xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision d6f11fddcbc5503a4d8fb26ab62e20dc044b7e4b)
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 = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
160       ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr);
161       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
162       break;
163 #endif
164     default:
165       /* do R=P^T locally, then C=R*A*P */
166       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
167       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(A,P,fill,C);CHKERRQ(ierr);
168       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
169       break;
170     }
171   }
172   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
173   ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
174   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
175   PetscFunctionReturn(0);
176 }
177 
178 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,Mat C)
179 {
180   PetscErrorCode    ierr;
181   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
182   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->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(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
197     ierr = MatTranspose(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_assembled is PETSC_FALSE and */
247   /* when there are no off-processor parts.  */
248   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
249   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
250   /* a table, and other, more complex stuff has to be done. */
251   if (C->assembled) {
252     C->was_assembled = PETSC_TRUE;
253     C->assembled     = PETSC_FALSE;
254   }
255   if (C->was_assembled) {
256     for (i=0; i<cm; i++) {
257       ncols = c_seq->i[i+1] - c_seq->i[i];
258       row = rstart + i;
259       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
260       cols += ncols; vals += ncols;
261     }
262   } else {
263     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
264   }
265 
266   /* Co -> C, off-processor part */
267   cm = C_oth->rmap->N;
268   c_seq = (Mat_SeqAIJ*)C_oth->data;
269   cols = c_seq->j;
270   vals = c_seq->a;
271   for (i=0; i<cm; i++) {
272     ncols = c_seq->i[i+1] - c_seq->i[i];
273     row = p->garray[i];
274     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
275     cols += ncols; vals += ncols;
276   }
277   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
278   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
279 
280   ptap->reuse = MAT_REUSE_MATRIX;
281   PetscFunctionReturn(0);
282 }
283 
284 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,PetscReal fill,Mat *C)
285 {
286   PetscErrorCode      ierr;
287   Mat_PtAPMPI         *ptap;
288   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
289   MPI_Comm            comm;
290   PetscMPIInt         size,rank;
291   Mat                 Cmpi,P_loc,P_oth;
292   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
293   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
294   PetscInt            *lnk,i,k,pnz,row,nsend;
295   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
296   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
297   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
298   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
299   MPI_Request         *swaits,*rwaits;
300   MPI_Status          *sstatus,rstatus;
301   PetscLayout         rowmap;
302   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
303   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
304   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,Crmax,*aj,*ai,*pi;
305   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
306   PetscScalar         *apv;
307   PetscTable          ta;
308 #if defined(PETSC_USE_INFO)
309   PetscReal           apfill;
310 #endif
311 
312   PetscFunctionBegin;
313   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
314   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
315   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
316 
317   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
318 
319   /* create symbolic parallel matrix Cmpi */
320   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
321   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
322 
323   /* create struct Mat_PtAPMPI and attached it to C later */
324   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
325   ptap->reuse = MAT_INITIAL_MATRIX;
326   ptap->algType = 0;
327 
328   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
329   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&P_oth);CHKERRQ(ierr);
330   /* get P_loc by taking all local rows of P */
331   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&P_loc);CHKERRQ(ierr);
332 
333   ptap->P_loc = P_loc;
334   ptap->P_oth = P_oth;
335 
336   /* (0) compute Rd = Pd^T, Ro = Po^T  */
337   /* --------------------------------- */
338   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
339   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
340 
341   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
342   /* ----------------------------------------------------------------- */
343   p_loc  = (Mat_SeqAIJ*)P_loc->data;
344   if (P_oth) p_oth = (Mat_SeqAIJ*)P_oth->data;
345 
346   /* create and initialize a linked list */
347   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
348   MatRowMergeMax_SeqAIJ(p_loc,P_loc->rmap->N,ta);
349   MatRowMergeMax_SeqAIJ(p_oth,P_oth->rmap->N,ta);
350   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
351 
352   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
353 
354   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
355   if (ao) {
356     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
357   } else {
358     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
359   }
360   current_space = free_space;
361   nspacedouble  = 0;
362 
363   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
364   api[0] = 0;
365   for (i=0; i<am; i++) {
366     /* diagonal portion: Ad[i,:]*P */
367     ai = ad->i; pi = p_loc->i;
368     nzi = ai[i+1] - ai[i];
369     aj  = ad->j + ai[i];
370     for (j=0; j<nzi; j++) {
371       row  = aj[j];
372       pnz  = pi[row+1] - pi[row];
373       Jptr = p_loc->j + pi[row];
374       /* add non-zero cols of P into the sorted linked list lnk */
375       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
376     }
377     /* off-diagonal portion: Ao[i,:]*P */
378     if (ao) {
379       ai = ao->i; pi = p_oth->i;
380       nzi = ai[i+1] - ai[i];
381       aj  = ao->j + ai[i];
382       for (j=0; j<nzi; j++) {
383         row  = aj[j];
384         pnz  = pi[row+1] - pi[row];
385         Jptr = p_oth->j + pi[row];
386         ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
387       }
388     }
389     apnz     = lnk[0];
390     api[i+1] = api[i] + apnz;
391 
392     /* if free space is not available, double the total space in the list */
393     if (current_space->local_remaining<apnz) {
394       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
395       nspacedouble++;
396     }
397 
398     /* Copy data into free space, then initialize lnk */
399     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
400 
401     current_space->array           += apnz;
402     current_space->local_used      += apnz;
403     current_space->local_remaining -= apnz;
404   }
405   /* Allocate space for apj and apv, initialize apj, and */
406   /* destroy list of free space and other temporary array(s) */
407   ierr = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
408   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
409   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
410 
411   /* Create AP_loc for reuse */
412   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
413 
414 #if defined(PETSC_USE_INFO)
415   if (ao) {
416     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
417   } else {
418     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
419   }
420   ptap->AP_loc->info.mallocs           = nspacedouble;
421   ptap->AP_loc->info.fill_ratio_given  = fill;
422   ptap->AP_loc->info.fill_ratio_needed = apfill;
423 
424   if (api[am]) {
425     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);
426     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
427   } else {
428     ierr = PetscInfo(ptap->AP_loc,"Scalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
429   }
430 #endif
431 
432   /* (2-1) compute symbolic Co = Ro*AP_loc  */
433   /* ------------------------------------ */
434   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
435 
436   /* (3) send coj of C_oth to other processors  */
437   /* ------------------------------------------ */
438   /* determine row ownership */
439   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
440   rowmap->n  = pn;
441   rowmap->bs = 1;
442   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
443   owners = rowmap->range;
444 
445   /* determine the number of messages to send, their lengths */
446   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
447   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
448   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
449 
450   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
451   coi   = c_oth->i; coj = c_oth->j;
452   con   = ptap->C_oth->rmap->n;
453   proc  = 0;
454   for (i=0; i<con; i++) {
455     while (prmap[i] >= owners[proc+1]) proc++;
456     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
457     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
458   }
459 
460   len          = 0; /* max length of buf_si[], see (4) */
461   owners_co[0] = 0;
462   nsend        = 0;
463   for (proc=0; proc<size; proc++) {
464     owners_co[proc+1] = owners_co[proc] + len_si[proc];
465     if (len_s[proc]) {
466       nsend++;
467       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
468       len         += len_si[proc];
469     }
470   }
471 
472   /* determine the number and length of messages to receive for coi and coj  */
473   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
474   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
475 
476   /* post the Irecv and Isend of coj */
477   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
478   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
479   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
480   for (proc=0, k=0; proc<size; proc++) {
481     if (!len_s[proc]) continue;
482     i    = owners_co[proc];
483     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
484     k++;
485   }
486 
487   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
488   /* ---------------------------------------- */
489   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
490   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
491 
492   /* receives coj are complete */
493   for (i=0; i<nrecv; i++) {
494     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
495   }
496   ierr = PetscFree(rwaits);CHKERRQ(ierr);
497   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
498 
499   /* add received column indices into ta to update Crmax */
500   for (k=0; k<nrecv; k++) {/* k-th received message */
501     Jptr = buf_rj[k];
502     for (j=0; j<len_r[k]; j++) {
503       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
504     }
505   }
506   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
507   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
508 
509   /* (4) send and recv coi */
510   /*-----------------------*/
511   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
512   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
513   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
514   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
515   for (proc=0,k=0; proc<size; proc++) {
516     if (!len_s[proc]) continue;
517     /* form outgoing message for i-structure:
518          buf_si[0]:                 nrows to be sent
519                [1:nrows]:           row index (global)
520                [nrows+1:2*nrows+1]: i-structure index
521     */
522     /*-------------------------------------------*/
523     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
524     buf_si_i    = buf_si + nrows+1;
525     buf_si[0]   = nrows;
526     buf_si_i[0] = 0;
527     nrows       = 0;
528     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
529       nzi = coi[i+1] - coi[i];
530       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
531       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
532       nrows++;
533     }
534     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
535     k++;
536     buf_si += len_si[proc];
537   }
538   for (i=0; i<nrecv; i++) {
539     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
540   }
541   ierr = PetscFree(rwaits);CHKERRQ(ierr);
542   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
543 
544   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
545   ierr = PetscFree(len_ri);CHKERRQ(ierr);
546   ierr = PetscFree(swaits);CHKERRQ(ierr);
547   ierr = PetscFree(buf_s);CHKERRQ(ierr);
548 
549   /* (5) compute the local portion of Cmpi      */
550   /* ------------------------------------------ */
551   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
552   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
553   current_space = free_space;
554 
555   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
556   for (k=0; k<nrecv; k++) {
557     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
558     nrows       = *buf_ri_k[k];
559     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
560     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
561   }
562 
563   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
564   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
565   for (i=0; i<pn; i++) {
566     /* add C_loc into Cmpi */
567     nzi  = c_loc->i[i+1] - c_loc->i[i];
568     Jptr = c_loc->j + c_loc->i[i];
569     ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
570 
571     /* add received col data into lnk */
572     for (k=0; k<nrecv; k++) { /* k-th received message */
573       if (i == *nextrow[k]) { /* i-th row */
574         nzi  = *(nextci[k]+1) - *nextci[k];
575         Jptr = buf_rj[k] + *nextci[k];
576         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
577         nextrow[k]++; nextci[k]++;
578       }
579     }
580     nzi = lnk[0];
581 
582     /* copy data into free space, then initialize lnk */
583     ierr = PetscLLCondensedClean_Scalable(nzi,current_space->array,lnk);CHKERRQ(ierr);
584     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
585   }
586   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
587   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
588   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
589 
590   /* local sizes and preallocation */
591   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
592   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
593   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
594   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
595 
596   /* members in merge */
597   ierr = PetscFree(id_r);CHKERRQ(ierr);
598   ierr = PetscFree(len_r);CHKERRQ(ierr);
599   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
600   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
601   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
602   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
603   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
604 
605   /* attach the supporting struct to Cmpi for reuse */
606   c = (Mat_MPIAIJ*)Cmpi->data;
607   c->ptap         = ptap;
608   ptap->duplicate = Cmpi->ops->duplicate;
609   ptap->destroy   = Cmpi->ops->destroy;
610   ptap->view      = Cmpi->ops->view;
611 
612   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
613   Cmpi->assembled        = PETSC_FALSE;
614   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable;
615   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
616   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
617   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
618   *C                     = Cmpi;
619   PetscFunctionReturn(0);
620 }
621 
622 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
623 {
624   PetscErrorCode      ierr;
625   Mat_PtAPMPI         *ptap;
626   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
627   MPI_Comm            comm;
628   PetscMPIInt         size,rank;
629   Mat                 Cmpi;
630   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
631   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
632   PetscInt            *lnk,i,k,pnz,row,nsend;
633   PetscBT             lnkbt;
634   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
635   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
636   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
637   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
638   MPI_Request         *swaits,*rwaits;
639   MPI_Status          *sstatus,rstatus;
640   PetscLayout         rowmap;
641   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
642   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
643   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,ap_rmax=0,Crmax,*aj,*ai,*pi;
644   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
645   PetscScalar         *apv;
646   PetscTable          ta;
647 #if defined(PETSC_USE_INFO)
648   PetscReal           apfill;
649 #endif
650 
651   PetscFunctionBegin;
652   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
653   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
654   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
655 
656   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
657 
658   /* create symbolic parallel matrix Cmpi */
659   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
660   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
661 
662   /* Do dense axpy in MatPtAPNumeric_MPIAIJ_MPIAIJ() */
663   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ;
664 
665   /* create struct Mat_PtAPMPI and attached it to C later */
666   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
667   ptap->reuse = MAT_INITIAL_MATRIX;
668   ptap->algType = 1;
669 
670   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
671   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
672   /* get P_loc by taking all local rows of P */
673   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
674 
675   /* (0) compute Rd = Pd^T, Ro = Po^T  */
676   /* --------------------------------- */
677   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
678   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
679 
680   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
681   /* ----------------------------------------------------------------- */
682   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
683   if (ptap->P_oth) p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
684 
685   /* create and initialize a linked list */
686   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
687   MatRowMergeMax_SeqAIJ(p_loc,ptap->P_loc->rmap->N,ta);
688   MatRowMergeMax_SeqAIJ(p_oth,ptap->P_oth->rmap->N,ta);
689   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
690   /* printf("[%d] est %d, Crmax %d; pN %d\n",rank,5*(p_loc->rmax+p_oth->rmax + (PetscInt)(1.e-2*pN)),Crmax,pN); */
691 
692   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
693 
694   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
695   if (ao) {
696     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
697   } else {
698     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
699   }
700   current_space = free_space;
701   nspacedouble  = 0;
702 
703   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
704   api[0] = 0;
705   for (i=0; i<am; i++) {
706     /* diagonal portion: Ad[i,:]*P */
707     ai = ad->i; pi = p_loc->i;
708     nzi = ai[i+1] - ai[i];
709     aj  = ad->j + ai[i];
710     for (j=0; j<nzi; j++) {
711       row  = aj[j];
712       pnz  = pi[row+1] - pi[row];
713       Jptr = p_loc->j + pi[row];
714       /* add non-zero cols of P into the sorted linked list lnk */
715       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
716     }
717     /* off-diagonal portion: Ao[i,:]*P */
718     if (ao) {
719       ai = ao->i; pi = p_oth->i;
720       nzi = ai[i+1] - ai[i];
721       aj  = ao->j + ai[i];
722       for (j=0; j<nzi; j++) {
723         row  = aj[j];
724         pnz  = pi[row+1] - pi[row];
725         Jptr = p_oth->j + pi[row];
726         ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
727       }
728     }
729     apnz     = lnk[0];
730     api[i+1] = api[i] + apnz;
731     if (ap_rmax < apnz) ap_rmax = apnz;
732 
733     /* if free space is not available, double the total space in the list */
734     if (current_space->local_remaining<apnz) {
735       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
736       nspacedouble++;
737     }
738 
739     /* Copy data into free space, then initialize lnk */
740     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
741 
742     current_space->array           += apnz;
743     current_space->local_used      += apnz;
744     current_space->local_remaining -= apnz;
745   }
746   /* Allocate space for apj and apv, initialize apj, and */
747   /* destroy list of free space and other temporary array(s) */
748   ierr   = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
749   ierr   = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
750   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
751 
752   /* Create AP_loc for reuse */
753   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
754 
755 #if defined(PETSC_USE_INFO)
756   if (ao) {
757     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
758   } else {
759     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
760   }
761   ptap->AP_loc->info.mallocs           = nspacedouble;
762   ptap->AP_loc->info.fill_ratio_given  = fill;
763   ptap->AP_loc->info.fill_ratio_needed = apfill;
764 
765   if (api[am]) {
766     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);
767     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
768   } else {
769     ierr = PetscInfo(ptap->AP_loc,"Nonscalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
770   }
771 #endif
772 
773   /* (2-1) compute symbolic Co = Ro*AP_loc  */
774   /* ------------------------------------ */
775   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
776 
777   /* (3) send coj of C_oth to other processors  */
778   /* ------------------------------------------ */
779   /* determine row ownership */
780   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
781   rowmap->n  = pn;
782   rowmap->bs = 1;
783   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
784   owners = rowmap->range;
785 
786   /* determine the number of messages to send, their lengths */
787   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
788   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
789   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
790 
791   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
792   coi   = c_oth->i; coj = c_oth->j;
793   con   = ptap->C_oth->rmap->n;
794   proc  = 0;
795   for (i=0; i<con; i++) {
796     while (prmap[i] >= owners[proc+1]) proc++;
797     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
798     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
799   }
800 
801   len          = 0; /* max length of buf_si[], see (4) */
802   owners_co[0] = 0;
803   nsend        = 0;
804   for (proc=0; proc<size; proc++) {
805     owners_co[proc+1] = owners_co[proc] + len_si[proc];
806     if (len_s[proc]) {
807       nsend++;
808       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
809       len         += len_si[proc];
810     }
811   }
812 
813   /* determine the number and length of messages to receive for coi and coj  */
814   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
815   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
816 
817   /* post the Irecv and Isend of coj */
818   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
819   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
820   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
821   for (proc=0, k=0; proc<size; proc++) {
822     if (!len_s[proc]) continue;
823     i    = owners_co[proc];
824     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
825     k++;
826   }
827 
828   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
829   /* ---------------------------------------- */
830   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
831   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
832 
833   /* receives coj are complete */
834   for (i=0; i<nrecv; i++) {
835     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
836   }
837   ierr = PetscFree(rwaits);CHKERRQ(ierr);
838   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
839 
840   /* add received column indices into ta to update Crmax */
841   for (k=0; k<nrecv; k++) {/* k-th received message */
842     Jptr = buf_rj[k];
843     for (j=0; j<len_r[k]; j++) {
844       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
845     }
846   }
847   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
848   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
849 
850   /* (4) send and recv coi */
851   /*-----------------------*/
852   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
853   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
854   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
855   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
856   for (proc=0,k=0; proc<size; proc++) {
857     if (!len_s[proc]) continue;
858     /* form outgoing message for i-structure:
859          buf_si[0]:                 nrows to be sent
860                [1:nrows]:           row index (global)
861                [nrows+1:2*nrows+1]: i-structure index
862     */
863     /*-------------------------------------------*/
864     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
865     buf_si_i    = buf_si + nrows+1;
866     buf_si[0]   = nrows;
867     buf_si_i[0] = 0;
868     nrows       = 0;
869     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
870       nzi = coi[i+1] - coi[i];
871       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
872       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
873       nrows++;
874     }
875     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
876     k++;
877     buf_si += len_si[proc];
878   }
879   for (i=0; i<nrecv; i++) {
880     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
881   }
882   ierr = PetscFree(rwaits);CHKERRQ(ierr);
883   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
884 
885   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
886   ierr = PetscFree(len_ri);CHKERRQ(ierr);
887   ierr = PetscFree(swaits);CHKERRQ(ierr);
888   ierr = PetscFree(buf_s);CHKERRQ(ierr);
889 
890   /* (5) compute the local portion of Cmpi      */
891   /* ------------------------------------------ */
892   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
893   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
894   current_space = free_space;
895 
896   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
897   for (k=0; k<nrecv; k++) {
898     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
899     nrows       = *buf_ri_k[k];
900     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
901     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
902   }
903 
904   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
905   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
906   for (i=0; i<pn; i++) {
907     /* add C_loc into Cmpi */
908     nzi  = c_loc->i[i+1] - c_loc->i[i];
909     Jptr = c_loc->j + c_loc->i[i];
910     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
911 
912     /* add received col data into lnk */
913     for (k=0; k<nrecv; k++) { /* k-th received message */
914       if (i == *nextrow[k]) { /* i-th row */
915         nzi  = *(nextci[k]+1) - *nextci[k];
916         Jptr = buf_rj[k] + *nextci[k];
917         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
918         nextrow[k]++; nextci[k]++;
919       }
920     }
921     nzi = lnk[0];
922 
923     /* copy data into free space, then initialize lnk */
924     ierr = PetscLLCondensedClean(pN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
925     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
926   }
927   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
928   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
929   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
930 
931   /* local sizes and preallocation */
932   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
933   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
934   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
935   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
936 
937   /* members in merge */
938   ierr = PetscFree(id_r);CHKERRQ(ierr);
939   ierr = PetscFree(len_r);CHKERRQ(ierr);
940   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
941   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
942   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
943   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
944   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
945 
946   /* attach the supporting struct to Cmpi for reuse */
947   c = (Mat_MPIAIJ*)Cmpi->data;
948   c->ptap         = ptap;
949   ptap->duplicate = Cmpi->ops->duplicate;
950   ptap->destroy   = Cmpi->ops->destroy;
951   ptap->view      = Cmpi->ops->view;
952   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
953 
954   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
955   Cmpi->assembled        = PETSC_FALSE;
956   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
957   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
958   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
959   *C                     = Cmpi;
960   PetscFunctionReturn(0);
961 }
962 
963 
964 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
965 {
966   PetscErrorCode    ierr;
967   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
968   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
969   Mat_SeqAIJ        *ap,*p_loc,*p_oth=NULL,*c_seq;
970   Mat_PtAPMPI       *ptap = c->ptap;
971   Mat               AP_loc,C_loc,C_oth;
972   PetscInt          i,rstart,rend,cm,ncols,row;
973   PetscInt          *api,*apj,am = A->rmap->n,j,col,apnz;
974   PetscScalar       *apa;
975   const PetscInt    *cols;
976   const PetscScalar *vals;
977 
978   PetscFunctionBegin;
979   ierr = MatZeroEntries(C);CHKERRQ(ierr);
980   /* 1) get R = Pd^T,Ro = Po^T */
981   if (ptap->reuse == MAT_REUSE_MATRIX) {
982     ierr = MatTranspose(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
983     ierr = MatTranspose(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
984   }
985 
986   /* 2) get AP_loc */
987   AP_loc = ptap->AP_loc;
988   ap = (Mat_SeqAIJ*)AP_loc->data;
989 
990   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
991   /*-----------------------------------------------------*/
992   if (ptap->reuse == MAT_REUSE_MATRIX) {
993     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
994     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
995     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
996   }
997 
998   /* 2-2) compute numeric A_loc*P - dominating part */
999   /* ---------------------------------------------- */
1000   /* get data from symbolic products */
1001   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1002   if (ptap->P_oth) {
1003     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1004   }
1005   apa   = ptap->apa;
1006   api   = ap->i;
1007   apj   = ap->j;
1008   for (i=0; i<am; i++) {
1009     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
1010     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
1011     apnz = api[i+1] - api[i];
1012     for (j=0; j<apnz; j++) {
1013       col = apj[j+api[i]];
1014       ap->a[j+ap->i[i]] = apa[col];
1015       apa[col] = 0.0;
1016     }
1017     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
1018   }
1019 
1020   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
1021   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
1022   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
1023   C_loc = ptap->C_loc;
1024   C_oth = ptap->C_oth;
1025 
1026   /* add C_loc and Co to to C */
1027   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1028 
1029   /* C_loc -> C */
1030   cm    = C_loc->rmap->N;
1031   c_seq = (Mat_SeqAIJ*)C_loc->data;
1032   cols = c_seq->j;
1033   vals = c_seq->a;
1034 
1035 
1036   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assembled is PETSC_FALSE and */
1037   /* when there are no off-processor parts.  */
1038   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
1039   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
1040   /* a table, and other, more complex stuff has to be done. */
1041   if (C->assembled) {
1042     C->was_assembled = PETSC_TRUE;
1043     C->assembled     = PETSC_FALSE;
1044   }
1045   if (C->was_assembled) {
1046     for (i=0; i<cm; i++) {
1047       ncols = c_seq->i[i+1] - c_seq->i[i];
1048       row = rstart + i;
1049       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1050       cols += ncols; vals += ncols;
1051     }
1052   } else {
1053     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
1054   }
1055 
1056   /* Co -> C, off-processor part */
1057   cm = C_oth->rmap->N;
1058   c_seq = (Mat_SeqAIJ*)C_oth->data;
1059   cols = c_seq->j;
1060   vals = c_seq->a;
1061   for (i=0; i<cm; i++) {
1062     ncols = c_seq->i[i+1] - c_seq->i[i];
1063     row = p->garray[i];
1064     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1065     cols += ncols; vals += ncols;
1066   }
1067 
1068   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1069   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1070 
1071   ptap->reuse = MAT_REUSE_MATRIX;
1072   PetscFunctionReturn(0);
1073 }
1074