xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision 4584204d43f73ef3b72bb5c8536e0919c67600f3)
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 #include <petsc/private/hashmapiv.h>
13 #include <petsc/private/hashseti.h>
14 #include <petscsf.h>
15 
16 
17 PetscErrorCode MatView_MPIAIJ_PtAP(Mat A,PetscViewer viewer)
18 {
19   PetscErrorCode    ierr;
20   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
21   Mat_APMPI         *ptap=a->ap;
22   PetscBool         iascii;
23   PetscViewerFormat format;
24 
25   PetscFunctionBegin;
26   if (!ptap) {
27     /* hack: MatDuplicate() sets oldmat->ops->view to newmat which is a base mat class with null ptpa! */
28     A->ops->view = MatView_MPIAIJ;
29     ierr = (A->ops->view)(A,viewer);CHKERRQ(ierr);
30     PetscFunctionReturn(0);
31   }
32 
33   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
34   if (iascii) {
35     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
36     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
37       if (ptap->algType == 0) {
38         ierr = PetscViewerASCIIPrintf(viewer,"using scalable MatPtAP() implementation\n");CHKERRQ(ierr);
39       } else if (ptap->algType == 1) {
40         ierr = PetscViewerASCIIPrintf(viewer,"using nonscalable MatPtAP() implementation\n");CHKERRQ(ierr);
41       } else if (ptap->algType == 2) {
42         ierr = PetscViewerASCIIPrintf(viewer,"using allatonce MatPtAP() implementation\n");CHKERRQ(ierr);
43       } else if (ptap->algType == 3) {
44         ierr = PetscViewerASCIIPrintf(viewer,"using merged allatonce MatPtAP() implementation\n");CHKERRQ(ierr);
45       }
46     }
47   }
48   ierr = (ptap->view)(A,viewer);CHKERRQ(ierr);
49   PetscFunctionReturn(0);
50 }
51 
52 PetscErrorCode MatFreeIntermediateDataStructures_MPIAIJ_AP(Mat A)
53 {
54   PetscErrorCode      ierr;
55   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data;
56   Mat_APMPI           *ptap=a->ap;
57   Mat_Merge_SeqsToMPI *merge;
58 
59   PetscFunctionBegin;
60   if (!ptap) PetscFunctionReturn(0);
61 
62   ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
63   ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
64   ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
65   ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
66   ierr = MatDestroy(&ptap->A_loc);CHKERRQ(ierr); /* used by MatTransposeMatMult() */
67   ierr = MatDestroy(&ptap->Rd);CHKERRQ(ierr);
68   ierr = MatDestroy(&ptap->Ro);CHKERRQ(ierr);
69   if (ptap->AP_loc) { /* used by alg_rap */
70     Mat_SeqAIJ *ap = (Mat_SeqAIJ*)(ptap->AP_loc)->data;
71     ierr = PetscFree(ap->i);CHKERRQ(ierr);
72     ierr = PetscFree2(ap->j,ap->a);CHKERRQ(ierr);
73     ierr = MatDestroy(&ptap->AP_loc);CHKERRQ(ierr);
74   } else { /* used by alg_ptap */
75     ierr = PetscFree(ptap->api);CHKERRQ(ierr);
76     ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
77   }
78   ierr = MatDestroy(&ptap->C_loc);CHKERRQ(ierr);
79   ierr = MatDestroy(&ptap->C_oth);CHKERRQ(ierr);
80   if (ptap->apa) {ierr = PetscFree(ptap->apa);CHKERRQ(ierr);}
81 
82   ierr = MatDestroy(&ptap->Pt);CHKERRQ(ierr);
83 
84   merge=ptap->merge;
85   if (merge) { /* used by alg_ptap */
86     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
87     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
88     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
89     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
90     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
91     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
92     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
93     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
94     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
95     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
96     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
97     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
98     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
99     ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
100   }
101   ierr = ISLocalToGlobalMappingDestroy(&ptap->ltog);CHKERRQ(ierr);
102 
103   ierr = PetscSFDestroy(&ptap->sf);CHKERRQ(ierr);
104   ierr = PetscFree(ptap->c_othi);CHKERRQ(ierr);
105   ierr = PetscFree(ptap->c_rmti);CHKERRQ(ierr);
106   PetscFunctionReturn(0);
107 }
108 
109 PetscErrorCode MatDestroy_MPIAIJ_PtAP(Mat A)
110 {
111   PetscErrorCode ierr;
112   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
113   Mat_APMPI      *ptap=a->ap;
114 
115   PetscFunctionBegin;
116   ierr = (*A->ops->freeintermediatedatastructures)(A);CHKERRQ(ierr);
117   ierr = (*ptap->destroy)(A);CHKERRQ(ierr); /* MatDestroy_MPIAIJ(A) */
118   ierr = PetscFree(ptap);CHKERRQ(ierr);
119   PetscFunctionReturn(0);
120 }
121 
122 PETSC_INTERN PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
123 {
124   PetscErrorCode ierr;
125   PetscBool      flg;
126   MPI_Comm       comm;
127 #if !defined(PETSC_HAVE_HYPRE)
128   const char          *algTypes[4] = {"scalable","nonscalable","allatonce","allatonce_merged"};
129   PetscInt            nalg=4;
130 #else
131   const char          *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","hypre"};
132   PetscInt            nalg=5;
133 #endif
134   PetscInt            pN=P->cmap->N,alg=1; /* set default algorithm */
135 
136   PetscFunctionBegin;
137   /* check if matrix local sizes are compatible */
138   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
139   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);
140   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);
141 
142   if (scall == MAT_INITIAL_MATRIX) {
143     /* pick an algorithm */
144     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
145     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
146     ierr = PetscOptionsEnd();CHKERRQ(ierr);
147 
148     if (!flg && pN > 100000) { /* may switch to scalable algorithm as default */
149       MatInfo     Ainfo,Pinfo;
150       PetscInt    nz_local;
151       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
152 
153       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
154       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
155       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
156 
157       if (pN > fill*nz_local) alg_scalable_loc = PETSC_TRUE;
158       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
159 
160       if (alg_scalable) {
161         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
162       }
163     }
164 
165     switch (alg) {
166     case 1:
167       /* do R=P^T locally, then C=R*A*P -- nonscalable */
168       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
169       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
170       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
171       break;
172     case 2:
173       /* compute C=P^T*A*P allatonce */
174       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
175       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_allatonce(A,P,fill,C);CHKERRQ(ierr);
176       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
177       break;
178     case 3:
179       /* compute C=P^T*A*P allatonce */
180       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
181       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_allatonce_merged(A,P,fill,C);CHKERRQ(ierr);
182       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
183       break;
184 #if defined(PETSC_HAVE_HYPRE)
185     case 4:
186       /* Use boomerAMGBuildCoarseOperator */
187       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
188       ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr);
189       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
190       break;
191 #endif
192     default:
193       /* do R=P^T locally, then C=R*A*P */
194       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
195       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(A,P,fill,C);CHKERRQ(ierr);
196       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
197       break;
198     }
199 
200     if (alg == 0 || alg == 1 || alg == 2 || alg == 3) {
201       Mat_MPIAIJ *c  = (Mat_MPIAIJ*)(*C)->data;
202       Mat_APMPI  *ap = c->ap;
203       ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)(*C)),((PetscObject)(*C))->prefix,"MatFreeIntermediateDataStructures","Mat");CHKERRQ(ierr);
204       ap->freestruct = PETSC_FALSE;
205       ierr = PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",ap->freestruct,&ap->freestruct, NULL);CHKERRQ(ierr);
206       ierr = PetscOptionsEnd();CHKERRQ(ierr);
207     }
208   }
209 
210   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
211   ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
212   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
213   PetscFunctionReturn(0);
214 }
215 
216 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,Mat C)
217 {
218   PetscErrorCode    ierr;
219   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
220   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
221   Mat_SeqAIJ        *ap,*p_loc,*p_oth=NULL,*c_seq;
222   Mat_APMPI         *ptap = c->ap;
223   Mat               AP_loc,C_loc,C_oth;
224   PetscInt          i,rstart,rend,cm,ncols,row,*api,*apj,am = A->rmap->n,apnz,nout;
225   PetscScalar       *apa;
226   const PetscInt    *cols;
227   const PetscScalar *vals;
228 
229   PetscFunctionBegin;
230   if (!ptap->AP_loc) {
231     MPI_Comm comm;
232     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
233     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
234   }
235 
236   ierr = MatZeroEntries(C);CHKERRQ(ierr);
237 
238   /* 1) get R = Pd^T,Ro = Po^T */
239   if (ptap->reuse == MAT_REUSE_MATRIX) {
240     ierr = MatTranspose(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
241     ierr = MatTranspose(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
242   }
243 
244   /* 2) get AP_loc */
245   AP_loc = ptap->AP_loc;
246   ap = (Mat_SeqAIJ*)AP_loc->data;
247 
248   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
249   /*-----------------------------------------------------*/
250   if (ptap->reuse == MAT_REUSE_MATRIX) {
251     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
252     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
253     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
254   }
255 
256   /* 2-2) compute numeric A_loc*P - dominating part */
257   /* ---------------------------------------------- */
258   /* get data from symbolic products */
259   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
260   if (ptap->P_oth) p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
261 
262   api   = ap->i;
263   apj   = ap->j;
264   ierr = ISLocalToGlobalMappingApply(ptap->ltog,api[AP_loc->rmap->n],apj,apj);CHKERRQ(ierr);
265   for (i=0; i<am; i++) {
266     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
267     apnz = api[i+1] - api[i];
268     apa = ap->a + api[i];
269     ierr = PetscMemzero(apa,sizeof(PetscScalar)*apnz);CHKERRQ(ierr);
270     AProw_scalable(i,ad,ao,p_loc,p_oth,api,apj,apa);
271   }
272   ierr = ISGlobalToLocalMappingApply(ptap->ltog,IS_GTOLM_DROP,api[AP_loc->rmap->n],apj,&nout,apj);CHKERRQ(ierr);
273   if (api[AP_loc->rmap->n] != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incorrect mapping %D != %D\n",api[AP_loc->rmap->n],nout);
274 
275   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
276   /* Always use scalable version since we are in the MPI scalable version */
277   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
278   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
279 
280   C_loc = ptap->C_loc;
281   C_oth = ptap->C_oth;
282 
283   /* add C_loc and Co to to C */
284   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
285 
286   /* C_loc -> C */
287   cm    = C_loc->rmap->N;
288   c_seq = (Mat_SeqAIJ*)C_loc->data;
289   cols = c_seq->j;
290   vals = c_seq->a;
291   ierr = ISLocalToGlobalMappingApply(ptap->ltog,c_seq->i[C_loc->rmap->n],c_seq->j,c_seq->j);CHKERRQ(ierr);
292 
293   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assembled is PETSC_FALSE and */
294   /* when there are no off-processor parts.  */
295   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
296   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
297   /* a table, and other, more complex stuff has to be done. */
298   if (C->assembled) {
299     C->was_assembled = PETSC_TRUE;
300     C->assembled     = PETSC_FALSE;
301   }
302   if (C->was_assembled) {
303     for (i=0; i<cm; i++) {
304       ncols = c_seq->i[i+1] - c_seq->i[i];
305       row = rstart + i;
306       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
307       cols += ncols; vals += ncols;
308     }
309   } else {
310     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
311   }
312   ierr = ISGlobalToLocalMappingApply(ptap->ltog,IS_GTOLM_DROP,c_seq->i[C_loc->rmap->n],c_seq->j,&nout,c_seq->j);CHKERRQ(ierr);
313   if (c_seq->i[C_loc->rmap->n] != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incorrect mapping %D != %D\n",c_seq->i[C_loc->rmap->n],nout);
314 
315   /* Co -> C, off-processor part */
316   cm = C_oth->rmap->N;
317   c_seq = (Mat_SeqAIJ*)C_oth->data;
318   cols = c_seq->j;
319   vals = c_seq->a;
320   ierr = ISLocalToGlobalMappingApply(ptap->ltog,c_seq->i[C_oth->rmap->n],c_seq->j,c_seq->j);CHKERRQ(ierr);
321   for (i=0; i<cm; i++) {
322     ncols = c_seq->i[i+1] - c_seq->i[i];
323     row = p->garray[i];
324     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
325     cols += ncols; vals += ncols;
326   }
327   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
328   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
329 
330   ptap->reuse = MAT_REUSE_MATRIX;
331 
332   ierr = ISGlobalToLocalMappingApply(ptap->ltog,IS_GTOLM_DROP,c_seq->i[C_oth->rmap->n],c_seq->j,&nout,c_seq->j);CHKERRQ(ierr);
333   if (c_seq->i[C_oth->rmap->n] != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incorrect mapping %D != %D\n",c_seq->i[C_loc->rmap->n],nout);
334 
335   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
336   if (ptap->freestruct) {
337     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
338   }
339   PetscFunctionReturn(0);
340 }
341 
342 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,PetscReal fill,Mat *C)
343 {
344   PetscErrorCode      ierr;
345   Mat_APMPI           *ptap;
346   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
347   MPI_Comm            comm;
348   PetscMPIInt         size,rank;
349   Mat                 Cmpi,P_loc,P_oth;
350   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
351   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
352   PetscInt            *lnk,i,k,pnz,row,nsend;
353   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
354   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
355   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
356   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
357   MPI_Request         *swaits,*rwaits;
358   MPI_Status          *sstatus,rstatus;
359   PetscLayout         rowmap;
360   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
361   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
362   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,Crmax,*aj,*ai,*pi,nout;
363   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
364   PetscScalar         *apv;
365   PetscTable          ta;
366   MatType             mtype;
367   const char          *prefix;
368 #if defined(PETSC_USE_INFO)
369   PetscReal           apfill;
370 #endif
371 
372   PetscFunctionBegin;
373   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
374   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
375   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
376 
377   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
378 
379   /* create symbolic parallel matrix Cmpi */
380   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
381   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
382   ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr);
383 
384   /* create struct Mat_APMPI and attached it to C later */
385   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
386   ptap->reuse = MAT_INITIAL_MATRIX;
387   ptap->algType = 0;
388 
389   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
390   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&P_oth);CHKERRQ(ierr);
391   /* get P_loc by taking all local rows of P */
392   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&P_loc);CHKERRQ(ierr);
393 
394   ptap->P_loc = P_loc;
395   ptap->P_oth = P_oth;
396 
397   /* (0) compute Rd = Pd^T, Ro = Po^T  */
398   /* --------------------------------- */
399   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
400   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
401 
402   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
403   /* ----------------------------------------------------------------- */
404   p_loc  = (Mat_SeqAIJ*)P_loc->data;
405   if (P_oth) p_oth = (Mat_SeqAIJ*)P_oth->data;
406 
407   /* create and initialize a linked list */
408   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
409   MatRowMergeMax_SeqAIJ(p_loc,P_loc->rmap->N,ta);
410   MatRowMergeMax_SeqAIJ(p_oth,P_oth->rmap->N,ta);
411   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
412 
413   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
414 
415   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
416   if (ao) {
417     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
418   } else {
419     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
420   }
421   current_space = free_space;
422   nspacedouble  = 0;
423 
424   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
425   api[0] = 0;
426   for (i=0; i<am; i++) {
427     /* diagonal portion: Ad[i,:]*P */
428     ai = ad->i; pi = p_loc->i;
429     nzi = ai[i+1] - ai[i];
430     aj  = ad->j + ai[i];
431     for (j=0; j<nzi; j++) {
432       row  = aj[j];
433       pnz  = pi[row+1] - pi[row];
434       Jptr = p_loc->j + pi[row];
435       /* add non-zero cols of P into the sorted linked list lnk */
436       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
437     }
438     /* off-diagonal portion: Ao[i,:]*P */
439     if (ao) {
440       ai = ao->i; pi = p_oth->i;
441       nzi = ai[i+1] - ai[i];
442       aj  = ao->j + ai[i];
443       for (j=0; j<nzi; j++) {
444         row  = aj[j];
445         pnz  = pi[row+1] - pi[row];
446         Jptr = p_oth->j + pi[row];
447         ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
448       }
449     }
450     apnz     = lnk[0];
451     api[i+1] = api[i] + apnz;
452 
453     /* if free space is not available, double the total space in the list */
454     if (current_space->local_remaining<apnz) {
455       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
456       nspacedouble++;
457     }
458 
459     /* Copy data into free space, then initialize lnk */
460     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
461 
462     current_space->array           += apnz;
463     current_space->local_used      += apnz;
464     current_space->local_remaining -= apnz;
465   }
466   /* Allocate space for apj and apv, initialize apj, and */
467   /* destroy list of free space and other temporary array(s) */
468   ierr = PetscCalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
469   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
470   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
471 
472   /* Create AP_loc for reuse */
473   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
474   ierr = MatSeqAIJCompactOutExtraColumns_SeqAIJ(ptap->AP_loc, &ptap->ltog);CHKERRQ(ierr);
475 
476 #if defined(PETSC_USE_INFO)
477   if (ao) {
478     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
479   } else {
480     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
481   }
482   ptap->AP_loc->info.mallocs           = nspacedouble;
483   ptap->AP_loc->info.fill_ratio_given  = fill;
484   ptap->AP_loc->info.fill_ratio_needed = apfill;
485 
486   if (api[am]) {
487     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);
488     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
489   } else {
490     ierr = PetscInfo(ptap->AP_loc,"Scalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
491   }
492 #endif
493 
494   /* (2-1) compute symbolic Co = Ro*AP_loc  */
495   /* ------------------------------------ */
496   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
497   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
498   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
499   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
500 
501   /* (3) send coj of C_oth to other processors  */
502   /* ------------------------------------------ */
503   /* determine row ownership */
504   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
505   rowmap->n  = pn;
506   rowmap->bs = 1;
507   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
508   owners = rowmap->range;
509 
510   /* determine the number of messages to send, their lengths */
511   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
512   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
513   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
514 
515   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
516   coi   = c_oth->i; coj = c_oth->j;
517   con   = ptap->C_oth->rmap->n;
518   proc  = 0;
519   ierr = ISLocalToGlobalMappingApply(ptap->ltog,coi[con],coj,coj);CHKERRQ(ierr);
520   for (i=0; i<con; i++) {
521     while (prmap[i] >= owners[proc+1]) proc++;
522     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
523     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
524   }
525 
526   len          = 0; /* max length of buf_si[], see (4) */
527   owners_co[0] = 0;
528   nsend        = 0;
529   for (proc=0; proc<size; proc++) {
530     owners_co[proc+1] = owners_co[proc] + len_si[proc];
531     if (len_s[proc]) {
532       nsend++;
533       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
534       len         += len_si[proc];
535     }
536   }
537 
538   /* determine the number and length of messages to receive for coi and coj  */
539   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
540   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
541 
542   /* post the Irecv and Isend of coj */
543   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
544   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
545   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
546   for (proc=0, k=0; proc<size; proc++) {
547     if (!len_s[proc]) continue;
548     i    = owners_co[proc];
549     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
550     k++;
551   }
552 
553   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
554   /* ---------------------------------------- */
555   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
556   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
557   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
558   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
559   ierr = ISLocalToGlobalMappingApply(ptap->ltog,c_loc->i[ptap->C_loc->rmap->n],c_loc->j,c_loc->j);CHKERRQ(ierr);
560 
561   /* receives coj are complete */
562   for (i=0; i<nrecv; i++) {
563     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
564   }
565   ierr = PetscFree(rwaits);CHKERRQ(ierr);
566   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
567 
568   /* add received column indices into ta to update Crmax */
569   for (k=0; k<nrecv; k++) {/* k-th received message */
570     Jptr = buf_rj[k];
571     for (j=0; j<len_r[k]; j++) {
572       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
573     }
574   }
575   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
576   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
577 
578   /* (4) send and recv coi */
579   /*-----------------------*/
580   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
581   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
582   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
583   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
584   for (proc=0,k=0; proc<size; proc++) {
585     if (!len_s[proc]) continue;
586     /* form outgoing message for i-structure:
587          buf_si[0]:                 nrows to be sent
588                [1:nrows]:           row index (global)
589                [nrows+1:2*nrows+1]: i-structure index
590     */
591     /*-------------------------------------------*/
592     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
593     buf_si_i    = buf_si + nrows+1;
594     buf_si[0]   = nrows;
595     buf_si_i[0] = 0;
596     nrows       = 0;
597     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
598       nzi = coi[i+1] - coi[i];
599       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
600       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
601       nrows++;
602     }
603     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
604     k++;
605     buf_si += len_si[proc];
606   }
607   for (i=0; i<nrecv; i++) {
608     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
609   }
610   ierr = PetscFree(rwaits);CHKERRQ(ierr);
611   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
612 
613   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
614   ierr = PetscFree(len_ri);CHKERRQ(ierr);
615   ierr = PetscFree(swaits);CHKERRQ(ierr);
616   ierr = PetscFree(buf_s);CHKERRQ(ierr);
617 
618   /* (5) compute the local portion of Cmpi      */
619   /* ------------------------------------------ */
620   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
621   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
622   current_space = free_space;
623 
624   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
625   for (k=0; k<nrecv; k++) {
626     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
627     nrows       = *buf_ri_k[k];
628     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
629     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
630   }
631 
632   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
633   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
634   for (i=0; i<pn; i++) {
635     /* add C_loc into Cmpi */
636     nzi  = c_loc->i[i+1] - c_loc->i[i];
637     Jptr = c_loc->j + c_loc->i[i];
638     ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
639 
640     /* add received col data into lnk */
641     for (k=0; k<nrecv; k++) { /* k-th received message */
642       if (i == *nextrow[k]) { /* i-th row */
643         nzi  = *(nextci[k]+1) - *nextci[k];
644         Jptr = buf_rj[k] + *nextci[k];
645         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
646         nextrow[k]++; nextci[k]++;
647       }
648     }
649     nzi = lnk[0];
650 
651     /* copy data into free space, then initialize lnk */
652     ierr = PetscLLCondensedClean_Scalable(nzi,current_space->array,lnk);CHKERRQ(ierr);
653     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
654   }
655   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
656   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
657   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
658 
659   /* local sizes and preallocation */
660   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
661   if (P->cmap->bs > 0) {
662     ierr = PetscLayoutSetBlockSize(Cmpi->rmap,P->cmap->bs);CHKERRQ(ierr);
663     ierr = PetscLayoutSetBlockSize(Cmpi->cmap,P->cmap->bs);CHKERRQ(ierr);
664   }
665   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
666   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
667 
668   /* members in merge */
669   ierr = PetscFree(id_r);CHKERRQ(ierr);
670   ierr = PetscFree(len_r);CHKERRQ(ierr);
671   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
672   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
673   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
674   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
675   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
676 
677   /* attach the supporting struct to Cmpi for reuse */
678   c = (Mat_MPIAIJ*)Cmpi->data;
679   c->ap           = ptap;
680   ptap->duplicate = Cmpi->ops->duplicate;
681   ptap->destroy   = Cmpi->ops->destroy;
682   ptap->view      = Cmpi->ops->view;
683 
684   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
685   Cmpi->assembled        = PETSC_FALSE;
686   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable;
687   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
688   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
689   Cmpi->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
690   *C                     = Cmpi;
691 
692    nout = 0;
693    ierr = ISGlobalToLocalMappingApply(ptap->ltog,IS_GTOLM_DROP,c_oth->i[ptap->C_oth->rmap->n],c_oth->j,&nout,c_oth->j);CHKERRQ(ierr);
694    if (c_oth->i[ptap->C_oth->rmap->n] != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incorrect mapping %D != %D\n",c_oth->i[ptap->C_oth->rmap->n],nout);
695    ierr = ISGlobalToLocalMappingApply(ptap->ltog,IS_GTOLM_DROP,c_loc->i[ptap->C_loc->rmap->n],c_loc->j,&nout,c_loc->j);CHKERRQ(ierr);
696    if (c_loc->i[ptap->C_loc->rmap->n] != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incorrect mapping %D != %D\n",c_loc->i[ptap->C_loc->rmap->n],nout);
697 
698   PetscFunctionReturn(0);
699 }
700 
701 PETSC_STATIC_INLINE PetscErrorCode MatPtAPSymbolicComputeOneRowOfAP_private(Mat A,Mat P,Mat P_oth,PetscInt i,PetscHSetI dht,PetscHSetI oht)
702 {
703   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data;
704   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_oth=(Mat_SeqAIJ*)P_oth->data,*pd=(Mat_SeqAIJ*)p->A->data,*po=(Mat_SeqAIJ*)p->B->data;
705   PetscInt             *ai,nzi,j,*aj,row,col,*pi,*pj,pnz,nzpi,*p_othcols,k;
706   PetscInt             pcstart,pcend,column;
707   PetscErrorCode       ierr;
708 
709   PetscFunctionBegin;
710 
711   pcstart = P->cmap->rstart;
712   pcend   = P->cmap->rend;
713   /* diagonal portion: Ad[i,:]*P */
714   ai = ad->i;
715   nzi = ai[i+1] - ai[i];
716   aj  = ad->j + ai[i];
717   for (j=0; j<nzi; j++) {
718     row  = aj[j];
719     nzpi = pd->i[row+1] - pd->i[row];
720     pj  = pd->j + pd->i[row];
721     for (k=0; k<nzpi; k++) {
722       ierr = PetscHSetIAdd(dht,pj[k]+pcstart);CHKERRQ(ierr);
723     }
724   }
725   for (j=0; j<nzi; j++) {
726     row  = aj[j];
727     nzpi = po->i[row+1] - po->i[row];
728     pj  = po->j + po->i[row];
729     for (k=0; k<nzpi; k++) {
730       ierr = PetscHSetIAdd(oht,p->garray[pj[k]]);CHKERRQ(ierr);
731     }
732   }
733 
734   /* off diagonal part: Ao[i, :]*P_oth */
735   if (ao) {
736     ai = ao->i;
737     pi = p_oth->i;
738     nzi = ai[i+1] - ai[i];
739     aj  = ao->j + ai[i];
740     for (j=0; j<nzi; j++) {
741       row  = aj[j];
742       pnz  = pi[row+1] - pi[row];
743       p_othcols = p_oth->j + pi[row];
744       for (col=0; col<pnz; col++) {
745         column = p_othcols[col];
746         if (column>=pcstart && column<pcend) {
747           ierr = PetscHSetIAdd(dht,column);CHKERRQ(ierr);
748         } else {
749           ierr = PetscHSetIAdd(oht,column);CHKERRQ(ierr);
750         }
751       }
752     }
753   } /* end if (ao) */
754   PetscFunctionReturn(0);
755 }
756 
757 PETSC_STATIC_INLINE PetscErrorCode MatPtAPNumericComputeOneRowOfAP_private(Mat A,Mat P,Mat P_oth,PetscInt i,PetscHMapIV hmap)
758 {
759   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data;
760   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_oth=(Mat_SeqAIJ*)P_oth->data,*pd=(Mat_SeqAIJ*)p->A->data,*po=(Mat_SeqAIJ*)p->B->data;
761   PetscInt             *ai,nzi,j,*aj,row,col,*pi,pnz,*p_othcols,pcstart,*pj,k,nzpi;
762   PetscScalar          ra,*aa,*pa;
763   PetscLogDouble       flops=0.0;
764   PetscErrorCode       ierr;
765 
766   PetscFunctionBegin;
767   pcstart = P->cmap->rstart;
768   /* diagonal portion: Ad[i,:]*P */
769   ai  = ad->i;
770   nzi = ai[i+1] - ai[i];
771   aj  = ad->j + ai[i];
772   aa  = ad->a + ai[i];
773 
774   for (j=0; j<nzi; j++) {
775     ra   = aa[j];
776     row  = aj[j];
777     nzpi = pd->i[row+1] - pd->i[row];
778     pj = pd->j + pd->i[row];
779     pa = pd->a + pd->i[row];
780     for (k=0; k<nzpi; k++) {
781       ierr = PetscHMapIVAddValue(hmap,pj[k]+pcstart,ra*pa[k]);CHKERRQ(ierr);
782     }
783     flops += nzpi;
784   }
785   for (j=0; j<nzi; j++) {
786     ra   = aa[j];
787     row  = aj[j];
788     nzpi = po->i[row+1] - po->i[row];
789     pj = po->j + po->i[row];
790     pa = po->a + po->i[row];
791     for (k=0; k<nzpi; k++) {
792       ierr = PetscHMapIVAddValue(hmap,p->garray[pj[k]],ra*pa[k]);CHKERRQ(ierr);
793     }
794     flops += nzpi;
795   }
796 
797 
798   /* off diagonal part: Ao[i, :]*P_oth */
799   if (ao) {
800     ai = ao->i;
801     pi = p_oth->i;
802     nzi = ai[i+1] - ai[i];
803     aj  = ao->j + ai[i];
804     aa  = ao->a + ai[i];
805     for (j=0; j<nzi; j++) {
806       row  = aj[j];
807       ra   = aa[j];
808       pnz  = pi[row+1] - pi[row];
809       p_othcols = p_oth->j + pi[row];
810       pa   = p_oth->a + pi[row];
811       for (col=0; col<pnz; col++) {
812         ierr = PetscHMapIVAddValue(hmap,p_othcols[col],ra*pa[col]);CHKERRQ(ierr);
813       }
814       flops += pnz;
815     }
816   } /* end if (ao) */
817 
818   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
819   PetscFunctionReturn(0);
820 }
821 
822 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_allatonce(Mat A,Mat P,Mat C)
823 {
824   PetscErrorCode    ierr;
825   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
826   Mat_SeqAIJ        *cd,*co,*po,*pd;
827   Mat_APMPI         *ptap = c->ap;
828   PetscHMapIV       hmap;
829   PetscInt          i,j,jj,kk,nzi,*c_rmtj,voff,*c_othj,pn,pon,pcstart,pcend,ccstart,ccend,row,am,*poj,*pdj,*apindices,cmaxr,*c_rmtc,*c_rmtjj,*dcc,*occ,loc;
830   PetscScalar       *c_rmta,*c_otha,*poa,*pda,*apvalues,*apvaluestmp,*c_rmtaa;
831   PetscLogDouble    flops=0.0;
832   MPI_Comm          comm;
833 
834   PetscFunctionBegin;
835   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
836   if (!ptap->P_oth) SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
837 
838   ierr = MatZeroEntries(C);CHKERRQ(ierr);
839 
840   /* Get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
841   /*-----------------------------------------------------*/
842   if (ptap->reuse == MAT_REUSE_MATRIX) {
843     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
844     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
845   }
846 
847   po = (Mat_SeqAIJ*) p->B->data;
848   pd = (Mat_SeqAIJ*) p->A->data;
849 
850   ierr = MatGetLocalSize(p->B,NULL,&pon);CHKERRQ(ierr);
851 
852   ierr = PetscCalloc2(ptap->c_rmti[pon],&c_rmtj,ptap->c_rmti[pon],&c_rmta);CHKERRQ(ierr);
853   ierr = MatGetLocalSize(A,&am,NULL);CHKERRQ(ierr);
854   cmaxr = 0;
855   for (i=0; i<pon; i++) {
856     cmaxr = PetscMax(cmaxr,ptap->c_rmti[i+1]-ptap->c_rmti[i]);
857   }
858   ierr = PetscCalloc4(cmaxr,&apindices,cmaxr,&apvalues,cmaxr,&apvaluestmp,pon,&c_rmtc);CHKERRQ(ierr);
859   ierr = PetscHMapIVCreate(&hmap);CHKERRQ(ierr);
860   ierr = PetscHMapIVResize(hmap,cmaxr);CHKERRQ(ierr);
861   for (i=0; i<am && pon; i++) {
862     ierr = PetscHMapIVClear(hmap);CHKERRQ(ierr);
863     nzi = po->i[i+1] - po->i[i];
864     if (!nzi) continue;
865     ierr = MatPtAPNumericComputeOneRowOfAP_private(A,P,ptap->P_oth,i,hmap);CHKERRQ(ierr);
866     voff = 0;
867     ierr = PetscHMapIVGetPairs(hmap,&voff,apindices,apvalues);CHKERRQ(ierr);
868     if (!voff) continue;
869     /*ierr = PetscMemzero(c_rmtc,sizeof(PetscInt)*pon);CHKERRQ(ierr);*/
870 
871     /* Form C(ii, :) */
872     poj = po->j + po->i[i];
873     poa = po->a + po->i[i];
874     for (j=0; j<nzi; j++) {
875       c_rmtjj = c_rmtj + ptap->c_rmti[poj[j]];
876       c_rmtaa = c_rmta + ptap->c_rmti[poj[j]];
877       for (jj=0; jj<voff; jj++) {
878         apvaluestmp[jj] = apvalues[jj]*poa[j];
879         /*If the row is empty */
880         if (!c_rmtc[poj[j]]) {
881           c_rmtjj[jj] = apindices[jj];
882           c_rmtaa[jj] = apvaluestmp[jj];
883           c_rmtc[poj[j]]++;
884         } else {
885           ierr = PetscFindInt(apindices[jj],c_rmtc[poj[j]],c_rmtjj,&loc);CHKERRQ(ierr);
886           if (loc>=0){ /* hit */
887             c_rmtaa[loc] += apvaluestmp[jj];
888           } else { /* new element */
889             loc = -(loc+1);
890             /* Move data backward */
891             for (kk=c_rmtc[poj[j]]; kk>loc; kk--) {
892               c_rmtjj[kk] = c_rmtjj[kk-1];
893               c_rmtaa[kk] = c_rmtaa[kk-1];
894             }/* End kk */
895             c_rmtjj[loc] = apindices[jj];
896             c_rmtaa[loc] = apvaluestmp[jj];
897             c_rmtc[poj[j]]++;
898           }
899         }
900         flops += voff;
901       } /* End jj */
902     } /* End j */
903   } /* End i */
904 
905   ierr = PetscFree4(apindices,apvalues,apvaluestmp,c_rmtc);CHKERRQ(ierr);
906 
907   ierr = MatGetLocalSize(P,NULL,&pn);CHKERRQ(ierr);
908   ierr = PetscCalloc2(ptap->c_othi[pn],&c_othj,ptap->c_othi[pn],&c_otha);CHKERRQ(ierr);
909 
910   ierr = PetscSFReduceBegin(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPIU_REPLACE);CHKERRQ(ierr);
911   ierr = PetscSFReduceBegin(ptap->sf,MPIU_SCALAR,c_rmta,c_otha,MPIU_REPLACE);CHKERRQ(ierr);
912   ierr = MatGetOwnershipRangeColumn(P,&pcstart,&pcend);CHKERRQ(ierr);
913   cd = (Mat_SeqAIJ*)(c->A)->data;
914   co = (Mat_SeqAIJ*)(c->B)->data;
915 
916   cmaxr = 0;
917   for (i=0; i<pn; i++) {
918     cmaxr = PetscMax(cmaxr,(cd->i[i+1]-cd->i[i])+(co->i[i+1]-co->i[i]));
919   }
920   ierr = PetscCalloc5(cmaxr,&apindices,cmaxr,&apvalues,cmaxr,&apvaluestmp,pn,&dcc,pn,&occ);CHKERRQ(ierr);
921   ierr = PetscHMapIVCreate(&hmap);CHKERRQ(ierr);
922   ierr = PetscHMapIVResize(hmap,cmaxr);CHKERRQ(ierr);
923   for (i=0; i<am && pn; i++) {
924     ierr = PetscHMapIVClear(hmap);CHKERRQ(ierr);
925     nzi = pd->i[i+1] - pd->i[i];
926     if (!nzi) continue;
927     ierr = MatPtAPNumericComputeOneRowOfAP_private(A,P,ptap->P_oth,i,hmap);CHKERRQ(ierr);
928     voff = 0;
929     ierr = PetscHMapIVGetPairs(hmap,&voff,apindices,apvalues);CHKERRQ(ierr);
930     if (!voff) continue;
931     /* Form C(ii, :) */
932     pdj = pd->j + pd->i[i];
933     pda = pd->a + pd->i[i];
934     for (j=0; j<nzi; j++) {
935       row = pcstart + pdj[j];
936       for (jj=0; jj<voff; jj++) {
937         apvaluestmp[jj] = apvalues[jj]*pda[j];
938       }
939       ierr = MatSetValues(C,1,&row,voff,apindices,apvaluestmp,ADD_VALUES);CHKERRQ(ierr);
940       flops += voff;
941     }
942   }
943 
944   ierr = MatGetOwnershipRangeColumn(C,&ccstart,&ccend);CHKERRQ(ierr);
945   ierr = PetscFree5(apindices,apvalues,apvaluestmp,dcc,occ);CHKERRQ(ierr);
946   ierr = PetscHMapIVDestroy(&hmap);CHKERRQ(ierr);
947   ierr = PetscSFReduceEnd(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPI_SUM);CHKERRQ(ierr);
948   ierr = PetscSFReduceEnd(ptap->sf,MPIU_SCALAR,c_rmta,c_otha,MPIU_REPLACE);CHKERRQ(ierr);
949   ierr = PetscFree2(c_rmtj,c_rmta);CHKERRQ(ierr);
950 
951   /* Add contributions from remote */
952   for (i = 0; i < pn; i++) {
953     row = i + pcstart;
954     ierr = MatSetValues(C,1,&row,ptap->c_othi[i+1]-ptap->c_othi[i],c_othj+ptap->c_othi[i],c_otha+ptap->c_othi[i],ADD_VALUES);CHKERRQ(ierr);
955   }
956   ierr = PetscFree2(c_othj,c_otha);CHKERRQ(ierr);
957 
958   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
959   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
960   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
961 
962   ptap->reuse = MAT_REUSE_MATRIX;
963 
964   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
965   if (ptap->freestruct) {
966     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
967   }
968   PetscFunctionReturn(0);
969 }
970 
971 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_allatonce_merged(Mat A,Mat P,Mat C)
972 {
973   PetscErrorCode    ierr;
974   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
975   Mat_SeqAIJ        *cd,*co,*po,*pd;
976   Mat_APMPI         *ptap = c->ap;
977   PetscHMapIV       hmap;
978   PetscInt          i,j,jj,kk,nzi,dnzi,*c_rmtj,voff,*c_othj,pn,pon,pcstart,pcend,row,am,*poj,*pdj,*apindices,cmaxr,*c_rmtc,*c_rmtjj,loc;
979   PetscScalar       *c_rmta,*c_otha,*poa,*pda,*apvalues,*apvaluestmp,*c_rmtaa;
980   PetscLogDouble    flops=0.0;
981   MPI_Comm          comm;
982 
983   PetscFunctionBegin;
984   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
985   if (!ptap->P_oth) SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
986 
987   ierr = MatZeroEntries(C);CHKERRQ(ierr);
988 
989   /* 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   }
995 
996   po = (Mat_SeqAIJ*) p->B->data;
997   pd = (Mat_SeqAIJ*) p->A->data;
998 
999   ierr = MatGetLocalSize(p->B,NULL,&pon);CHKERRQ(ierr);
1000   ierr = MatGetLocalSize(P,NULL,&pn);CHKERRQ(ierr);
1001 
1002   ierr = PetscCalloc2(ptap->c_rmti[pon],&c_rmtj,ptap->c_rmti[pon],&c_rmta);CHKERRQ(ierr);
1003   ierr = MatGetLocalSize(A,&am,NULL);CHKERRQ(ierr);
1004   ierr = MatGetOwnershipRangeColumn(P,&pcstart,&pcend);CHKERRQ(ierr);
1005   cmaxr = 0;
1006   for (i=0; i<pon; i++) {
1007     cmaxr = PetscMax(cmaxr,ptap->c_rmti[i+1]-ptap->c_rmti[i]);
1008   }
1009   cd = (Mat_SeqAIJ*)(c->A)->data;
1010   co = (Mat_SeqAIJ*)(c->B)->data;
1011   for (i=0; i<pn; i++) {
1012     cmaxr = PetscMax(cmaxr,(cd->i[i+1]-cd->i[i])+(co->i[i+1]-co->i[i]));
1013   }
1014   ierr = PetscCalloc4(cmaxr,&apindices,cmaxr,&apvalues,cmaxr,&apvaluestmp,pon,&c_rmtc);CHKERRQ(ierr);
1015   ierr = PetscHMapIVCreate(&hmap);CHKERRQ(ierr);
1016   ierr = PetscHMapIVResize(hmap,cmaxr);CHKERRQ(ierr);
1017   for (i=0; i<am && (pon || pn); i++) {
1018     ierr = PetscHMapIVClear(hmap);CHKERRQ(ierr);
1019     nzi  = po->i[i+1] - po->i[i];
1020     dnzi = pd->i[i+1] - pd->i[i];
1021     if (!nzi && !dnzi) continue;
1022     ierr = MatPtAPNumericComputeOneRowOfAP_private(A,P,ptap->P_oth,i,hmap);CHKERRQ(ierr);
1023     voff = 0;
1024     ierr = PetscHMapIVGetPairs(hmap,&voff,apindices,apvalues);CHKERRQ(ierr);
1025     if (!voff) continue;
1026 
1027     /* Form remote C(ii, :) */
1028     poj = po->j + po->i[i];
1029     poa = po->a + po->i[i];
1030     for (j=0; j<nzi; j++) {
1031       c_rmtjj = c_rmtj + ptap->c_rmti[poj[j]];
1032       c_rmtaa = c_rmta + ptap->c_rmti[poj[j]];
1033       for (jj=0; jj<voff; jj++) {
1034         apvaluestmp[jj] = apvalues[jj]*poa[j];
1035         /*If the row is empty */
1036         if (!c_rmtc[poj[j]]) {
1037           c_rmtjj[jj] = apindices[jj];
1038           c_rmtaa[jj] = apvaluestmp[jj];
1039           c_rmtc[poj[j]]++;
1040         } else {
1041           ierr = PetscFindInt(apindices[jj],c_rmtc[poj[j]],c_rmtjj,&loc);CHKERRQ(ierr);
1042           if (loc>=0){ /* hit */
1043             c_rmtaa[loc] += apvaluestmp[jj];
1044           } else { /* new element */
1045             loc = -(loc+1);
1046             /* Move data backward */
1047             for (kk=c_rmtc[poj[j]]; kk>loc; kk--) {
1048               c_rmtjj[kk] = c_rmtjj[kk-1];
1049               c_rmtaa[kk] = c_rmtaa[kk-1];
1050             }/* End kk */
1051             c_rmtjj[loc] = apindices[jj];
1052             c_rmtaa[loc] = apvaluestmp[jj];
1053             c_rmtc[poj[j]]++;
1054           }
1055         }
1056       } /* End jj */
1057       flops += voff;
1058     } /* End j */
1059 
1060     /* Form local C(ii, :) */
1061     pdj = pd->j + pd->i[i];
1062     pda = pd->a + pd->i[i];
1063     for (j=0; j<dnzi; j++) {
1064       row = pcstart + pdj[j];
1065       for (jj=0; jj<voff; jj++) {
1066         apvaluestmp[jj] = apvalues[jj]*pda[j];
1067       }/* End kk */
1068       ierr = MatSetValues(C,1,&row,voff,apindices,apvaluestmp,ADD_VALUES);CHKERRQ(ierr);
1069       flops += voff;
1070     }/* End j */
1071   } /* End i */
1072 
1073   ierr = PetscFree4(apindices,apvalues,apvaluestmp,c_rmtc);CHKERRQ(ierr);
1074   ierr = PetscHMapIVDestroy(&hmap);CHKERRQ(ierr);
1075   ierr = PetscCalloc2(ptap->c_othi[pn],&c_othj,ptap->c_othi[pn],&c_otha);CHKERRQ(ierr);
1076 
1077   ierr = PetscSFReduceBegin(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPIU_REPLACE);CHKERRQ(ierr);
1078   ierr = PetscSFReduceBegin(ptap->sf,MPIU_SCALAR,c_rmta,c_otha,MPIU_REPLACE);CHKERRQ(ierr);
1079   ierr = PetscSFReduceEnd(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPI_SUM);CHKERRQ(ierr);
1080   ierr = PetscSFReduceEnd(ptap->sf,MPIU_SCALAR,c_rmta,c_otha,MPIU_REPLACE);CHKERRQ(ierr);
1081   ierr = PetscFree2(c_rmtj,c_rmta);CHKERRQ(ierr);
1082 
1083   /* Add contributions from remote */
1084   for (i = 0; i < pn; i++) {
1085     row = i + pcstart;
1086     ierr = MatSetValues(C,1,&row,ptap->c_othi[i+1]-ptap->c_othi[i],c_othj+ptap->c_othi[i],c_otha+ptap->c_othi[i],ADD_VALUES);CHKERRQ(ierr);
1087   }
1088   ierr = PetscFree2(c_othj,c_otha);CHKERRQ(ierr);
1089 
1090   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1091   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1092   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1093 
1094   ptap->reuse = MAT_REUSE_MATRIX;
1095 
1096   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
1097   if (ptap->freestruct) {
1098     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1099   }
1100   PetscFunctionReturn(0);
1101 }
1102 
1103 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_allatonce(Mat A,Mat P,PetscReal fill,Mat *C)
1104 {
1105   Mat_APMPI           *ptap;
1106   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*c;
1107   MPI_Comm            comm;
1108   Mat                 Cmpi;
1109   Mat_SeqAIJ          *pd,*po;
1110   MatType             mtype;
1111   PetscSF             sf;
1112   PetscSFNode         *iremote;
1113   PetscInt            rootspacesize,*rootspace,*rootspaceoffsets,nleaves;
1114   const PetscInt      *rootdegrees;
1115   PetscHSetI          ht,oht,*hta,*hto;
1116   PetscInt            pn,pon,*c_rmtc,i,j,nzi,htsize,htosize,*c_rmtj,off,*c_othj,rcvncols,sendncols,*c_rmtoffsets;
1117   PetscInt            owner,lidx,*rdj,col,pcstart,pcend,*dnz,*onz,am,arstart,arend,*poj,*pdj;
1118   PetscInt            nalg=2,alg=0;
1119   PetscBool           flg;
1120   const char          *algTypes[2] = {"overlapping","merged"};
1121   PetscErrorCode      ierr;
1122 
1123   PetscFunctionBegin;
1124   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1125 
1126   /* Create symbolic parallel matrix Cmpi */
1127   ierr = MatGetLocalSize(P,NULL,&pn);CHKERRQ(ierr);
1128   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
1129   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1130   ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr);
1131   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1132 
1133   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
1134   ptap->reuse = MAT_INITIAL_MATRIX;
1135   ptap->algType = 2;
1136 
1137   /* Get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1138   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1139 
1140   po = (Mat_SeqAIJ*)p->B->data;
1141   pd = (Mat_SeqAIJ*)p->A->data;
1142 
1143   /* This equals to the number of offdiag columns in P */
1144   ierr = MatGetLocalSize(p->B,NULL,&pon);CHKERRQ(ierr);
1145   /* offsets */
1146   ierr = PetscMalloc1(pon+1,&ptap->c_rmti);CHKERRQ(ierr);
1147   /* The number of columns we will send to remote ranks */
1148   ierr = PetscMalloc1(pon,&c_rmtc);CHKERRQ(ierr);
1149   ierr = PetscMalloc1(pon,&hta);CHKERRQ(ierr);
1150   for (i=0; i<pon; i++) {
1151     ierr = PetscHSetICreate(&hta[i]);CHKERRQ(ierr);
1152   }
1153   ierr = MatGetLocalSize(A,&am,NULL);CHKERRQ(ierr);
1154   ierr = MatGetOwnershipRange(A,&arstart,&arend);CHKERRQ(ierr);
1155   /* Create hash table to merge all columns for C(i, :) */
1156   ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
1157 
1158   ptap->c_rmti[0] = 0;
1159   /* 2) Pass 1: calculate the size for C_rmt (a matrix need to be sent to other processors)  */
1160   for (i=0; i<am && pon; i++) {
1161     /* Form one row of AP */
1162     ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
1163     /* If the off diag is empty, we should not do any calculation */
1164     nzi = po->i[i+1] - po->i[i];
1165     if (!nzi) continue;
1166 
1167     ierr = MatPtAPSymbolicComputeOneRowOfAP_private(A,P,ptap->P_oth,i,ht,ht);CHKERRQ(ierr);
1168     ierr = PetscHSetIGetSize(ht,&htsize);CHKERRQ(ierr);
1169     /* If AP is empty, just continue */
1170     if (!htsize) continue;
1171     /* Form C(ii, :) */
1172     poj = po->j + po->i[i];
1173     for (j=0; j<nzi; j++) {
1174       ierr = PetscHSetIUpdate(hta[poj[j]],ht);CHKERRQ(ierr);
1175     }
1176   }
1177 
1178   for (i=0; i<pon; i++) {
1179     ierr = PetscHSetIGetSize(hta[i],&htsize);CHKERRQ(ierr);
1180     ptap->c_rmti[i+1] = ptap->c_rmti[i] + htsize;
1181     c_rmtc[i] = htsize;
1182   }
1183 
1184   ierr = PetscMalloc1(ptap->c_rmti[pon],&c_rmtj);CHKERRQ(ierr);
1185 
1186   for (i=0; i<pon; i++) {
1187     off = 0;
1188     ierr = PetscHSetIGetElems(hta[i],&off,c_rmtj+ptap->c_rmti[i]);CHKERRQ(ierr);
1189     ierr = PetscHSetIDestroy(&hta[i]);CHKERRQ(ierr);
1190   }
1191   ierr = PetscFree(hta);CHKERRQ(ierr);
1192 
1193   ierr = PetscCalloc1(pon,&iremote);CHKERRQ(ierr);
1194   for (i=0; i<pon; i++) {
1195     owner = 0; lidx = 0;
1196     ierr = PetscLayoutFindOwnerIndex(P->cmap,p->garray[i],&owner,&lidx);CHKERRQ(ierr);
1197     iremote[i].index = lidx;
1198     iremote[i].rank  = owner;
1199   }
1200 
1201   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
1202   ierr = PetscSFSetGraph(sf,pn,pon,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER);CHKERRQ(ierr);
1203   /* Reorder ranks properly so that the data handled by gather and scatter have the same order */
1204   ierr = PetscSFSetRankOrder(sf,PETSC_TRUE);CHKERRQ(ierr);
1205   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1206   ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
1207   /* How many neighbors have contributions to my rows? */
1208   ierr = PetscSFComputeDegreeBegin(sf,&rootdegrees);CHKERRQ(ierr);
1209   ierr = PetscSFComputeDegreeEnd(sf,&rootdegrees);CHKERRQ(ierr);
1210   rootspacesize = 0;
1211   for (i = 0; i < pn; i++) {
1212     rootspacesize += rootdegrees[i];
1213   }
1214   ierr = PetscCalloc1(rootspacesize,&rootspace);CHKERRQ(ierr);
1215   ierr = PetscCalloc1(rootspacesize+1,&rootspaceoffsets);CHKERRQ(ierr);
1216   /* Get information from leaves
1217    * Number of columns other people contribute to my rows
1218    * */
1219   ierr = PetscSFGatherBegin(sf,MPIU_INT,c_rmtc,rootspace);CHKERRQ(ierr);
1220   ierr = PetscSFGatherEnd(sf,MPIU_INT,c_rmtc,rootspace);CHKERRQ(ierr);
1221   ierr = PetscFree(c_rmtc);CHKERRQ(ierr);
1222   ierr = PetscCalloc1(pn+1,&ptap->c_othi);CHKERRQ(ierr);
1223   /* The number of columns is received for each row */
1224   ptap->c_othi[0] = 0;
1225   rootspacesize = 0;
1226   rootspaceoffsets[0] = 0;
1227   for (i = 0; i < pn; i++) {
1228     rcvncols = 0;
1229     for (j = 0; j<rootdegrees[i]; j++) {
1230       rcvncols += rootspace[rootspacesize];
1231       rootspaceoffsets[rootspacesize+1] = rootspaceoffsets[rootspacesize] + rootspace[rootspacesize];
1232       rootspacesize++;
1233     }
1234     ptap->c_othi[i+1] = ptap->c_othi[i] + rcvncols;
1235   }
1236   ierr = PetscFree(rootspace);CHKERRQ(ierr);
1237 
1238   ierr = PetscCalloc1(pon,&c_rmtoffsets);CHKERRQ(ierr);
1239   ierr = PetscSFScatterBegin(sf,MPIU_INT,rootspaceoffsets,c_rmtoffsets);CHKERRQ(ierr);
1240   ierr = PetscSFScatterEnd(sf,MPIU_INT,rootspaceoffsets,c_rmtoffsets);CHKERRQ(ierr);
1241   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1242   ierr = PetscFree(rootspaceoffsets);CHKERRQ(ierr);
1243 
1244   ierr = PetscCalloc1(ptap->c_rmti[pon],&iremote);CHKERRQ(ierr);
1245   nleaves = 0;
1246   for (i = 0; i<pon; i++) {
1247     owner = 0; lidx = 0;
1248     ierr = PetscLayoutFindOwnerIndex(P->cmap,p->garray[i],&owner,&lidx);CHKERRQ(ierr);
1249     sendncols = ptap->c_rmti[i+1] - ptap->c_rmti[i];
1250     for (j=0; j<sendncols; j++) {
1251       iremote[nleaves].rank = owner;
1252       iremote[nleaves++].index = c_rmtoffsets[i] + j;
1253     }
1254   }
1255   ierr = PetscFree(c_rmtoffsets);CHKERRQ(ierr);
1256   ierr = PetscCalloc1(ptap->c_othi[pn],&c_othj);CHKERRQ(ierr);
1257 
1258   ierr = PetscSFCreate(comm,&ptap->sf);CHKERRQ(ierr);
1259   ierr = PetscSFSetGraph(ptap->sf,ptap->c_othi[pn],nleaves,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER);CHKERRQ(ierr);
1260   ierr = PetscSFSetFromOptions(ptap->sf);CHKERRQ(ierr);
1261   /* One to one map */
1262   ierr = PetscSFReduceBegin(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPIU_REPLACE);CHKERRQ(ierr);
1263 
1264   ierr = PetscCalloc2(pn,&dnz,pn,&onz);CHKERRQ(ierr);
1265   ierr = PetscHSetICreate(&oht);CHKERRQ(ierr);
1266   ierr = MatGetOwnershipRangeColumn(P,&pcstart,&pcend);CHKERRQ(ierr);
1267   ierr = PetscMalloc2(pn,&hta,pn,&hto);CHKERRQ(ierr);
1268   for (i=0; i<pn; i++) {
1269     ierr = PetscHSetICreate(&hta[i]);CHKERRQ(ierr);
1270     ierr = PetscHSetICreate(&hto[i]);CHKERRQ(ierr);
1271   }
1272   /* Work on local part */
1273   /* 4) Pass 1: Estimate memory for C_loc */
1274   for (i=0; i<am && pn; i++) {
1275     ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
1276     ierr = PetscHSetIClear(oht);CHKERRQ(ierr);
1277     nzi = pd->i[i+1] - pd->i[i];
1278     if (!nzi) continue;
1279 
1280     ierr = MatPtAPSymbolicComputeOneRowOfAP_private(A,P,ptap->P_oth,i,ht,oht);CHKERRQ(ierr);
1281     ierr = PetscHSetIGetSize(ht,&htsize);CHKERRQ(ierr);
1282     ierr = PetscHSetIGetSize(oht,&htosize);CHKERRQ(ierr);
1283     if (!(htsize+htosize)) continue;
1284     /* Form C(ii, :) */
1285     pdj = pd->j + pd->i[i];
1286     for (j=0; j<nzi; j++) {
1287       ierr = PetscHSetIUpdate(hta[pdj[j]],ht);CHKERRQ(ierr);
1288       ierr = PetscHSetIUpdate(hto[pdj[j]],oht);CHKERRQ(ierr);
1289     }
1290   }
1291 
1292   ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
1293   ierr = PetscHSetIDestroy(&oht);CHKERRQ(ierr);
1294 
1295   /* Get remote data */
1296   ierr = PetscSFReduceEnd(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPIU_REPLACE);CHKERRQ(ierr);
1297   ierr = PetscFree(c_rmtj);CHKERRQ(ierr);
1298 
1299   for (i = 0; i < pn; i++) {
1300     nzi = ptap->c_othi[i+1] - ptap->c_othi[i];
1301     rdj = c_othj + ptap->c_othi[i];
1302     for (j = 0; j < nzi; j++) {
1303       col =  rdj[j];
1304       /* diag part */
1305       if (col>=pcstart && col<pcend) {
1306         ierr = PetscHSetIAdd(hta[i],col);CHKERRQ(ierr);
1307       } else { /* off diag */
1308         ierr = PetscHSetIAdd(hto[i],col);CHKERRQ(ierr);
1309       }
1310     }
1311     ierr = PetscHSetIGetSize(hta[i],&htsize);CHKERRQ(ierr);
1312     dnz[i] = htsize;
1313     ierr = PetscHSetIDestroy(&hta[i]);CHKERRQ(ierr);
1314     ierr = PetscHSetIGetSize(hto[i],&htsize);CHKERRQ(ierr);
1315     onz[i] = htsize;
1316     ierr = PetscHSetIDestroy(&hto[i]);CHKERRQ(ierr);
1317   }
1318 
1319   ierr = PetscFree2(hta,hto);CHKERRQ(ierr);
1320   ierr = PetscFree(c_othj);CHKERRQ(ierr);
1321 
1322   /* local sizes and preallocation */
1323   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1324   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
1325   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
1326   ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);
1327 
1328   /* attach the supporting struct to Cmpi for reuse */
1329   c = (Mat_MPIAIJ*)Cmpi->data;
1330   c->ap           = ptap;
1331   ptap->duplicate = Cmpi->ops->duplicate;
1332   ptap->destroy   = Cmpi->ops->destroy;
1333   ptap->view      = Cmpi->ops->view;
1334 
1335   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
1336   Cmpi->assembled        = PETSC_FALSE;
1337   /* pick an algorithm */
1338   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
1339   alg = 0;
1340   ierr = PetscOptionsEList("-matptap_allatonce_via","PtAP allatonce numeric approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
1341   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1342   switch (alg) {
1343     case 0:
1344       Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_allatonce;
1345       break;
1346     case 1:
1347       Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_allatonce_merged;
1348       break;
1349     default:
1350       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG," Unsupported allatonce numerical algorithm \n");
1351   }
1352   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
1353   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
1354   Cmpi->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
1355   *C                     = Cmpi;
1356   PetscFunctionReturn(0);
1357 }
1358 
1359 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_allatonce_merged(Mat A,Mat P,PetscReal fill,Mat *C)
1360 {
1361   Mat_APMPI           *ptap;
1362   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*c;
1363   MPI_Comm            comm;
1364   Mat                 Cmpi;
1365   Mat_SeqAIJ          *pd,*po;
1366   MatType             mtype;
1367   PetscSF             sf;
1368   PetscSFNode         *iremote;
1369   PetscInt            rootspacesize,*rootspace,*rootspaceoffsets,nleaves;
1370   const PetscInt      *rootdegrees;
1371   PetscHSetI          ht,oht,*hta,*hto,*htd;
1372   PetscInt            pn,pon,*c_rmtc,i,j,nzi,dnzi,htsize,htosize,*c_rmtj,off,*c_othj,rcvncols,sendncols,*c_rmtoffsets;
1373   PetscInt            owner,lidx,*rdj,col,pcstart,pcend,*dnz,*onz,am,arstart,arend,*poj,*pdj;
1374   PetscInt            nalg=2,alg=0;
1375   PetscBool           flg;
1376   const char          *algTypes[2] = {"merged","overlapping"};
1377   PetscErrorCode      ierr;
1378 
1379   PetscFunctionBegin;
1380   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1381 
1382   /* Create symbolic parallel matrix Cmpi */
1383   ierr = MatGetLocalSize(P,NULL,&pn);CHKERRQ(ierr);
1384   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
1385   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1386   ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr);
1387   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1388 
1389   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
1390   ptap->reuse = MAT_INITIAL_MATRIX;
1391   ptap->algType = 3;
1392 
1393   /* 0) Get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1394   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1395 
1396   po = (Mat_SeqAIJ*)p->B->data;
1397   pd = (Mat_SeqAIJ*)p->A->data;
1398 
1399   /* This equals to the number of offdiag columns in P */
1400   ierr = MatGetLocalSize(p->B,NULL,&pon);CHKERRQ(ierr);
1401   /* offsets */
1402   ierr = PetscMalloc1(pon+1,&ptap->c_rmti);CHKERRQ(ierr);
1403   /* The number of columns we will send to remote ranks */
1404   ierr = PetscMalloc1(pon,&c_rmtc);CHKERRQ(ierr);
1405   ierr = PetscMalloc1(pon,&hta);CHKERRQ(ierr);
1406   for (i=0; i<pon; i++) {
1407     ierr = PetscHSetICreate(&hta[i]);CHKERRQ(ierr);
1408   }
1409   ierr = MatGetLocalSize(A,&am,NULL);CHKERRQ(ierr);
1410   ierr = MatGetOwnershipRange(A,&arstart,&arend);CHKERRQ(ierr);
1411   /* Create hash table to merge all columns for C(i, :) */
1412   ierr = PetscHSetICreate(&ht);CHKERRQ(ierr);
1413   ierr = PetscHSetICreate(&oht);CHKERRQ(ierr);
1414   ierr = PetscMalloc2(pn,&htd,pn,&hto);CHKERRQ(ierr);
1415   for (i=0; i<pn; i++) {
1416     ierr = PetscHSetICreate(&htd[i]);CHKERRQ(ierr);
1417     ierr = PetscHSetICreate(&hto[i]);CHKERRQ(ierr);
1418   }
1419   ptap->c_rmti[0] = 0;
1420   /* 2) Pass 1: calculate the size for C_rmt (a matrix need to be sent to other processors)  */
1421   for (i=0; i<am && (pon || pn); i++) {
1422     /* Form one row of AP */
1423     ierr = PetscHSetIClear(ht);CHKERRQ(ierr);
1424     ierr = PetscHSetIClear(oht);CHKERRQ(ierr);
1425     /* If the off diag is empty, we should not do any calculation */
1426     nzi = po->i[i+1] - po->i[i];
1427     dnzi = pd->i[i+1] - pd->i[i];
1428     if (!nzi && !dnzi) continue;
1429 
1430     ierr = MatPtAPSymbolicComputeOneRowOfAP_private(A,P,ptap->P_oth,i,ht,oht);CHKERRQ(ierr);
1431     ierr = PetscHSetIGetSize(ht,&htsize);CHKERRQ(ierr);
1432     ierr = PetscHSetIGetSize(oht,&htosize);CHKERRQ(ierr);
1433     /* If AP is empty, just continue */
1434     if (!(htsize+htosize)) continue;
1435 
1436     /* Form remote C(ii, :) */
1437     poj = po->j + po->i[i];
1438     for (j=0; j<nzi; j++) {
1439       ierr = PetscHSetIUpdate(hta[poj[j]],ht);CHKERRQ(ierr);
1440       ierr = PetscHSetIUpdate(hta[poj[j]],oht);CHKERRQ(ierr);
1441     }
1442 
1443     /* Form local C(ii, :) */
1444     pdj = pd->j + pd->i[i];
1445     for (j=0; j<dnzi; j++) {
1446       ierr = PetscHSetIUpdate(htd[pdj[j]],ht);CHKERRQ(ierr);
1447       ierr = PetscHSetIUpdate(hto[pdj[j]],oht);CHKERRQ(ierr);
1448     }
1449   }
1450 
1451   ierr = PetscHSetIDestroy(&ht);CHKERRQ(ierr);
1452   ierr = PetscHSetIDestroy(&oht);CHKERRQ(ierr);
1453 
1454   for (i=0; i<pon; i++) {
1455     ierr = PetscHSetIGetSize(hta[i],&htsize);CHKERRQ(ierr);
1456     ptap->c_rmti[i+1] = ptap->c_rmti[i] + htsize;
1457     c_rmtc[i] = htsize;
1458   }
1459 
1460   ierr = PetscMalloc1(ptap->c_rmti[pon],&c_rmtj);CHKERRQ(ierr);
1461 
1462   for (i=0; i<pon; i++) {
1463     off = 0;
1464     ierr = PetscHSetIGetElems(hta[i],&off,c_rmtj+ptap->c_rmti[i]);CHKERRQ(ierr);
1465     ierr = PetscHSetIDestroy(&hta[i]);CHKERRQ(ierr);
1466   }
1467   ierr = PetscFree(hta);CHKERRQ(ierr);
1468 
1469   ierr = PetscCalloc1(pon,&iremote);CHKERRQ(ierr);
1470   for (i=0; i<pon; i++) {
1471     owner = 0; lidx = 0;
1472     ierr = PetscLayoutFindOwnerIndex(P->cmap,p->garray[i],&owner,&lidx);CHKERRQ(ierr);
1473     iremote[i].index = lidx;
1474     iremote[i].rank  = owner;
1475   }
1476 
1477   ierr = PetscSFCreate(comm,&sf);CHKERRQ(ierr);
1478   ierr = PetscSFSetGraph(sf,pn,pon,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER);CHKERRQ(ierr);
1479   /* Reorder ranks properly so that the data handled by gather and scatter have the same order */
1480   ierr = PetscSFSetRankOrder(sf,PETSC_TRUE);CHKERRQ(ierr);
1481   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1482   ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
1483   /* How many neighbors have contributions to my rows? */
1484   ierr = PetscSFComputeDegreeBegin(sf,&rootdegrees);CHKERRQ(ierr);
1485   ierr = PetscSFComputeDegreeEnd(sf,&rootdegrees);CHKERRQ(ierr);
1486   rootspacesize = 0;
1487   for (i = 0; i < pn; i++) {
1488     rootspacesize += rootdegrees[i];
1489   }
1490   ierr = PetscCalloc1(rootspacesize,&rootspace);CHKERRQ(ierr);
1491   ierr = PetscCalloc1(rootspacesize+1,&rootspaceoffsets);CHKERRQ(ierr);
1492   /* Get information from leaves
1493    * Number of columns other people contribute to my rows
1494    * */
1495   ierr = PetscSFGatherBegin(sf,MPIU_INT,c_rmtc,rootspace);CHKERRQ(ierr);
1496   ierr = PetscSFGatherEnd(sf,MPIU_INT,c_rmtc,rootspace);CHKERRQ(ierr);
1497   ierr = PetscFree(c_rmtc);CHKERRQ(ierr);
1498   ierr = PetscCalloc1(pn+1,&ptap->c_othi);CHKERRQ(ierr);
1499   /* The number of columns is received for each row */
1500   ptap->c_othi[0] = 0;
1501   rootspacesize = 0;
1502   rootspaceoffsets[0] = 0;
1503   for (i = 0; i < pn; i++) {
1504     rcvncols = 0;
1505     for (j = 0; j<rootdegrees[i]; j++) {
1506       rcvncols += rootspace[rootspacesize];
1507       rootspaceoffsets[rootspacesize+1] = rootspaceoffsets[rootspacesize] + rootspace[rootspacesize];
1508       rootspacesize++;
1509     }
1510     ptap->c_othi[i+1] = ptap->c_othi[i] + rcvncols;
1511   }
1512   ierr = PetscFree(rootspace);CHKERRQ(ierr);
1513 
1514   ierr = PetscCalloc1(pon,&c_rmtoffsets);CHKERRQ(ierr);
1515   ierr = PetscSFScatterBegin(sf,MPIU_INT,rootspaceoffsets,c_rmtoffsets);CHKERRQ(ierr);
1516   ierr = PetscSFScatterEnd(sf,MPIU_INT,rootspaceoffsets,c_rmtoffsets);CHKERRQ(ierr);
1517   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1518   ierr = PetscFree(rootspaceoffsets);CHKERRQ(ierr);
1519 
1520   ierr = PetscCalloc1(ptap->c_rmti[pon],&iremote);CHKERRQ(ierr);
1521   nleaves = 0;
1522   for (i = 0; i<pon; i++) {
1523     owner = 0; lidx = 0;
1524     ierr = PetscLayoutFindOwnerIndex(P->cmap,p->garray[i],&owner,&lidx);CHKERRQ(ierr);
1525     sendncols = ptap->c_rmti[i+1] - ptap->c_rmti[i];
1526     for (j=0; j<sendncols; j++) {
1527       iremote[nleaves].rank = owner;
1528       iremote[nleaves++].index = c_rmtoffsets[i] + j;
1529     }
1530   }
1531   ierr = PetscFree(c_rmtoffsets);CHKERRQ(ierr);
1532   ierr = PetscCalloc1(ptap->c_othi[pn],&c_othj);CHKERRQ(ierr);
1533 
1534   ierr = PetscSFCreate(comm,&ptap->sf);CHKERRQ(ierr);
1535   ierr = PetscSFSetGraph(ptap->sf,ptap->c_othi[pn],nleaves,NULL,PETSC_OWN_POINTER,iremote,PETSC_OWN_POINTER);CHKERRQ(ierr);
1536   ierr = PetscSFSetFromOptions(ptap->sf);CHKERRQ(ierr);
1537   /* One to one map */
1538   ierr = PetscSFReduceBegin(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPIU_REPLACE);CHKERRQ(ierr);
1539   /* Get remote data */
1540   ierr = PetscSFReduceEnd(ptap->sf,MPIU_INT,c_rmtj,c_othj,MPIU_REPLACE);CHKERRQ(ierr);
1541   ierr = PetscFree(c_rmtj);CHKERRQ(ierr);
1542   ierr = PetscCalloc2(pn,&dnz,pn,&onz);CHKERRQ(ierr);
1543   ierr = MatGetOwnershipRangeColumn(P,&pcstart,&pcend);CHKERRQ(ierr);
1544 
1545   for (i = 0; i < pn; i++) {
1546     nzi = ptap->c_othi[i+1] - ptap->c_othi[i];
1547     rdj = c_othj + ptap->c_othi[i];
1548     for (j = 0; j < nzi; j++) {
1549       col =  rdj[j];
1550       /* diag part */
1551       if (col>=pcstart && col<pcend) {
1552         ierr = PetscHSetIAdd(htd[i],col);CHKERRQ(ierr);
1553       } else { /* off diag */
1554         ierr = PetscHSetIAdd(hto[i],col);CHKERRQ(ierr);
1555       }
1556     }
1557     ierr = PetscHSetIGetSize(htd[i],&htsize);CHKERRQ(ierr);
1558     dnz[i] = htsize;
1559     ierr = PetscHSetIDestroy(&htd[i]);CHKERRQ(ierr);
1560     ierr = PetscHSetIGetSize(hto[i],&htsize);CHKERRQ(ierr);
1561     onz[i] = htsize;
1562     ierr = PetscHSetIDestroy(&hto[i]);CHKERRQ(ierr);
1563   }
1564 
1565   ierr = PetscFree2(htd,hto);CHKERRQ(ierr);
1566   ierr = PetscFree(c_othj);CHKERRQ(ierr);
1567 
1568   /* local sizes and preallocation */
1569   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1570   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
1571   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
1572   ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);
1573 
1574   /* attach the supporting struct to Cmpi for reuse */
1575   c = (Mat_MPIAIJ*)Cmpi->data;
1576   c->ap           = ptap;
1577   ptap->duplicate = Cmpi->ops->duplicate;
1578   ptap->destroy   = Cmpi->ops->destroy;
1579   ptap->view      = Cmpi->ops->view;
1580 
1581   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
1582   Cmpi->assembled        = PETSC_FALSE;
1583   /* pick an algorithm */
1584   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
1585   alg = 0;
1586   ierr = PetscOptionsEList("-matptap_allatonce_via","PtAP allatonce numeric approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
1587   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1588   switch (alg) {
1589     case 0:
1590       Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_allatonce_merged;
1591       break;
1592     case 1:
1593       Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_allatonce;
1594       break;
1595     default:
1596       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG," Unsupported allatonce numerical algorithm \n");
1597   }
1598   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
1599   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
1600   Cmpi->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
1601   *C                     = Cmpi;
1602   PetscFunctionReturn(0);
1603 }
1604 
1605 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
1606 {
1607   PetscErrorCode      ierr;
1608   Mat_APMPI           *ptap;
1609   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
1610   MPI_Comm            comm;
1611   PetscMPIInt         size,rank;
1612   Mat                 Cmpi;
1613   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1614   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
1615   PetscInt            *lnk,i,k,pnz,row,nsend;
1616   PetscBT             lnkbt;
1617   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
1618   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1619   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
1620   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1621   MPI_Request         *swaits,*rwaits;
1622   MPI_Status          *sstatus,rstatus;
1623   PetscLayout         rowmap;
1624   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1625   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1626   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,ap_rmax=0,Crmax,*aj,*ai,*pi;
1627   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
1628   PetscScalar         *apv;
1629   PetscTable          ta;
1630   MatType             mtype;
1631   const char          *prefix;
1632 #if defined(PETSC_USE_INFO)
1633   PetscReal           apfill;
1634 #endif
1635 
1636   PetscFunctionBegin;
1637   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1638   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1639   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1640 
1641   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
1642 
1643   /* create symbolic parallel matrix Cmpi */
1644   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
1645   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1646   ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr);
1647 
1648   /* Do dense axpy in MatPtAPNumeric_MPIAIJ_MPIAIJ() */
1649   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ;
1650 
1651   /* create struct Mat_APMPI and attached it to C later */
1652   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
1653   ptap->reuse = MAT_INITIAL_MATRIX;
1654   ptap->algType = 1;
1655 
1656   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1657   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1658   /* get P_loc by taking all local rows of P */
1659   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1660 
1661   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1662   /* --------------------------------- */
1663   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1664   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1665 
1666   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
1667   /* ----------------------------------------------------------------- */
1668   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1669   if (ptap->P_oth) p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1670 
1671   /* create and initialize a linked list */
1672   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
1673   MatRowMergeMax_SeqAIJ(p_loc,ptap->P_loc->rmap->N,ta);
1674   MatRowMergeMax_SeqAIJ(p_oth,ptap->P_oth->rmap->N,ta);
1675   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
1676   /* printf("[%d] est %d, Crmax %d; pN %d\n",rank,5*(p_loc->rmax+p_oth->rmax + (PetscInt)(1.e-2*pN)),Crmax,pN); */
1677 
1678   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1679 
1680   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
1681   if (ao) {
1682     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
1683   } else {
1684     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
1685   }
1686   current_space = free_space;
1687   nspacedouble  = 0;
1688 
1689   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
1690   api[0] = 0;
1691   for (i=0; i<am; i++) {
1692     /* diagonal portion: Ad[i,:]*P */
1693     ai = ad->i; pi = p_loc->i;
1694     nzi = ai[i+1] - ai[i];
1695     aj  = ad->j + ai[i];
1696     for (j=0; j<nzi; j++) {
1697       row  = aj[j];
1698       pnz  = pi[row+1] - pi[row];
1699       Jptr = p_loc->j + pi[row];
1700       /* add non-zero cols of P into the sorted linked list lnk */
1701       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1702     }
1703     /* off-diagonal portion: Ao[i,:]*P */
1704     if (ao) {
1705       ai = ao->i; pi = p_oth->i;
1706       nzi = ai[i+1] - ai[i];
1707       aj  = ao->j + ai[i];
1708       for (j=0; j<nzi; j++) {
1709         row  = aj[j];
1710         pnz  = pi[row+1] - pi[row];
1711         Jptr = p_oth->j + pi[row];
1712         ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1713       }
1714     }
1715     apnz     = lnk[0];
1716     api[i+1] = api[i] + apnz;
1717     if (ap_rmax < apnz) ap_rmax = apnz;
1718 
1719     /* if free space is not available, double the total space in the list */
1720     if (current_space->local_remaining<apnz) {
1721       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1722       nspacedouble++;
1723     }
1724 
1725     /* Copy data into free space, then initialize lnk */
1726     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1727 
1728     current_space->array           += apnz;
1729     current_space->local_used      += apnz;
1730     current_space->local_remaining -= apnz;
1731   }
1732   /* Allocate space for apj and apv, initialize apj, and */
1733   /* destroy list of free space and other temporary array(s) */
1734   ierr   = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
1735   ierr   = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
1736   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1737 
1738   /* Create AP_loc for reuse */
1739   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
1740 
1741 #if defined(PETSC_USE_INFO)
1742   if (ao) {
1743     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
1744   } else {
1745     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
1746   }
1747   ptap->AP_loc->info.mallocs           = nspacedouble;
1748   ptap->AP_loc->info.fill_ratio_given  = fill;
1749   ptap->AP_loc->info.fill_ratio_needed = apfill;
1750 
1751   if (api[am]) {
1752     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);
1753     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
1754   } else {
1755     ierr = PetscInfo(ptap->AP_loc,"Nonscalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
1756   }
1757 #endif
1758 
1759   /* (2-1) compute symbolic Co = Ro*AP_loc  */
1760   /* ------------------------------------ */
1761   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1762   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
1763   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
1764   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
1765 
1766   /* (3) send coj of C_oth to other processors  */
1767   /* ------------------------------------------ */
1768   /* determine row ownership */
1769   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
1770   rowmap->n  = pn;
1771   rowmap->bs = 1;
1772   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
1773   owners = rowmap->range;
1774 
1775   /* determine the number of messages to send, their lengths */
1776   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
1777   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
1778   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
1779 
1780   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1781   coi   = c_oth->i; coj = c_oth->j;
1782   con   = ptap->C_oth->rmap->n;
1783   proc  = 0;
1784   for (i=0; i<con; i++) {
1785     while (prmap[i] >= owners[proc+1]) proc++;
1786     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
1787     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1788   }
1789 
1790   len          = 0; /* max length of buf_si[], see (4) */
1791   owners_co[0] = 0;
1792   nsend        = 0;
1793   for (proc=0; proc<size; proc++) {
1794     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1795     if (len_s[proc]) {
1796       nsend++;
1797       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1798       len         += len_si[proc];
1799     }
1800   }
1801 
1802   /* determine the number and length of messages to receive for coi and coj  */
1803   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
1804   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
1805 
1806   /* post the Irecv and Isend of coj */
1807   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1808   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1809   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
1810   for (proc=0, k=0; proc<size; proc++) {
1811     if (!len_s[proc]) continue;
1812     i    = owners_co[proc];
1813     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1814     k++;
1815   }
1816 
1817   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
1818   /* ---------------------------------------- */
1819   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
1820   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
1821   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
1822   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1823 
1824   /* receives coj are complete */
1825   for (i=0; i<nrecv; i++) {
1826     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1827   }
1828   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1829   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
1830 
1831   /* add received column indices into ta to update Crmax */
1832   for (k=0; k<nrecv; k++) {/* k-th received message */
1833     Jptr = buf_rj[k];
1834     for (j=0; j<len_r[k]; j++) {
1835       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1836     }
1837   }
1838   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
1839   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
1840 
1841   /* (4) send and recv coi */
1842   /*-----------------------*/
1843   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1844   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1845   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1846   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1847   for (proc=0,k=0; proc<size; proc++) {
1848     if (!len_s[proc]) continue;
1849     /* form outgoing message for i-structure:
1850          buf_si[0]:                 nrows to be sent
1851                [1:nrows]:           row index (global)
1852                [nrows+1:2*nrows+1]: i-structure index
1853     */
1854     /*-------------------------------------------*/
1855     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1856     buf_si_i    = buf_si + nrows+1;
1857     buf_si[0]   = nrows;
1858     buf_si_i[0] = 0;
1859     nrows       = 0;
1860     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1861       nzi = coi[i+1] - coi[i];
1862       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1863       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1864       nrows++;
1865     }
1866     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
1867     k++;
1868     buf_si += len_si[proc];
1869   }
1870   for (i=0; i<nrecv; i++) {
1871     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1872   }
1873   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1874   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
1875 
1876   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
1877   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1878   ierr = PetscFree(swaits);CHKERRQ(ierr);
1879   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1880 
1881   /* (5) compute the local portion of Cmpi      */
1882   /* ------------------------------------------ */
1883   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
1884   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
1885   current_space = free_space;
1886 
1887   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
1888   for (k=0; k<nrecv; k++) {
1889     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1890     nrows       = *buf_ri_k[k];
1891     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1892     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1893   }
1894 
1895   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
1896   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1897   for (i=0; i<pn; i++) {
1898     /* add C_loc into Cmpi */
1899     nzi  = c_loc->i[i+1] - c_loc->i[i];
1900     Jptr = c_loc->j + c_loc->i[i];
1901     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1902 
1903     /* add received col data into lnk */
1904     for (k=0; k<nrecv; k++) { /* k-th received message */
1905       if (i == *nextrow[k]) { /* i-th row */
1906         nzi  = *(nextci[k]+1) - *nextci[k];
1907         Jptr = buf_rj[k] + *nextci[k];
1908         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1909         nextrow[k]++; nextci[k]++;
1910       }
1911     }
1912     nzi = lnk[0];
1913 
1914     /* copy data into free space, then initialize lnk */
1915     ierr = PetscLLCondensedClean(pN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1916     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
1917   }
1918   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1919   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1920   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
1921 
1922   /* local sizes and preallocation */
1923   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1924   if (P->cmap->bs > 0) {
1925     ierr = PetscLayoutSetBlockSize(Cmpi->rmap,P->cmap->bs);CHKERRQ(ierr);
1926     ierr = PetscLayoutSetBlockSize(Cmpi->cmap,P->cmap->bs);CHKERRQ(ierr);
1927   }
1928   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
1929   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1930 
1931   /* members in merge */
1932   ierr = PetscFree(id_r);CHKERRQ(ierr);
1933   ierr = PetscFree(len_r);CHKERRQ(ierr);
1934   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
1935   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
1936   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
1937   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
1938   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
1939 
1940   /* attach the supporting struct to Cmpi for reuse */
1941   c = (Mat_MPIAIJ*)Cmpi->data;
1942   c->ap           = ptap;
1943   ptap->duplicate = Cmpi->ops->duplicate;
1944   ptap->destroy   = Cmpi->ops->destroy;
1945   ptap->view      = Cmpi->ops->view;
1946   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
1947 
1948   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
1949   Cmpi->assembled        = PETSC_FALSE;
1950   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
1951   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
1952   Cmpi->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
1953   *C                     = Cmpi;
1954   PetscFunctionReturn(0);
1955 }
1956 
1957 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
1958 {
1959   PetscErrorCode    ierr;
1960   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1961   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
1962   Mat_SeqAIJ        *ap,*p_loc,*p_oth=NULL,*c_seq;
1963   Mat_APMPI         *ptap = c->ap;
1964   Mat               AP_loc,C_loc,C_oth;
1965   PetscInt          i,rstart,rend,cm,ncols,row;
1966   PetscInt          *api,*apj,am = A->rmap->n,j,col,apnz;
1967   PetscScalar       *apa;
1968   const PetscInt    *cols;
1969   const PetscScalar *vals;
1970 
1971   PetscFunctionBegin;
1972   if (!ptap->AP_loc) {
1973     MPI_Comm comm;
1974     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1975     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
1976   }
1977 
1978   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1979   /* 1) get R = Pd^T,Ro = Po^T */
1980   if (ptap->reuse == MAT_REUSE_MATRIX) {
1981     ierr = MatTranspose(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1982     ierr = MatTranspose(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1983   }
1984 
1985   /* 2) get AP_loc */
1986   AP_loc = ptap->AP_loc;
1987   ap = (Mat_SeqAIJ*)AP_loc->data;
1988 
1989   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
1990   /*-----------------------------------------------------*/
1991   if (ptap->reuse == MAT_REUSE_MATRIX) {
1992     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
1993     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1994     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1995   }
1996 
1997   /* 2-2) compute numeric A_loc*P - dominating part */
1998   /* ---------------------------------------------- */
1999   /* get data from symbolic products */
2000   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
2001   if (ptap->P_oth) {
2002     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
2003   }
2004   apa   = ptap->apa;
2005   api   = ap->i;
2006   apj   = ap->j;
2007   for (i=0; i<am; i++) {
2008     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
2009     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
2010     apnz = api[i+1] - api[i];
2011     for (j=0; j<apnz; j++) {
2012       col = apj[j+api[i]];
2013       ap->a[j+ap->i[i]] = apa[col];
2014       apa[col] = 0.0;
2015     }
2016   }
2017 
2018   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
2019   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
2020   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
2021   C_loc = ptap->C_loc;
2022   C_oth = ptap->C_oth;
2023 
2024   /* add C_loc and Co to to C */
2025   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
2026 
2027   /* C_loc -> C */
2028   cm    = C_loc->rmap->N;
2029   c_seq = (Mat_SeqAIJ*)C_loc->data;
2030   cols = c_seq->j;
2031   vals = c_seq->a;
2032 
2033 
2034   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assembled is PETSC_FALSE and */
2035   /* when there are no off-processor parts.  */
2036   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
2037   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
2038   /* a table, and other, more complex stuff has to be done. */
2039   if (C->assembled) {
2040     C->was_assembled = PETSC_TRUE;
2041     C->assembled     = PETSC_FALSE;
2042   }
2043   if (C->was_assembled) {
2044     for (i=0; i<cm; i++) {
2045       ncols = c_seq->i[i+1] - c_seq->i[i];
2046       row = rstart + i;
2047       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
2048       cols += ncols; vals += ncols;
2049     }
2050   } else {
2051     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
2052   }
2053 
2054   /* Co -> C, off-processor part */
2055   cm = C_oth->rmap->N;
2056   c_seq = (Mat_SeqAIJ*)C_oth->data;
2057   cols = c_seq->j;
2058   vals = c_seq->a;
2059   for (i=0; i<cm; i++) {
2060     ncols = c_seq->i[i+1] - c_seq->i[i];
2061     row = p->garray[i];
2062     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
2063     cols += ncols; vals += ncols;
2064   }
2065 
2066   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2067   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2068 
2069   ptap->reuse = MAT_REUSE_MATRIX;
2070 
2071   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
2072   if (ptap->freestruct) {
2073     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
2074   }
2075   PetscFunctionReturn(0);
2076 }
2077