xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision edeac6de2254af88f460af5743b3540402af52ea)
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 PetscErrorCode MatView_MPIAIJ_PtAP(Mat A,PetscViewer viewer)
16 {
17   PetscErrorCode    ierr;
18   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
19   Mat_PtAPMPI       *ptap=a->ptap;
20   PetscBool         iascii;
21   PetscViewerFormat format;
22 
23   PetscFunctionBegin;
24   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
25   if (iascii) {
26     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
27     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
28       if (ptap->algType == 0) {
29         ierr = PetscViewerASCIIPrintf(viewer,"using scalable MatPtAP() implementation\n");CHKERRQ(ierr);
30       } else if (ptap->algType == 1) {
31         ierr = PetscViewerASCIIPrintf(viewer,"using nonscalable MatPtAP() implementation\n");CHKERRQ(ierr);
32       }
33     }
34   }
35   ierr = (ptap->view)(A,viewer);CHKERRQ(ierr);
36   PetscFunctionReturn(0);
37 }
38 
39 PetscErrorCode MatDestroy_MPIAIJ_PtAP(Mat A)
40 {
41   PetscErrorCode ierr;
42   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
43   Mat_PtAPMPI    *ptap=a->ptap;
44 
45   PetscFunctionBegin;
46   if (ptap) {
47     Mat_Merge_SeqsToMPI *merge=ptap->merge;
48     ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
49     ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
50     ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
51     ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
52     ierr = MatDestroy(&ptap->A_loc);CHKERRQ(ierr); /* used by MatTransposeMatMult() */
53     ierr = MatDestroy(&ptap->Rd);CHKERRQ(ierr);
54     ierr = MatDestroy(&ptap->Ro);CHKERRQ(ierr);
55     if (ptap->AP_loc) { /* used by alg_rap */
56       Mat_SeqAIJ *ap = (Mat_SeqAIJ*)(ptap->AP_loc)->data;
57       ierr = PetscFree(ap->i);CHKERRQ(ierr);
58       ierr = PetscFree2(ap->j,ap->a);CHKERRQ(ierr);
59       ierr = MatDestroy(&ptap->AP_loc);CHKERRQ(ierr);
60     } else { /* used by alg_ptap */
61       ierr = PetscFree(ptap->api);CHKERRQ(ierr);
62       ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
63     }
64     ierr = MatDestroy(&ptap->C_loc);CHKERRQ(ierr);
65     ierr = MatDestroy(&ptap->C_oth);CHKERRQ(ierr);
66     if (ptap->apa) {ierr = PetscFree(ptap->apa);CHKERRQ(ierr);}
67 
68     if (merge) { /* used by alg_ptap */
69       ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
70       ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
71       ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
72       ierr = PetscFree(merge->bi);CHKERRQ(ierr);
73       ierr = PetscFree(merge->bj);CHKERRQ(ierr);
74       ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
75       ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
76       ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
77       ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
78       ierr = PetscFree(merge->coi);CHKERRQ(ierr);
79       ierr = PetscFree(merge->coj);CHKERRQ(ierr);
80       ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
81       ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
82       ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
83     }
84 
85     ierr = ptap->destroy(A);CHKERRQ(ierr);
86     ierr = PetscFree(ptap);CHKERRQ(ierr);
87   }
88   PetscFunctionReturn(0);
89 }
90 
91 PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat A, MatDuplicateOption op, Mat *M)
92 {
93   PetscErrorCode ierr;
94   Mat_MPIAIJ     *a     = (Mat_MPIAIJ*)A->data;
95   Mat_PtAPMPI    *ptap  = a->ptap;
96 
97   PetscFunctionBegin;
98   ierr = (*ptap->duplicate)(A,op,M);CHKERRQ(ierr);
99   (*M)->ops->destroy   = ptap->destroy;
100   (*M)->ops->duplicate = ptap->duplicate;
101   (*M)->ops->view      = ptap->view;
102   PetscFunctionReturn(0);
103 }
104 
105 PETSC_INTERN PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
106 {
107   PetscErrorCode ierr;
108   PetscBool      flg;
109   MPI_Comm       comm;
110 #if !defined(PETSC_HAVE_HYPRE)
111   const char          *algTypes[2] = {"scalable","nonscalable"};
112   PetscInt            nalg=2;
113 #else
114   const char          *algTypes[3] = {"scalable","nonscalable","hypre"};
115   PetscInt            nalg=3;
116 #endif
117   PetscInt            pN=P->cmap->N,alg=1; /* set default algorithm */
118 
119   PetscFunctionBegin;
120   /* check if matrix local sizes are compatible */
121   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
122   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) 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);
123   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) 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);
124 
125   if (scall == MAT_INITIAL_MATRIX) {
126     /* pick an algorithm */
127     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
128     PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
129     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
130     ierr = PetscOptionsEnd();CHKERRQ(ierr);
131 
132     if (!flg && pN > 100000) { /* may switch to scalable algorithm as default */
133       MatInfo     Ainfo,Pinfo;
134       PetscInt    nz_local;
135       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
136 
137       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
138       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
139       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
140 
141       if (pN > fill*nz_local) alg_scalable_loc = PETSC_TRUE;
142       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
143 
144       if (alg_scalable) {
145         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
146       }
147     }
148 
149     switch (alg) {
150     case 1:
151       /* do R=P^T locally, then C=R*A*P */
152       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
153       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
154       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
155       break;
156 #if defined(PETSC_HAVE_HYPRE)
157     case 2:
158       /* Use boomerAMGBuildCoarseOperator */
159       ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr);
160       PetscFunctionReturn(0);
161       break;
162 #endif
163     default:
164       /* do R=P^T locally, then C=R*A*P */
165       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
166       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(A,P,fill,C);CHKERRQ(ierr);
167       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
168       break;
169     }
170   }
171   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
172   ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
173   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
174   PetscFunctionReturn(0);
175 }
176 
177 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,Mat C)
178 {
179   PetscErrorCode    ierr;
180   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
181   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
182   Mat_SeqAIJ        *cd=(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
183   Mat_SeqAIJ        *ap,*p_loc,*p_oth,*c_seq;
184   Mat_PtAPMPI       *ptap = c->ptap;
185   Mat               AP_loc,C_loc,C_oth;
186   PetscInt          i,rstart,rend,cm,ncols,row,*api,*apj,am = A->rmap->n,apnz;
187   PetscScalar       *apa;
188   const PetscInt    *cols;
189   const PetscScalar *vals;
190 
191   PetscFunctionBegin;
192   ierr = MatZeroEntries(C);CHKERRQ(ierr);
193 
194   /* 1) get R = Pd^T,Ro = Po^T */
195   if (ptap->reuse == MAT_REUSE_MATRIX) {
196     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
197     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
198   }
199 
200   /* 2) get AP_loc */
201   AP_loc = ptap->AP_loc;
202   ap = (Mat_SeqAIJ*)AP_loc->data;
203 
204   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
205   /*-----------------------------------------------------*/
206   if (ptap->reuse == MAT_REUSE_MATRIX) {
207     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
208     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
209     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
210   }
211 
212   /* 2-2) compute numeric A_loc*P - dominating part */
213   /* ---------------------------------------------- */
214   /* get data from symbolic products */
215   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
216   if (ptap->P_oth) p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
217   else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"ptap->P_oth is NULL. Cannot proceed!");
218 
219   api   = ap->i;
220   apj   = ap->j;
221   for (i=0; i<am; i++) {
222     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
223     apnz = api[i+1] - api[i];
224     apa = ap->a + api[i];
225     ierr = PetscMemzero(apa,sizeof(PetscScalar)*apnz);CHKERRQ(ierr);
226     AProw_scalable(i,ad,ao,p_loc,p_oth,api,apj,apa);
227     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
228   }
229 
230   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
231   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
232   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
233 
234   C_loc = ptap->C_loc;
235   C_oth = ptap->C_oth;
236 
237   /* add C_loc and Co to to C */
238   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
239 
240   /* C_loc -> C */
241   cm    = C_loc->rmap->N;
242   c_seq = (Mat_SeqAIJ*)C_loc->data;
243   cols = c_seq->j;
244   vals = c_seq->a;
245 
246   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assemled is PETSC_FALSE and */
247   /* when there are no off-processor parts.  */
248   if (C->assembled) {
249     C->was_assembled = PETSC_TRUE;
250     C->assembled     = PETSC_FALSE;
251   }
252   if (C->was_assembled) {
253     for (i=0; i<cm; i++) {
254       ncols = c_seq->i[i+1] - c_seq->i[i];
255       row = rstart + i;
256       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
257       cols += ncols; vals += ncols;
258     }
259   } else {
260     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a,cd->i,co->i);CHKERRQ(ierr);
261   }
262 
263   /* Co -> C, off-processor part */
264   cm = C_oth->rmap->N;
265   c_seq = (Mat_SeqAIJ*)C_oth->data;
266   cols = c_seq->j;
267   vals = c_seq->a;
268   for (i=0; i<cm; i++) {
269     ncols = c_seq->i[i+1] - c_seq->i[i];
270     row = p->garray[i];
271     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
272     cols += ncols; vals += ncols;
273   }
274   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
275   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
276 
277   ptap->reuse = MAT_REUSE_MATRIX;
278   PetscFunctionReturn(0);
279 }
280 
281 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,PetscReal fill,Mat *C)
282 {
283   PetscErrorCode      ierr;
284   Mat_PtAPMPI         *ptap;
285   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
286   MPI_Comm            comm;
287   PetscMPIInt         size,rank;
288   Mat                 Cmpi,P_loc,P_oth;
289   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
290   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
291   PetscInt            *lnk,i,k,pnz,row,nsend;
292   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
293   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
294   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
295   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
296   MPI_Request         *swaits,*rwaits;
297   MPI_Status          *sstatus,rstatus;
298   PetscLayout         rowmap;
299   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
300   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
301   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,Crmax,*aj,*ai,*pi;
302   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
303   PetscScalar         *apv;
304   PetscTable          ta;
305 #if defined(PETSC_USE_INFO)
306   PetscReal           apfill;
307 #endif
308 
309   PetscFunctionBegin;
310   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
311   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
312   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
313 
314   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
315 
316   /* create symbolic parallel matrix Cmpi */
317   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
318   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
319 
320   /* create struct Mat_PtAPMPI and attached it to C later */
321   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
322   ptap->reuse = MAT_INITIAL_MATRIX;
323   ptap->algType = 0;
324 
325   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
326   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&P_oth);CHKERRQ(ierr);
327   /* get P_loc by taking all local rows of P */
328   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&P_loc);CHKERRQ(ierr);
329 
330   ptap->P_loc = P_loc;
331   ptap->P_oth = P_oth;
332 
333   /* (0) compute Rd = Pd^T, Ro = Po^T  */
334   /* --------------------------------- */
335   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
336   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
337 
338   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
339   /* ----------------------------------------------------------------- */
340   p_loc  = (Mat_SeqAIJ*)P_loc->data;
341   if (P_oth) p_oth = (Mat_SeqAIJ*)P_oth->data;
342 
343   /* create and initialize a linked list */
344   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
345   MatRowMergeMax_SeqAIJ(p_loc,P_loc->rmap->N,ta);
346   MatRowMergeMax_SeqAIJ(p_oth,P_oth->rmap->N,ta);
347   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
348 
349   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
350 
351   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
352   if (ao) {
353     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
354   } else {
355     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
356   }
357   current_space = free_space;
358   nspacedouble  = 0;
359 
360   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
361   api[0] = 0;
362   for (i=0; i<am; i++) {
363     /* diagonal portion: Ad[i,:]*P */
364     ai = ad->i; pi = p_loc->i;
365     nzi = ai[i+1] - ai[i];
366     aj  = ad->j + ai[i];
367     for (j=0; j<nzi; j++) {
368       row  = aj[j];
369       pnz  = pi[row+1] - pi[row];
370       Jptr = p_loc->j + pi[row];
371       /* add non-zero cols of P into the sorted linked list lnk */
372       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
373     }
374     /* off-diagonal portion: Ao[i,:]*P */
375     if (ao) {
376       ai = ao->i; pi = p_oth->i;
377       nzi = ai[i+1] - ai[i];
378       aj  = ao->j + ai[i];
379       for (j=0; j<nzi; j++) {
380         row  = aj[j];
381         pnz  = pi[row+1] - pi[row];
382         Jptr = p_oth->j + pi[row];
383         ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
384       }
385     }
386     apnz     = lnk[0];
387     api[i+1] = api[i] + apnz;
388 
389     /* if free space is not available, double the total space in the list */
390     if (current_space->local_remaining<apnz) {
391       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
392       nspacedouble++;
393     }
394 
395     /* Copy data into free space, then initialize lnk */
396     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
397 
398     current_space->array           += apnz;
399     current_space->local_used      += apnz;
400     current_space->local_remaining -= apnz;
401   }
402   /* Allocate space for apj and apv, initialize apj, and */
403   /* destroy list of free space and other temporary array(s) */
404   ierr = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
405   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
406   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
407 
408   /* Create AP_loc for reuse */
409   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
410 
411 #if defined(PETSC_USE_INFO)
412   if (ao) {
413     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
414   } else {
415     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
416   }
417   ptap->AP_loc->info.mallocs           = nspacedouble;
418   ptap->AP_loc->info.fill_ratio_given  = fill;
419   ptap->AP_loc->info.fill_ratio_needed = apfill;
420 
421   if (api[am]) {
422     ierr = PetscInfo3(ptap->AP_loc,"Scalable algorithm, AP_loc reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)apfill);CHKERRQ(ierr);
423     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
424   } else {
425     ierr = PetscInfo(ptap->AP_loc,"Scalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
426   }
427 #endif
428 
429   /* (2-1) compute symbolic Co = Ro*AP_loc  */
430   /* ------------------------------------ */
431   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
432 
433   /* (3) send coj of C_oth to other processors  */
434   /* ------------------------------------------ */
435   /* determine row ownership */
436   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
437   rowmap->n  = pn;
438   rowmap->bs = 1;
439   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
440   owners = rowmap->range;
441 
442   /* determine the number of messages to send, their lengths */
443   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
444   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
445   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
446 
447   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
448   coi   = c_oth->i; coj = c_oth->j;
449   con   = ptap->C_oth->rmap->n;
450   proc  = 0;
451   for (i=0; i<con; i++) {
452     while (prmap[i] >= owners[proc+1]) proc++;
453     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
454     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
455   }
456 
457   len          = 0; /* max length of buf_si[], see (4) */
458   owners_co[0] = 0;
459   nsend        = 0;
460   for (proc=0; proc<size; proc++) {
461     owners_co[proc+1] = owners_co[proc] + len_si[proc];
462     if (len_s[proc]) {
463       nsend++;
464       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
465       len         += len_si[proc];
466     }
467   }
468 
469   /* determine the number and length of messages to receive for coi and coj  */
470   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
471   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
472 
473   /* post the Irecv and Isend of coj */
474   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
475   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
476   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
477   for (proc=0, k=0; proc<size; proc++) {
478     if (!len_s[proc]) continue;
479     i    = owners_co[proc];
480     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
481     k++;
482   }
483 
484   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
485   /* ---------------------------------------- */
486   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
487   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
488 
489   /* receives coj are complete */
490   for (i=0; i<nrecv; i++) {
491     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
492   }
493   ierr = PetscFree(rwaits);CHKERRQ(ierr);
494   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
495 
496   /* add received column indices into ta to update Crmax */
497   for (k=0; k<nrecv; k++) {/* k-th received message */
498     Jptr = buf_rj[k];
499     for (j=0; j<len_r[k]; j++) {
500       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
501     }
502   }
503   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
504   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
505 
506   /* (4) send and recv coi */
507   /*-----------------------*/
508   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
509   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
510   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
511   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
512   for (proc=0,k=0; proc<size; proc++) {
513     if (!len_s[proc]) continue;
514     /* form outgoing message for i-structure:
515          buf_si[0]:                 nrows to be sent
516                [1:nrows]:           row index (global)
517                [nrows+1:2*nrows+1]: i-structure index
518     */
519     /*-------------------------------------------*/
520     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
521     buf_si_i    = buf_si + nrows+1;
522     buf_si[0]   = nrows;
523     buf_si_i[0] = 0;
524     nrows       = 0;
525     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
526       nzi = coi[i+1] - coi[i];
527       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
528       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
529       nrows++;
530     }
531     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
532     k++;
533     buf_si += len_si[proc];
534   }
535   for (i=0; i<nrecv; i++) {
536     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
537   }
538   ierr = PetscFree(rwaits);CHKERRQ(ierr);
539   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
540 
541   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
542   ierr = PetscFree(len_ri);CHKERRQ(ierr);
543   ierr = PetscFree(swaits);CHKERRQ(ierr);
544   ierr = PetscFree(buf_s);CHKERRQ(ierr);
545 
546   /* (5) compute the local portion of Cmpi      */
547   /* ------------------------------------------ */
548   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
549   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
550   current_space = free_space;
551 
552   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
553   for (k=0; k<nrecv; k++) {
554     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
555     nrows       = *buf_ri_k[k];
556     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
557     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
558   }
559 
560   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
561   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
562   for (i=0; i<pn; i++) {
563     /* add C_loc into Cmpi */
564     nzi  = c_loc->i[i+1] - c_loc->i[i];
565     Jptr = c_loc->j + c_loc->i[i];
566     ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
567 
568     /* add received col data into lnk */
569     for (k=0; k<nrecv; k++) { /* k-th received message */
570       if (i == *nextrow[k]) { /* i-th row */
571         nzi  = *(nextci[k]+1) - *nextci[k];
572         Jptr = buf_rj[k] + *nextci[k];
573         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
574         nextrow[k]++; nextci[k]++;
575       }
576     }
577     nzi = lnk[0];
578 
579     /* copy data into free space, then initialize lnk */
580     ierr = PetscLLCondensedClean_Scalable(nzi,current_space->array,lnk);CHKERRQ(ierr);
581     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
582   }
583   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
584   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
585   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
586 
587   /* local sizes and preallocation */
588   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
589   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
590   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
591   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
592 
593   /* members in merge */
594   ierr = PetscFree(id_r);CHKERRQ(ierr);
595   ierr = PetscFree(len_r);CHKERRQ(ierr);
596   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
597   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
598   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
599   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
600   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
601 
602   /* attach the supporting struct to Cmpi for reuse */
603   c = (Mat_MPIAIJ*)Cmpi->data;
604   c->ptap         = ptap;
605   ptap->duplicate = Cmpi->ops->duplicate;
606   ptap->destroy   = Cmpi->ops->destroy;
607   ptap->view      = Cmpi->ops->view;
608 
609   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
610   Cmpi->assembled        = PETSC_FALSE;
611   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable;
612   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
613   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
614   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
615   *C                     = Cmpi;
616   PetscFunctionReturn(0);
617 }
618 
619 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
620 {
621   PetscErrorCode      ierr;
622   Mat_PtAPMPI         *ptap;
623   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
624   MPI_Comm            comm;
625   PetscMPIInt         size,rank;
626   Mat                 Cmpi;
627   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
628   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
629   PetscInt            *lnk,i,k,pnz,row,nsend;
630   PetscBT             lnkbt;
631   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
632   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
633   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
634   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
635   MPI_Request         *swaits,*rwaits;
636   MPI_Status          *sstatus,rstatus;
637   PetscLayout         rowmap;
638   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
639   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
640   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,ap_rmax=0,Crmax,*aj,*ai,*pi;
641   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
642   PetscScalar         *apv;
643   PetscTable          ta;
644 #if defined(PETSC_USE_INFO)
645   PetscReal           apfill;
646 #endif
647 
648   PetscFunctionBegin;
649   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
650   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
651   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
652 
653   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
654 
655   /* create symbolic parallel matrix Cmpi */
656   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
657   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
658 
659   /* Do dense axpy in MatPtAPNumeric_MPIAIJ_MPIAIJ() */
660   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ;
661 
662   /* create struct Mat_PtAPMPI and attached it to C later */
663   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
664   ptap->reuse = MAT_INITIAL_MATRIX;
665   ptap->algType = 1;
666 
667   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
668   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
669   /* get P_loc by taking all local rows of P */
670   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
671 
672   /* (0) compute Rd = Pd^T, Ro = Po^T  */
673   /* --------------------------------- */
674   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
675   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
676 
677   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
678   /* ----------------------------------------------------------------- */
679   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
680   if (ptap->P_oth) p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
681 
682   /* create and initialize a linked list */
683   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
684   MatRowMergeMax_SeqAIJ(p_loc,ptap->P_loc->rmap->N,ta);
685   MatRowMergeMax_SeqAIJ(p_oth,ptap->P_oth->rmap->N,ta);
686   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
687   /* printf("[%d] est %d, Crmax %d; pN %d\n",rank,5*(p_loc->rmax+p_oth->rmax + (PetscInt)(1.e-2*pN)),Crmax,pN); */
688 
689   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
690 
691   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
692   if (ao) {
693     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
694   } else {
695     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
696   }
697   current_space = free_space;
698   nspacedouble  = 0;
699 
700   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
701   api[0] = 0;
702   for (i=0; i<am; i++) {
703     /* diagonal portion: Ad[i,:]*P */
704     ai = ad->i; pi = p_loc->i;
705     nzi = ai[i+1] - ai[i];
706     aj  = ad->j + ai[i];
707     for (j=0; j<nzi; j++) {
708       row  = aj[j];
709       pnz  = pi[row+1] - pi[row];
710       Jptr = p_loc->j + pi[row];
711       /* add non-zero cols of P into the sorted linked list lnk */
712       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
713     }
714     /* off-diagonal portion: Ao[i,:]*P */
715     if (ao) {
716       ai = ao->i; pi = p_oth->i;
717       nzi = ai[i+1] - ai[i];
718       aj  = ao->j + ai[i];
719       for (j=0; j<nzi; j++) {
720         row  = aj[j];
721         pnz  = pi[row+1] - pi[row];
722         Jptr = p_oth->j + pi[row];
723         ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
724       }
725     }
726     apnz     = lnk[0];
727     api[i+1] = api[i] + apnz;
728     if (ap_rmax < apnz) ap_rmax = apnz;
729 
730     /* if free space is not available, double the total space in the list */
731     if (current_space->local_remaining<apnz) {
732       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
733       nspacedouble++;
734     }
735 
736     /* Copy data into free space, then initialize lnk */
737     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
738 
739     current_space->array           += apnz;
740     current_space->local_used      += apnz;
741     current_space->local_remaining -= apnz;
742   }
743   /* Allocate space for apj and apv, initialize apj, and */
744   /* destroy list of free space and other temporary array(s) */
745   ierr   = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
746   ierr   = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
747   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
748 
749   /* Create AP_loc for reuse */
750   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
751 
752 #if defined(PETSC_USE_INFO)
753   if (ao) {
754     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
755   } else {
756     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
757   }
758   ptap->AP_loc->info.mallocs           = nspacedouble;
759   ptap->AP_loc->info.fill_ratio_given  = fill;
760   ptap->AP_loc->info.fill_ratio_needed = apfill;
761 
762   if (api[am]) {
763     ierr = PetscInfo3(ptap->AP_loc,"Nonscalable algorithm, AP_loc reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)apfill);CHKERRQ(ierr);
764     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
765   } else {
766     ierr = PetscInfo(ptap->AP_loc,"Nonscalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
767   }
768 #endif
769 
770   /* (2-1) compute symbolic Co = Ro*AP_loc  */
771   /* ------------------------------------ */
772   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
773 
774   /* (3) send coj of C_oth to other processors  */
775   /* ------------------------------------------ */
776   /* determine row ownership */
777   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
778   rowmap->n  = pn;
779   rowmap->bs = 1;
780   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
781   owners = rowmap->range;
782 
783   /* determine the number of messages to send, their lengths */
784   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
785   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
786   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
787 
788   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
789   coi   = c_oth->i; coj = c_oth->j;
790   con   = ptap->C_oth->rmap->n;
791   proc  = 0;
792   for (i=0; i<con; i++) {
793     while (prmap[i] >= owners[proc+1]) proc++;
794     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
795     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
796   }
797 
798   len          = 0; /* max length of buf_si[], see (4) */
799   owners_co[0] = 0;
800   nsend        = 0;
801   for (proc=0; proc<size; proc++) {
802     owners_co[proc+1] = owners_co[proc] + len_si[proc];
803     if (len_s[proc]) {
804       nsend++;
805       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
806       len         += len_si[proc];
807     }
808   }
809 
810   /* determine the number and length of messages to receive for coi and coj  */
811   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
812   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
813 
814   /* post the Irecv and Isend of coj */
815   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
816   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
817   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
818   for (proc=0, k=0; proc<size; proc++) {
819     if (!len_s[proc]) continue;
820     i    = owners_co[proc];
821     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
822     k++;
823   }
824 
825   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
826   /* ---------------------------------------- */
827   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
828   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
829 
830   /* receives coj are complete */
831   for (i=0; i<nrecv; i++) {
832     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
833   }
834   ierr = PetscFree(rwaits);CHKERRQ(ierr);
835   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
836 
837   /* add received column indices into ta to update Crmax */
838   for (k=0; k<nrecv; k++) {/* k-th received message */
839     Jptr = buf_rj[k];
840     for (j=0; j<len_r[k]; j++) {
841       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
842     }
843   }
844   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
845   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
846 
847   /* (4) send and recv coi */
848   /*-----------------------*/
849   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
850   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
851   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
852   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
853   for (proc=0,k=0; proc<size; proc++) {
854     if (!len_s[proc]) continue;
855     /* form outgoing message for i-structure:
856          buf_si[0]:                 nrows to be sent
857                [1:nrows]:           row index (global)
858                [nrows+1:2*nrows+1]: i-structure index
859     */
860     /*-------------------------------------------*/
861     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
862     buf_si_i    = buf_si + nrows+1;
863     buf_si[0]   = nrows;
864     buf_si_i[0] = 0;
865     nrows       = 0;
866     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
867       nzi = coi[i+1] - coi[i];
868       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
869       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
870       nrows++;
871     }
872     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
873     k++;
874     buf_si += len_si[proc];
875   }
876   for (i=0; i<nrecv; i++) {
877     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
878   }
879   ierr = PetscFree(rwaits);CHKERRQ(ierr);
880   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
881 
882   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
883   ierr = PetscFree(len_ri);CHKERRQ(ierr);
884   ierr = PetscFree(swaits);CHKERRQ(ierr);
885   ierr = PetscFree(buf_s);CHKERRQ(ierr);
886 
887   /* (5) compute the local portion of Cmpi      */
888   /* ------------------------------------------ */
889   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
890   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
891   current_space = free_space;
892 
893   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
894   for (k=0; k<nrecv; k++) {
895     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
896     nrows       = *buf_ri_k[k];
897     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
898     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
899   }
900 
901   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
902   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
903   for (i=0; i<pn; i++) {
904     /* add C_loc into Cmpi */
905     nzi  = c_loc->i[i+1] - c_loc->i[i];
906     Jptr = c_loc->j + c_loc->i[i];
907     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
908 
909     /* add received col data into lnk */
910     for (k=0; k<nrecv; k++) { /* k-th received message */
911       if (i == *nextrow[k]) { /* i-th row */
912         nzi  = *(nextci[k]+1) - *nextci[k];
913         Jptr = buf_rj[k] + *nextci[k];
914         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
915         nextrow[k]++; nextci[k]++;
916       }
917     }
918     nzi = lnk[0];
919 
920     /* copy data into free space, then initialize lnk */
921     ierr = PetscLLCondensedClean(pN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
922     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
923   }
924   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
925   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
926   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
927 
928   /* local sizes and preallocation */
929   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
930   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
931   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
932   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
933 
934   /* members in merge */
935   ierr = PetscFree(id_r);CHKERRQ(ierr);
936   ierr = PetscFree(len_r);CHKERRQ(ierr);
937   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
938   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
939   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
940   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
941   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
942 
943   /* attach the supporting struct to Cmpi for reuse */
944   c = (Mat_MPIAIJ*)Cmpi->data;
945   c->ptap         = ptap;
946   ptap->duplicate = Cmpi->ops->duplicate;
947   ptap->destroy   = Cmpi->ops->destroy;
948   ptap->view      = Cmpi->ops->view;
949   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
950 
951   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
952   Cmpi->assembled        = PETSC_FALSE;
953   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
954   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
955   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
956   *C                     = Cmpi;
957   PetscFunctionReturn(0);
958 }
959 
960 
961 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
962 {
963   PetscErrorCode    ierr;
964   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
965   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
966   Mat_SeqAIJ        *cd=(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
967   Mat_SeqAIJ        *ap,*p_loc,*p_oth=NULL,*c_seq;
968   Mat_PtAPMPI       *ptap = c->ptap;
969   Mat               AP_loc,C_loc,C_oth;
970   PetscInt          i,rstart,rend,cm,ncols,row;
971   PetscInt          *api,*apj,am = A->rmap->n,j,col,apnz;
972   PetscScalar       *apa;
973   const PetscInt    *cols;
974   const PetscScalar *vals;
975 
976   PetscFunctionBegin;
977   ierr = MatZeroEntries(C);CHKERRQ(ierr);
978   /* 1) get R = Pd^T,Ro = Po^T */
979   if (ptap->reuse == MAT_REUSE_MATRIX) {
980     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
981     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
982   }
983 
984   /* 2) get AP_loc */
985   AP_loc = ptap->AP_loc;
986   ap = (Mat_SeqAIJ*)AP_loc->data;
987 
988   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
989   /*-----------------------------------------------------*/
990   if (ptap->reuse == MAT_REUSE_MATRIX) {
991     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
992     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
993     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
994   }
995 
996   /* 2-2) compute numeric A_loc*P - dominating part */
997   /* ---------------------------------------------- */
998   /* get data from symbolic products */
999   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1000   if (ptap->P_oth) {
1001     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1002   }
1003   apa   = ptap->apa;
1004   api   = ap->i;
1005   apj   = ap->j;
1006   for (i=0; i<am; i++) {
1007     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
1008     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
1009     apnz = api[i+1] - api[i];
1010     for (j=0; j<apnz; j++) {
1011       col = apj[j+api[i]];
1012       ap->a[j+ap->i[i]] = apa[col];
1013       apa[col] = 0.0;
1014     }
1015     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
1016   }
1017 
1018   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
1019   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
1020   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
1021   C_loc = ptap->C_loc;
1022   C_oth = ptap->C_oth;
1023 
1024   /* add C_loc and Co to to C */
1025   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1026 
1027   /* C_loc -> C */
1028   cm    = C_loc->rmap->N;
1029   c_seq = (Mat_SeqAIJ*)C_loc->data;
1030   cols = c_seq->j;
1031   vals = c_seq->a;
1032 
1033 
1034   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assemled is PETSC_FALSE and */
1035   /* when there are no off-processor parts.  */
1036   if (C->assembled) {
1037     C->was_assembled = PETSC_TRUE;
1038     C->assembled     = PETSC_FALSE;
1039   }
1040   if (C->was_assembled) {
1041     for (i=0; i<cm; i++) {
1042       ncols = c_seq->i[i+1] - c_seq->i[i];
1043       row = rstart + i;
1044       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1045       cols += ncols; vals += ncols;
1046     }
1047   } else {
1048     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a,cd->i,co->i);CHKERRQ(ierr);
1049   }
1050 
1051   /* Co -> C, off-processor part */
1052   cm = C_oth->rmap->N;
1053   c_seq = (Mat_SeqAIJ*)C_oth->data;
1054   cols = c_seq->j;
1055   vals = c_seq->a;
1056   for (i=0; i<cm; i++) {
1057     ncols = c_seq->i[i+1] - c_seq->i[i];
1058     row = p->garray[i];
1059     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1060     cols += ncols; vals += ncols;
1061   }
1062 
1063   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1064   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1065 
1066   ptap->reuse = MAT_REUSE_MATRIX;
1067   PetscFunctionReturn(0);
1068 }
1069