xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision 487a658c8b32ba712a1dc8280daad2fd70c1dcd9)
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        *ap,*p_loc,*p_oth,*c_seq;
183   Mat_PtAPMPI       *ptap = c->ptap;
184   Mat               AP_loc,C_loc,C_oth;
185   PetscInt          i,rstart,rend,cm,ncols,row,*api,*apj,am = A->rmap->n,apnz;
186   PetscScalar       *apa;
187   const PetscInt    *cols;
188   const PetscScalar *vals;
189 
190   PetscFunctionBegin;
191   ierr = MatZeroEntries(C);CHKERRQ(ierr);
192 
193   /* 1) get R = Pd^T,Ro = Po^T */
194   if (ptap->reuse == MAT_REUSE_MATRIX) {
195     ierr = MatTranspose(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
196     ierr = MatTranspose(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
197   }
198 
199   /* 2) get AP_loc */
200   AP_loc = ptap->AP_loc;
201   ap = (Mat_SeqAIJ*)AP_loc->data;
202 
203   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
204   /*-----------------------------------------------------*/
205   if (ptap->reuse == MAT_REUSE_MATRIX) {
206     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
207     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
208     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
209   }
210 
211   /* 2-2) compute numeric A_loc*P - dominating part */
212   /* ---------------------------------------------- */
213   /* get data from symbolic products */
214   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
215   if (ptap->P_oth) p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
216   else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"ptap->P_oth is NULL. Cannot proceed!");
217 
218   api   = ap->i;
219   apj   = ap->j;
220   for (i=0; i<am; i++) {
221     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
222     apnz = api[i+1] - api[i];
223     apa = ap->a + api[i];
224     ierr = PetscMemzero(apa,sizeof(PetscScalar)*apnz);CHKERRQ(ierr);
225     AProw_scalable(i,ad,ao,p_loc,p_oth,api,apj,apa);
226     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
227   }
228 
229   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
230   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
231   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
232 
233   C_loc = ptap->C_loc;
234   C_oth = ptap->C_oth;
235 
236   /* add C_loc and Co to to C */
237   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
238 
239   /* C_loc -> C */
240   cm    = C_loc->rmap->N;
241   c_seq = (Mat_SeqAIJ*)C_loc->data;
242   cols = c_seq->j;
243   vals = c_seq->a;
244 
245   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assembled is PETSC_FALSE and */
246   /* when there are no off-processor parts.  */
247   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
248   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
249   /* a table, and other, more complex stuff has to be done. */
250   if (C->assembled) {
251     C->was_assembled = PETSC_TRUE;
252     C->assembled     = PETSC_FALSE;
253   }
254   if (C->was_assembled) {
255     for (i=0; i<cm; i++) {
256       ncols = c_seq->i[i+1] - c_seq->i[i];
257       row = rstart + i;
258       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
259       cols += ncols; vals += ncols;
260     }
261   } else {
262     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
263   }
264 
265   /* Co -> C, off-processor part */
266   cm = C_oth->rmap->N;
267   c_seq = (Mat_SeqAIJ*)C_oth->data;
268   cols = c_seq->j;
269   vals = c_seq->a;
270   for (i=0; i<cm; i++) {
271     ncols = c_seq->i[i+1] - c_seq->i[i];
272     row = p->garray[i];
273     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
274     cols += ncols; vals += ncols;
275   }
276   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
277   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
278 
279   ptap->reuse = MAT_REUSE_MATRIX;
280   PetscFunctionReturn(0);
281 }
282 
283 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,PetscReal fill,Mat *C)
284 {
285   PetscErrorCode      ierr;
286   Mat_PtAPMPI         *ptap;
287   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
288   MPI_Comm            comm;
289   PetscMPIInt         size,rank;
290   Mat                 Cmpi,P_loc,P_oth;
291   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
292   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
293   PetscInt            *lnk,i,k,pnz,row,nsend;
294   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
295   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
296   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
297   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
298   MPI_Request         *swaits,*rwaits;
299   MPI_Status          *sstatus,rstatus;
300   PetscLayout         rowmap;
301   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
302   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
303   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,Crmax,*aj,*ai,*pi;
304   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
305   PetscScalar         *apv;
306   PetscTable          ta;
307 #if defined(PETSC_USE_INFO)
308   PetscReal           apfill;
309 #endif
310 
311   PetscFunctionBegin;
312   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
313   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
314   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
315 
316   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
317 
318   /* create symbolic parallel matrix Cmpi */
319   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
320   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
321 
322   /* create struct Mat_PtAPMPI and attached it to C later */
323   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
324   ptap->reuse = MAT_INITIAL_MATRIX;
325   ptap->algType = 0;
326 
327   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
328   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&P_oth);CHKERRQ(ierr);
329   /* get P_loc by taking all local rows of P */
330   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&P_loc);CHKERRQ(ierr);
331 
332   ptap->P_loc = P_loc;
333   ptap->P_oth = P_oth;
334 
335   /* (0) compute Rd = Pd^T, Ro = Po^T  */
336   /* --------------------------------- */
337   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
338   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
339 
340   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
341   /* ----------------------------------------------------------------- */
342   p_loc  = (Mat_SeqAIJ*)P_loc->data;
343   if (P_oth) p_oth = (Mat_SeqAIJ*)P_oth->data;
344 
345   /* create and initialize a linked list */
346   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
347   MatRowMergeMax_SeqAIJ(p_loc,P_loc->rmap->N,ta);
348   MatRowMergeMax_SeqAIJ(p_oth,P_oth->rmap->N,ta);
349   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
350 
351   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
352 
353   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
354   if (ao) {
355     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
356   } else {
357     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
358   }
359   current_space = free_space;
360   nspacedouble  = 0;
361 
362   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
363   api[0] = 0;
364   for (i=0; i<am; i++) {
365     /* diagonal portion: Ad[i,:]*P */
366     ai = ad->i; pi = p_loc->i;
367     nzi = ai[i+1] - ai[i];
368     aj  = ad->j + ai[i];
369     for (j=0; j<nzi; j++) {
370       row  = aj[j];
371       pnz  = pi[row+1] - pi[row];
372       Jptr = p_loc->j + pi[row];
373       /* add non-zero cols of P into the sorted linked list lnk */
374       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
375     }
376     /* off-diagonal portion: Ao[i,:]*P */
377     if (ao) {
378       ai = ao->i; pi = p_oth->i;
379       nzi = ai[i+1] - ai[i];
380       aj  = ao->j + ai[i];
381       for (j=0; j<nzi; j++) {
382         row  = aj[j];
383         pnz  = pi[row+1] - pi[row];
384         Jptr = p_oth->j + pi[row];
385         ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
386       }
387     }
388     apnz     = lnk[0];
389     api[i+1] = api[i] + apnz;
390 
391     /* if free space is not available, double the total space in the list */
392     if (current_space->local_remaining<apnz) {
393       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
394       nspacedouble++;
395     }
396 
397     /* Copy data into free space, then initialize lnk */
398     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
399 
400     current_space->array           += apnz;
401     current_space->local_used      += apnz;
402     current_space->local_remaining -= apnz;
403   }
404   /* Allocate space for apj and apv, initialize apj, and */
405   /* destroy list of free space and other temporary array(s) */
406   ierr = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
407   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
408   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
409 
410   /* Create AP_loc for reuse */
411   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
412 
413 #if defined(PETSC_USE_INFO)
414   if (ao) {
415     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
416   } else {
417     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
418   }
419   ptap->AP_loc->info.mallocs           = nspacedouble;
420   ptap->AP_loc->info.fill_ratio_given  = fill;
421   ptap->AP_loc->info.fill_ratio_needed = apfill;
422 
423   if (api[am]) {
424     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);
425     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
426   } else {
427     ierr = PetscInfo(ptap->AP_loc,"Scalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
428   }
429 #endif
430 
431   /* (2-1) compute symbolic Co = Ro*AP_loc  */
432   /* ------------------------------------ */
433   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
434 
435   /* (3) send coj of C_oth to other processors  */
436   /* ------------------------------------------ */
437   /* determine row ownership */
438   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
439   rowmap->n  = pn;
440   rowmap->bs = 1;
441   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
442   owners = rowmap->range;
443 
444   /* determine the number of messages to send, their lengths */
445   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
446   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
447   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
448 
449   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
450   coi   = c_oth->i; coj = c_oth->j;
451   con   = ptap->C_oth->rmap->n;
452   proc  = 0;
453   for (i=0; i<con; i++) {
454     while (prmap[i] >= owners[proc+1]) proc++;
455     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
456     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
457   }
458 
459   len          = 0; /* max length of buf_si[], see (4) */
460   owners_co[0] = 0;
461   nsend        = 0;
462   for (proc=0; proc<size; proc++) {
463     owners_co[proc+1] = owners_co[proc] + len_si[proc];
464     if (len_s[proc]) {
465       nsend++;
466       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
467       len         += len_si[proc];
468     }
469   }
470 
471   /* determine the number and length of messages to receive for coi and coj  */
472   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
473   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
474 
475   /* post the Irecv and Isend of coj */
476   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
477   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
478   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
479   for (proc=0, k=0; proc<size; proc++) {
480     if (!len_s[proc]) continue;
481     i    = owners_co[proc];
482     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
483     k++;
484   }
485 
486   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
487   /* ---------------------------------------- */
488   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
489   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
490 
491   /* receives coj are complete */
492   for (i=0; i<nrecv; i++) {
493     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
494   }
495   ierr = PetscFree(rwaits);CHKERRQ(ierr);
496   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
497 
498   /* add received column indices into ta to update Crmax */
499   for (k=0; k<nrecv; k++) {/* k-th received message */
500     Jptr = buf_rj[k];
501     for (j=0; j<len_r[k]; j++) {
502       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
503     }
504   }
505   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
506   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
507 
508   /* (4) send and recv coi */
509   /*-----------------------*/
510   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
511   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
512   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
513   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
514   for (proc=0,k=0; proc<size; proc++) {
515     if (!len_s[proc]) continue;
516     /* form outgoing message for i-structure:
517          buf_si[0]:                 nrows to be sent
518                [1:nrows]:           row index (global)
519                [nrows+1:2*nrows+1]: i-structure index
520     */
521     /*-------------------------------------------*/
522     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
523     buf_si_i    = buf_si + nrows+1;
524     buf_si[0]   = nrows;
525     buf_si_i[0] = 0;
526     nrows       = 0;
527     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
528       nzi = coi[i+1] - coi[i];
529       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
530       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
531       nrows++;
532     }
533     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
534     k++;
535     buf_si += len_si[proc];
536   }
537   for (i=0; i<nrecv; i++) {
538     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
539   }
540   ierr = PetscFree(rwaits);CHKERRQ(ierr);
541   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
542 
543   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
544   ierr = PetscFree(len_ri);CHKERRQ(ierr);
545   ierr = PetscFree(swaits);CHKERRQ(ierr);
546   ierr = PetscFree(buf_s);CHKERRQ(ierr);
547 
548   /* (5) compute the local portion of Cmpi      */
549   /* ------------------------------------------ */
550   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
551   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
552   current_space = free_space;
553 
554   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
555   for (k=0; k<nrecv; k++) {
556     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
557     nrows       = *buf_ri_k[k];
558     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
559     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
560   }
561 
562   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
563   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
564   for (i=0; i<pn; i++) {
565     /* add C_loc into Cmpi */
566     nzi  = c_loc->i[i+1] - c_loc->i[i];
567     Jptr = c_loc->j + c_loc->i[i];
568     ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
569 
570     /* add received col data into lnk */
571     for (k=0; k<nrecv; k++) { /* k-th received message */
572       if (i == *nextrow[k]) { /* i-th row */
573         nzi  = *(nextci[k]+1) - *nextci[k];
574         Jptr = buf_rj[k] + *nextci[k];
575         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
576         nextrow[k]++; nextci[k]++;
577       }
578     }
579     nzi = lnk[0];
580 
581     /* copy data into free space, then initialize lnk */
582     ierr = PetscLLCondensedClean_Scalable(nzi,current_space->array,lnk);CHKERRQ(ierr);
583     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
584   }
585   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
586   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
587   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
588 
589   /* local sizes and preallocation */
590   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
591   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
592   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
593   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
594 
595   /* members in merge */
596   ierr = PetscFree(id_r);CHKERRQ(ierr);
597   ierr = PetscFree(len_r);CHKERRQ(ierr);
598   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
599   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
600   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
601   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
602   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
603 
604   /* attach the supporting struct to Cmpi for reuse */
605   c = (Mat_MPIAIJ*)Cmpi->data;
606   c->ptap         = ptap;
607   ptap->duplicate = Cmpi->ops->duplicate;
608   ptap->destroy   = Cmpi->ops->destroy;
609   ptap->view      = Cmpi->ops->view;
610 
611   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
612   Cmpi->assembled        = PETSC_FALSE;
613   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable;
614   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
615   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
616   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
617   *C                     = Cmpi;
618   PetscFunctionReturn(0);
619 }
620 
621 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
622 {
623   PetscErrorCode      ierr;
624   Mat_PtAPMPI         *ptap;
625   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
626   MPI_Comm            comm;
627   PetscMPIInt         size,rank;
628   Mat                 Cmpi;
629   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
630   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
631   PetscInt            *lnk,i,k,pnz,row,nsend;
632   PetscBT             lnkbt;
633   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
634   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
635   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
636   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
637   MPI_Request         *swaits,*rwaits;
638   MPI_Status          *sstatus,rstatus;
639   PetscLayout         rowmap;
640   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
641   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
642   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,ap_rmax=0,Crmax,*aj,*ai,*pi;
643   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
644   PetscScalar         *apv;
645   PetscTable          ta;
646 #if defined(PETSC_USE_INFO)
647   PetscReal           apfill;
648 #endif
649 
650   PetscFunctionBegin;
651   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
652   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
653   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
654 
655   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
656 
657   /* create symbolic parallel matrix Cmpi */
658   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
659   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
660 
661   /* Do dense axpy in MatPtAPNumeric_MPIAIJ_MPIAIJ() */
662   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ;
663 
664   /* create struct Mat_PtAPMPI and attached it to C later */
665   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
666   ptap->reuse = MAT_INITIAL_MATRIX;
667   ptap->algType = 1;
668 
669   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
670   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
671   /* get P_loc by taking all local rows of P */
672   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
673 
674   /* (0) compute Rd = Pd^T, Ro = Po^T  */
675   /* --------------------------------- */
676   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
677   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
678 
679   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
680   /* ----------------------------------------------------------------- */
681   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
682   if (ptap->P_oth) p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
683 
684   /* create and initialize a linked list */
685   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
686   MatRowMergeMax_SeqAIJ(p_loc,ptap->P_loc->rmap->N,ta);
687   MatRowMergeMax_SeqAIJ(p_oth,ptap->P_oth->rmap->N,ta);
688   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
689   /* printf("[%d] est %d, Crmax %d; pN %d\n",rank,5*(p_loc->rmax+p_oth->rmax + (PetscInt)(1.e-2*pN)),Crmax,pN); */
690 
691   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
692 
693   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
694   if (ao) {
695     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
696   } else {
697     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
698   }
699   current_space = free_space;
700   nspacedouble  = 0;
701 
702   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
703   api[0] = 0;
704   for (i=0; i<am; i++) {
705     /* diagonal portion: Ad[i,:]*P */
706     ai = ad->i; pi = p_loc->i;
707     nzi = ai[i+1] - ai[i];
708     aj  = ad->j + ai[i];
709     for (j=0; j<nzi; j++) {
710       row  = aj[j];
711       pnz  = pi[row+1] - pi[row];
712       Jptr = p_loc->j + pi[row];
713       /* add non-zero cols of P into the sorted linked list lnk */
714       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
715     }
716     /* off-diagonal portion: Ao[i,:]*P */
717     if (ao) {
718       ai = ao->i; pi = p_oth->i;
719       nzi = ai[i+1] - ai[i];
720       aj  = ao->j + ai[i];
721       for (j=0; j<nzi; j++) {
722         row  = aj[j];
723         pnz  = pi[row+1] - pi[row];
724         Jptr = p_oth->j + pi[row];
725         ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
726       }
727     }
728     apnz     = lnk[0];
729     api[i+1] = api[i] + apnz;
730     if (ap_rmax < apnz) ap_rmax = apnz;
731 
732     /* if free space is not available, double the total space in the list */
733     if (current_space->local_remaining<apnz) {
734       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
735       nspacedouble++;
736     }
737 
738     /* Copy data into free space, then initialize lnk */
739     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
740 
741     current_space->array           += apnz;
742     current_space->local_used      += apnz;
743     current_space->local_remaining -= apnz;
744   }
745   /* Allocate space for apj and apv, initialize apj, and */
746   /* destroy list of free space and other temporary array(s) */
747   ierr   = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
748   ierr   = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
749   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
750 
751   /* Create AP_loc for reuse */
752   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
753 
754 #if defined(PETSC_USE_INFO)
755   if (ao) {
756     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
757   } else {
758     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
759   }
760   ptap->AP_loc->info.mallocs           = nspacedouble;
761   ptap->AP_loc->info.fill_ratio_given  = fill;
762   ptap->AP_loc->info.fill_ratio_needed = apfill;
763 
764   if (api[am]) {
765     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);
766     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
767   } else {
768     ierr = PetscInfo(ptap->AP_loc,"Nonscalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
769   }
770 #endif
771 
772   /* (2-1) compute symbolic Co = Ro*AP_loc  */
773   /* ------------------------------------ */
774   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
775 
776   /* (3) send coj of C_oth to other processors  */
777   /* ------------------------------------------ */
778   /* determine row ownership */
779   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
780   rowmap->n  = pn;
781   rowmap->bs = 1;
782   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
783   owners = rowmap->range;
784 
785   /* determine the number of messages to send, their lengths */
786   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
787   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
788   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
789 
790   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
791   coi   = c_oth->i; coj = c_oth->j;
792   con   = ptap->C_oth->rmap->n;
793   proc  = 0;
794   for (i=0; i<con; i++) {
795     while (prmap[i] >= owners[proc+1]) proc++;
796     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
797     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
798   }
799 
800   len          = 0; /* max length of buf_si[], see (4) */
801   owners_co[0] = 0;
802   nsend        = 0;
803   for (proc=0; proc<size; proc++) {
804     owners_co[proc+1] = owners_co[proc] + len_si[proc];
805     if (len_s[proc]) {
806       nsend++;
807       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
808       len         += len_si[proc];
809     }
810   }
811 
812   /* determine the number and length of messages to receive for coi and coj  */
813   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
814   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
815 
816   /* post the Irecv and Isend of coj */
817   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
818   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
819   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
820   for (proc=0, k=0; proc<size; proc++) {
821     if (!len_s[proc]) continue;
822     i    = owners_co[proc];
823     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
824     k++;
825   }
826 
827   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
828   /* ---------------------------------------- */
829   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
830   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
831 
832   /* receives coj are complete */
833   for (i=0; i<nrecv; i++) {
834     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
835   }
836   ierr = PetscFree(rwaits);CHKERRQ(ierr);
837   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
838 
839   /* add received column indices into ta to update Crmax */
840   for (k=0; k<nrecv; k++) {/* k-th received message */
841     Jptr = buf_rj[k];
842     for (j=0; j<len_r[k]; j++) {
843       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
844     }
845   }
846   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
847   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
848 
849   /* (4) send and recv coi */
850   /*-----------------------*/
851   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
852   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
853   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
854   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
855   for (proc=0,k=0; proc<size; proc++) {
856     if (!len_s[proc]) continue;
857     /* form outgoing message for i-structure:
858          buf_si[0]:                 nrows to be sent
859                [1:nrows]:           row index (global)
860                [nrows+1:2*nrows+1]: i-structure index
861     */
862     /*-------------------------------------------*/
863     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
864     buf_si_i    = buf_si + nrows+1;
865     buf_si[0]   = nrows;
866     buf_si_i[0] = 0;
867     nrows       = 0;
868     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
869       nzi = coi[i+1] - coi[i];
870       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
871       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
872       nrows++;
873     }
874     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
875     k++;
876     buf_si += len_si[proc];
877   }
878   for (i=0; i<nrecv; i++) {
879     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
880   }
881   ierr = PetscFree(rwaits);CHKERRQ(ierr);
882   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
883 
884   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
885   ierr = PetscFree(len_ri);CHKERRQ(ierr);
886   ierr = PetscFree(swaits);CHKERRQ(ierr);
887   ierr = PetscFree(buf_s);CHKERRQ(ierr);
888 
889   /* (5) compute the local portion of Cmpi      */
890   /* ------------------------------------------ */
891   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
892   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
893   current_space = free_space;
894 
895   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
896   for (k=0; k<nrecv; k++) {
897     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
898     nrows       = *buf_ri_k[k];
899     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
900     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
901   }
902 
903   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
904   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
905   for (i=0; i<pn; i++) {
906     /* add C_loc into Cmpi */
907     nzi  = c_loc->i[i+1] - c_loc->i[i];
908     Jptr = c_loc->j + c_loc->i[i];
909     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
910 
911     /* add received col data into lnk */
912     for (k=0; k<nrecv; k++) { /* k-th received message */
913       if (i == *nextrow[k]) { /* i-th row */
914         nzi  = *(nextci[k]+1) - *nextci[k];
915         Jptr = buf_rj[k] + *nextci[k];
916         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
917         nextrow[k]++; nextci[k]++;
918       }
919     }
920     nzi = lnk[0];
921 
922     /* copy data into free space, then initialize lnk */
923     ierr = PetscLLCondensedClean(pN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
924     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
925   }
926   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
927   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
928   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
929 
930   /* local sizes and preallocation */
931   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
932   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
933   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
934   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
935 
936   /* members in merge */
937   ierr = PetscFree(id_r);CHKERRQ(ierr);
938   ierr = PetscFree(len_r);CHKERRQ(ierr);
939   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
940   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
941   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
942   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
943   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
944 
945   /* attach the supporting struct to Cmpi for reuse */
946   c = (Mat_MPIAIJ*)Cmpi->data;
947   c->ptap         = ptap;
948   ptap->duplicate = Cmpi->ops->duplicate;
949   ptap->destroy   = Cmpi->ops->destroy;
950   ptap->view      = Cmpi->ops->view;
951   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
952 
953   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
954   Cmpi->assembled        = PETSC_FALSE;
955   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
956   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
957   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
958   *C                     = Cmpi;
959   PetscFunctionReturn(0);
960 }
961 
962 
963 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
964 {
965   PetscErrorCode    ierr;
966   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
967   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
968   Mat_SeqAIJ        *ap,*p_loc,*p_oth=NULL,*c_seq;
969   Mat_PtAPMPI       *ptap = c->ptap;
970   Mat               AP_loc,C_loc,C_oth;
971   PetscInt          i,rstart,rend,cm,ncols,row;
972   PetscInt          *api,*apj,am = A->rmap->n,j,col,apnz;
973   PetscScalar       *apa;
974   const PetscInt    *cols;
975   const PetscScalar *vals;
976 
977   PetscFunctionBegin;
978   ierr = MatZeroEntries(C);CHKERRQ(ierr);
979   /* 1) get R = Pd^T,Ro = Po^T */
980   if (ptap->reuse == MAT_REUSE_MATRIX) {
981     ierr = MatTranspose(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
982     ierr = MatTranspose(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
983   }
984 
985   /* 2) get AP_loc */
986   AP_loc = ptap->AP_loc;
987   ap = (Mat_SeqAIJ*)AP_loc->data;
988 
989   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
990   /*-----------------------------------------------------*/
991   if (ptap->reuse == MAT_REUSE_MATRIX) {
992     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
993     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
994     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
995   }
996 
997   /* 2-2) compute numeric A_loc*P - dominating part */
998   /* ---------------------------------------------- */
999   /* get data from symbolic products */
1000   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1001   if (ptap->P_oth) {
1002     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1003   }
1004   apa   = ptap->apa;
1005   api   = ap->i;
1006   apj   = ap->j;
1007   for (i=0; i<am; i++) {
1008     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
1009     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
1010     apnz = api[i+1] - api[i];
1011     for (j=0; j<apnz; j++) {
1012       col = apj[j+api[i]];
1013       ap->a[j+ap->i[i]] = apa[col];
1014       apa[col] = 0.0;
1015     }
1016     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
1017   }
1018 
1019   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
1020   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
1021   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
1022   C_loc = ptap->C_loc;
1023   C_oth = ptap->C_oth;
1024 
1025   /* add C_loc and Co to to C */
1026   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1027 
1028   /* C_loc -> C */
1029   cm    = C_loc->rmap->N;
1030   c_seq = (Mat_SeqAIJ*)C_loc->data;
1031   cols = c_seq->j;
1032   vals = c_seq->a;
1033 
1034 
1035   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assembled is PETSC_FALSE and */
1036   /* when there are no off-processor parts.  */
1037   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
1038   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
1039   /* a table, and other, more complex stuff has to be done. */
1040   if (C->assembled) {
1041     C->was_assembled = PETSC_TRUE;
1042     C->assembled     = PETSC_FALSE;
1043   }
1044   if (C->was_assembled) {
1045     for (i=0; i<cm; i++) {
1046       ncols = c_seq->i[i+1] - c_seq->i[i];
1047       row = rstart + i;
1048       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1049       cols += ncols; vals += ncols;
1050     }
1051   } else {
1052     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
1053   }
1054 
1055   /* Co -> C, off-processor part */
1056   cm = C_oth->rmap->N;
1057   c_seq = (Mat_SeqAIJ*)C_oth->data;
1058   cols = c_seq->j;
1059   vals = c_seq->a;
1060   for (i=0; i<cm; i++) {
1061     ncols = c_seq->i[i+1] - c_seq->i[i];
1062     row = p->garray[i];
1063     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1064     cols += ncols; vals += ncols;
1065   }
1066 
1067   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1068   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1069 
1070   ptap->reuse = MAT_REUSE_MATRIX;
1071   PetscFunctionReturn(0);
1072 }
1073