1] - pd->i[i];
901       pdJ = pd->j + pd->i[i];
902       pA  = pd->a + pd->i[i];
903       for (j=0; j<pnz; j++) {
904         row = pdJ[j];
905         cnz = bi[row+1] - bi[row];
906         cj  = bj + bi[row];
907         ca  = ba + bi[row];
908         /* perform dense axpy */
909         valtmp = pA[j];
910         for (k=0; k<cnz; k++) {
911           ca[k] += valtmp*apa[cj[k]];
912         }
913         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
914       }
915 #endif
916       /* zero the current row of A*P */
917       for (k=0; k<apnz; k++) apa[apJ[k]] = 0.0;
918 #if defined(PTAP_PROFILE)
919       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
920       ePtAP += t2_2 - t2_1;
921 #endif
922     }
923 
924     if (rank == 100) {
925     for (row=0; row<cm; row++) {
926       printf("[%d] row %d: ",rank,row);
927       cnz = bi[row+1] - bi[row];
928       for (j=0; j<cnz; j++) printf(" %g,",ba[bi[row]+j]);
929       printf("\n");
930     }
931     }
932 
933   } else { /* Do sparse axpy on apa (length of ap_rmax, stores A[i,:]*P) - scalable, but slower */
934     ierr = PetscInfo(C,"Using scalable sparse axpy\n");CHKERRQ(ierr);
935     /*-----------------------------------------------------------------------------------------*/
936     pA=pa_loc;
937     for (i=0; i<am; i++) {
938 #if defined(PTAP_PROFILE)
939       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
940 #endif
941       /* form i-th sparse row of A*P */
942       apnz = api[i+1] - api[i];
943       apJ  = apj + api[i];
944       /* diagonal portion of A */
945       anz = adi[i+1] - adi[i];
946       adj = ad->j + adi[i];
947       ada = ad->a + adi[i];
948       for (j=0; j<anz; j++) {
949         row    = adj[j];
950         pnz    = pi_loc[row+1] - pi_loc[row];
951         pj     = pj_loc + pi_loc[row];
952         pa     = pa_loc + pi_loc[row];
953         valtmp = ada[j];
954         nextp  = 0;
955         for (k=0; nextp<pnz; k++) {
956           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
957             apa[k] += valtmp*pa[nextp++];
958           }
959         }
960         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
961       }
962       /* off-diagonal portion of A */
963       anz = aoi[i+1] - aoi[i];
964       aoj = ao->j + aoi[i];
965       aoa = ao->a + aoi[i];
966       for (j=0; j<anz; j++) {
967         row    = aoj[j];
968         pnz    = pi_oth[row+1] - pi_oth[row];
969         pj     = pj_oth + pi_oth[row];
970         pa     = pa_oth + pi_oth[row];
971         valtmp = aoa[j];
972         nextp  = 0;
973         for (k=0; nextp<pnz; k++) {
974           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
975             apa[k] += valtmp*pa[nextp++];
976           }
977         }
978         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
979       }
980 #if defined(PTAP_PROFILE)
981       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
982       et2_AP += t2_1 - t2_0;
983 #endif
984 
985       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
986       /*--------------------------------------------------------------*/
987       pnz = pi_loc[i+1] - pi_loc[i];
988       pJ  = pj_loc + pi_loc[i];
989       for (j=0; j<pnz; j++) {
990         nextap = 0;
991         row    = pJ[j]; /* global index */
992         if (row < pcstart || row >=pcend) { /* put the value into Co */
993           row = *poJ;
994           cj  = coj + coi[row];
995           ca  = coa + coi[row]; poJ++;
996         } else {                            /* put the value into Cd */
997           row = *pdJ;
998           cj  = bj + bi[row];
999           ca  = ba + bi[row]; pdJ++;
1000         }
1001         valtmp = pA[j];
1002         for (k=0; nextap<apnz; k++) {
1003           if (cj[k]==apJ[nextap]) ca[k] += valtmp*apa[nextap++];
1004         }
1005         ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
1006       }
1007       pA += pnz;
1008       /* zero the current row info for A*P */
1009       ierr = PetscMemzero(apa,apnz*sizeof(MatScalar));CHKERRQ(ierr);
1010 #if defined(PTAP_PROFILE)
1011       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
1012       ePtAP += t2_2 - t2_1;
1013 #endif
1014     }
1015   }
1016 #if defined(PTAP_PROFILE)
1017   ierr = PetscTime(&t2);CHKERRQ(ierr);
1018 #endif
1019 
1020   /* 3) send and recv matrix values coa */
1021   /*------------------------------------*/
1022   buf_ri = merge->buf_ri;
1023   buf_rj = merge->buf_rj;
1024   len_s  = merge->len_s;
1025   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1026   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1027 
1028   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1029   for (proc=0,k=0; proc<size; proc++) {
1030     if (!len_s[proc]) continue;
1031     i    = merge->owners_co[proc];
1032     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
1033     k++;
1034   }
1035   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
1036   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
1037 
1038   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1039   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1040   ierr = PetscFree(coa);CHKERRQ(ierr);
1041 #if defined(PTAP_PROFILE)
1042   ierr = PetscTime(&t3);CHKERRQ(ierr);
1043 #endif
1044 
1045   /* 4) insert local Cseq and received values into Cmpi */
1046   /*------------------------------------------------------*/
1047   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1048   for (k=0; k<merge->nrecv; k++) {
1049     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1050     nrows       = *(buf_ri_k[k]);
1051     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1052     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1053   }
1054 
1055   for (i=0; i<cm; i++) {
1056     row  = owners[rank] + i; /* global row index of C_seq */
1057     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1058     ba_i = ba + bi[i];
1059     bnz  = bi[i+1] - bi[i];
1060     /* add received vals into ba */
1061     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1062       /* i-th row */
1063       if (i == *nextrow[k]) {
1064         cnz    = *(nextci[k]+1) - *nextci[k];
1065         cj     = buf_rj[k] + *(nextci[k]);
1066         ca     = abuf_r[k] + *(nextci[k]);
1067         nextcj = 0;
1068         for (j=0; nextcj<cnz; j++) {
1069           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1070             ba_i[j] += ca[nextcj++];
1071           }
1072         }
1073         nextrow[k]++; nextci[k]++;
1074         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1075       }
1076     }
1077     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1078   }
1079   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1080   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1081 
1082   ierr = PetscFree(ba);CHKERRQ(ierr);
1083   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1084   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1085   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1086 #if defined(PTAP_PROFILE)
1087   ierr = PetscTime(&t4);CHKERRQ(ierr);
1088   if (rank==1) {
1089     ierr = PetscPrintf(MPI_COMM_SELF," R=Pd^T %g; AP %g\n", t_tran1-t_tran0,t_tran2-t_tran1);CHKERRQ(ierr);
1090     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,eP,t2-t1,et2_AP,ePtAP,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr);
1091   }
1092 #endif
1093   PetscFunctionReturn(0);
1094 }
1095