1 2 /* 3 Defines matrix-matrix product routines for pairs of MPIAIJ matrices 4 C = A * B 5 */ 6 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/ 7 #include <../src/mat/utils/freespace.h> 8 #include <../src/mat/impls/aij/mpi/mpiaij.h> 9 #include <petscbt.h> 10 #include <../src/mat/impls/dense/mpi/mpidense.h> 11 #include <petsc/private/vecimpl.h> 12 13 #if defined(PETSC_HAVE_HYPRE) 14 PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*); 15 #endif 16 17 PETSC_INTERN PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C) 18 { 19 PetscErrorCode ierr; 20 #if defined(PETSC_HAVE_HYPRE) 21 const char *algTypes[4] = {"scalable","nonscalable","seqmpi","hypre"}; 22 PetscInt nalg = 4; 23 #else 24 const char *algTypes[3] = {"scalable","nonscalable","seqmpi"}; 25 PetscInt nalg = 3; 26 #endif 27 PetscInt alg = 1; /* set nonscalable algorithm as default */ 28 MPI_Comm comm; 29 PetscBool flg; 30 31 PetscFunctionBegin; 32 if (scall == MAT_INITIAL_MATRIX) { 33 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 34 if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend); 35 36 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 37 PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */ 38 ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[1],&alg,&flg);CHKERRQ(ierr); 39 ierr = PetscOptionsEnd();CHKERRQ(ierr); 40 41 if (!flg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */ 42 MatInfo Ainfo,Binfo; 43 PetscInt nz_local; 44 PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable; 45 46 ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr); 47 ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr); 48 nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated); 49 50 if (B->cmap->N > fill*nz_local) alg_scalable_loc = PETSC_TRUE; 51 ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr); 52 53 if (alg_scalable) { 54 alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */ 55 ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,fill*nz_local);CHKERRQ(ierr); 56 } 57 } 58 59 ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 60 switch (alg) { 61 case 1: 62 ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr); 63 break; 64 case 2: 65 ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);CHKERRQ(ierr); 66 break; 67 #if defined(PETSC_HAVE_HYPRE) 68 case 3: 69 ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr); 70 break; 71 #endif 72 default: 73 ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr); 74 break; 75 } 76 ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 77 } 78 ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 79 ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr); 80 ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 81 PetscFunctionReturn(0); 82 } 83 84 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A) 85 { 86 PetscErrorCode ierr; 87 Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data; 88 Mat_PtAPMPI *ptap = a->ptap; 89 90 PetscFunctionBegin; 91 ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr); 92 ierr = PetscFree(ptap->bufa);CHKERRQ(ierr); 93 ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr); 94 ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr); 95 ierr = MatDestroy(&ptap->Pt);CHKERRQ(ierr); 96 ierr = PetscFree(ptap->api);CHKERRQ(ierr); 97 ierr = PetscFree(ptap->apj);CHKERRQ(ierr); 98 ierr = PetscFree(ptap->apa);CHKERRQ(ierr); 99 ierr = ptap->destroy(A);CHKERRQ(ierr); 100 ierr = PetscFree(ptap);CHKERRQ(ierr); 101 PetscFunctionReturn(0); 102 } 103 104 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C) 105 { 106 PetscErrorCode ierr; 107 Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data; 108 Mat_SeqAIJ *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data; 109 Mat_SeqAIJ *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data; 110 PetscScalar *cda=cd->a,*coa=co->a; 111 Mat_SeqAIJ *p_loc,*p_oth; 112 PetscScalar *apa,*ca; 113 PetscInt cm =C->rmap->n; 114 Mat_PtAPMPI *ptap=c->ptap; 115 PetscInt *api,*apj,*apJ,i,k; 116 PetscInt cstart=C->cmap->rstart; 117 PetscInt cdnz,conz,k0,k1; 118 MPI_Comm comm; 119 PetscMPIInt size; 120 121 PetscFunctionBegin; 122 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 123 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 124 125 /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */ 126 /*-----------------------------------------------------*/ 127 /* update numerical values of P_oth and P_loc */ 128 ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr); 129 ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr); 130 131 /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */ 132 /*----------------------------------------------------------*/ 133 /* get data from symbolic products */ 134 p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data; 135 p_oth = NULL; 136 if (size >1) { 137 p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data; 138 } 139 140 /* get apa for storing dense row A[i,:]*P */ 141 apa = ptap->apa; 142 143 api = ptap->api; 144 apj = ptap->apj; 145 for (i=0; i<cm; i++) { 146 /* compute apa = A[i,:]*P */ 147 AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa); 148 149 /* set values in C */ 150 apJ = apj + api[i]; 151 cdnz = cd->i[i+1] - cd->i[i]; 152 conz = co->i[i+1] - co->i[i]; 153 154 /* 1st off-diagoanl part of C */ 155 ca = coa + co->i[i]; 156 k = 0; 157 for (k0=0; k0<conz; k0++) { 158 if (apJ[k] >= cstart) break; 159 ca[k0] = apa[apJ[k]]; 160 apa[apJ[k++]] = 0.0; 161 } 162 163 /* diagonal part of C */ 164 ca = cda + cd->i[i]; 165 for (k1=0; k1<cdnz; k1++) { 166 ca[k1] = apa[apJ[k]]; 167 apa[apJ[k++]] = 0.0; 168 } 169 170 /* 2nd off-diagoanl part of C */ 171 ca = coa + co->i[i]; 172 for (; k0<conz; k0++) { 173 ca[k0] = apa[apJ[k]]; 174 apa[apJ[k++]] = 0.0; 175 } 176 } 177 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 178 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 179 PetscFunctionReturn(0); 180 } 181 182 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat *C) 183 { 184 PetscErrorCode ierr; 185 MPI_Comm comm; 186 PetscMPIInt size; 187 Mat Cmpi; 188 Mat_PtAPMPI *ptap; 189 PetscFreeSpaceList free_space=NULL,current_space=NULL; 190 Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data,*c; 191 Mat_SeqAIJ *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth; 192 PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz; 193 PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart; 194 PetscInt *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi; 195 PetscInt am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n; 196 PetscBT lnkbt; 197 PetscScalar *apa; 198 PetscReal afill; 199 MatType mtype; 200 201 PetscFunctionBegin; 202 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 203 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 204 205 /* create struct Mat_PtAPMPI and attached it to C later */ 206 ierr = PetscNew(&ptap);CHKERRQ(ierr); 207 208 /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */ 209 ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr); 210 211 /* get P_loc by taking all local rows of P */ 212 ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr); 213 214 p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data; 215 pi_loc = p_loc->i; pj_loc = p_loc->j; 216 if (size > 1) { 217 p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data; 218 pi_oth = p_oth->i; pj_oth = p_oth->j; 219 } else { 220 p_oth = NULL; 221 pi_oth = NULL; pj_oth = NULL; 222 } 223 224 /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */ 225 /*-------------------------------------------------------------------*/ 226 ierr = PetscMalloc1(am+2,&api);CHKERRQ(ierr); 227 ptap->api = api; 228 api[0] = 0; 229 230 /* create and initialize a linked list */ 231 ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr); 232 233 /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */ 234 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr); 235 current_space = free_space; 236 237 ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr); 238 for (i=0; i<am; i++) { 239 /* diagonal portion of A */ 240 nzi = adi[i+1] - adi[i]; 241 for (j=0; j<nzi; j++) { 242 row = *adj++; 243 pnz = pi_loc[row+1] - pi_loc[row]; 244 Jptr = pj_loc + pi_loc[row]; 245 /* add non-zero cols of P into the sorted linked list lnk */ 246 ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr); 247 } 248 /* off-diagonal portion of A */ 249 nzi = aoi[i+1] - aoi[i]; 250 for (j=0; j<nzi; j++) { 251 row = *aoj++; 252 pnz = pi_oth[row+1] - pi_oth[row]; 253 Jptr = pj_oth + pi_oth[row]; 254 ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr); 255 } 256 257 apnz = lnk[0]; 258 api[i+1] = api[i] + apnz; 259 260 /* if free space is not available, double the total space in the list */ 261 if (current_space->local_remaining<apnz) { 262 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 263 nspacedouble++; 264 } 265 266 /* Copy data into free space, then initialize lnk */ 267 ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr); 268 ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr); 269 270 current_space->array += apnz; 271 current_space->local_used += apnz; 272 current_space->local_remaining -= apnz; 273 } 274 275 /* Allocate space for apj, initialize apj, and */ 276 /* destroy list of free space and other temporary array(s) */ 277 ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr); 278 apj = ptap->apj; 279 ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr); 280 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 281 282 /* malloc apa to store dense row A[i,:]*P */ 283 ierr = PetscCalloc1(pN,&apa);CHKERRQ(ierr); 284 285 ptap->apa = apa; 286 287 /* create and assemble symbolic parallel matrix Cmpi */ 288 /*----------------------------------------------------*/ 289 ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr); 290 ierr = MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 291 ierr = MatSetBlockSizesFromMats(Cmpi,A,P);CHKERRQ(ierr); 292 293 ierr = MatGetType(A,&mtype);CHKERRQ(ierr); 294 ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr); 295 ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr); 296 297 ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Cmpi, apj, api);CHKERRQ(ierr); 298 ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 299 ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 300 ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr); 301 302 ptap->destroy = Cmpi->ops->destroy; 303 ptap->duplicate = Cmpi->ops->duplicate; 304 Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable; 305 Cmpi->ops->destroy = MatDestroy_MPIAIJ_MatMatMult; 306 307 /* attach the supporting struct to Cmpi for reuse */ 308 c = (Mat_MPIAIJ*)Cmpi->data; 309 c->ptap = ptap; 310 311 *C = Cmpi; 312 313 /* set MatInfo */ 314 afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5; 315 if (afill < 1.0) afill = 1.0; 316 Cmpi->info.mallocs = nspacedouble; 317 Cmpi->info.fill_ratio_given = fill; 318 Cmpi->info.fill_ratio_needed = afill; 319 320 #if defined(PETSC_USE_INFO) 321 if (api[am]) { 322 ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 323 ierr = PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 324 } else { 325 ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr); 326 } 327 #endif 328 PetscFunctionReturn(0); 329 } 330 331 PETSC_INTERN PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 332 { 333 PetscErrorCode ierr; 334 335 PetscFunctionBegin; 336 if (scall == MAT_INITIAL_MATRIX) { 337 ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 338 ierr = MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);CHKERRQ(ierr); 339 ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 340 } 341 ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 342 ierr = MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);CHKERRQ(ierr); 343 ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 344 PetscFunctionReturn(0); 345 } 346 347 typedef struct { 348 Mat workB; 349 PetscScalar *rvalues,*svalues; 350 MPI_Request *rwaits,*swaits; 351 } MPIAIJ_MPIDense; 352 353 PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx) 354 { 355 MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx; 356 PetscErrorCode ierr; 357 358 PetscFunctionBegin; 359 ierr = MatDestroy(&contents->workB);CHKERRQ(ierr); 360 ierr = PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);CHKERRQ(ierr); 361 ierr = PetscFree(contents);CHKERRQ(ierr); 362 PetscFunctionReturn(0); 363 } 364 365 #include <petsc/private/vecscatterimpl.h> 366 /* 367 This is a "dummy function" that handles the case where matrix C was created as a dense matrix 368 directly by the user and passed to MatMatMult() with the MAT_REUSE_MATRIX option 369 370 It is the same as MatMatMultSymbolic_MPIAIJ_MPIDense() except does not create C 371 372 Developer Notes: This directly accesses information inside the VecScatter associated with the matrix-vector product 373 for this matrix. This is not desirable.. 374 375 */ 376 PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat B,Mat C) 377 { 378 PetscErrorCode ierr; 379 PetscBool flg; 380 Mat_MPIAIJ *aij = (Mat_MPIAIJ*) A->data; 381 PetscInt nz = aij->B->cmap->n; 382 PetscContainer container; 383 MPIAIJ_MPIDense *contents; 384 VecScatter ctx = aij->Mvctx; 385 VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata; 386 VecScatter_MPI_General *to = (VecScatter_MPI_General*) ctx->todata; 387 388 PetscFunctionBegin; 389 ierr = PetscObjectTypeCompare((PetscObject)B,MATMPIDENSE,&flg);CHKERRQ(ierr); 390 if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Second matrix must be mpidense"); 391 392 /* Handle case where where user provided the final C matrix rather than calling MatMatMult() with MAT_INITIAL_MATRIX*/ 393 ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr); 394 if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"First matrix must be MPIAIJ"); 395 396 C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense; 397 398 ierr = PetscNew(&contents);CHKERRQ(ierr); 399 /* Create work matrix used to store off processor rows of B needed for local product */ 400 ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);CHKERRQ(ierr); 401 /* Create work arrays needed */ 402 ierr = PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues, 403 B->cmap->N*to->starts[to->n],&contents->svalues, 404 from->n,&contents->rwaits, 405 to->n,&contents->swaits);CHKERRQ(ierr); 406 407 ierr = PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);CHKERRQ(ierr); 408 ierr = PetscContainerSetPointer(container,contents);CHKERRQ(ierr); 409 ierr = PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);CHKERRQ(ierr); 410 ierr = PetscObjectCompose((PetscObject)C,"workB",(PetscObject)container);CHKERRQ(ierr); 411 ierr = PetscContainerDestroy(&container);CHKERRQ(ierr); 412 413 ierr = (*C->ops->matmultnumeric)(A,B,C);CHKERRQ(ierr); 414 PetscFunctionReturn(0); 415 } 416 417 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C) 418 { 419 PetscErrorCode ierr; 420 Mat_MPIAIJ *aij = (Mat_MPIAIJ*) A->data; 421 PetscInt nz = aij->B->cmap->n; 422 PetscContainer container; 423 MPIAIJ_MPIDense *contents; 424 VecScatter ctx = aij->Mvctx; 425 VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata; 426 VecScatter_MPI_General *to = (VecScatter_MPI_General*) ctx->todata; 427 PetscInt m = A->rmap->n,n=B->cmap->n; 428 429 PetscFunctionBegin; 430 ierr = MatCreate(PetscObjectComm((PetscObject)B),C);CHKERRQ(ierr); 431 ierr = MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);CHKERRQ(ierr); 432 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 433 ierr = MatSetType(*C,MATMPIDENSE);CHKERRQ(ierr); 434 ierr = MatMPIDenseSetPreallocation(*C,NULL);CHKERRQ(ierr); 435 ierr = MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 436 ierr = MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 437 438 (*C)->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense; 439 440 ierr = PetscNew(&contents);CHKERRQ(ierr); 441 /* Create work matrix used to store off processor rows of B needed for local product */ 442 ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);CHKERRQ(ierr); 443 /* Create work arrays needed */ 444 ierr = PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues, 445 B->cmap->N*to->starts[to->n],&contents->svalues, 446 from->n,&contents->rwaits, 447 to->n,&contents->swaits);CHKERRQ(ierr); 448 449 ierr = PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);CHKERRQ(ierr); 450 ierr = PetscContainerSetPointer(container,contents);CHKERRQ(ierr); 451 ierr = PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);CHKERRQ(ierr); 452 ierr = PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);CHKERRQ(ierr); 453 ierr = PetscContainerDestroy(&container);CHKERRQ(ierr); 454 PetscFunctionReturn(0); 455 } 456 457 /* 458 Performs an efficient scatter on the rows of B needed by this process; this is 459 a modification of the VecScatterBegin_() routines. 460 */ 461 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB) 462 { 463 Mat_MPIAIJ *aij = (Mat_MPIAIJ*)A->data; 464 PetscErrorCode ierr; 465 PetscScalar *b,*w,*svalues,*rvalues; 466 VecScatter ctx = aij->Mvctx; 467 VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata; 468 VecScatter_MPI_General *to = (VecScatter_MPI_General*) ctx->todata; 469 PetscInt i,j,k; 470 PetscInt *sindices,*sstarts,*rindices,*rstarts; 471 PetscMPIInt *sprocs,*rprocs,nrecvs; 472 MPI_Request *swaits,*rwaits; 473 MPI_Comm comm; 474 PetscMPIInt tag = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n; 475 MPI_Status status; 476 MPIAIJ_MPIDense *contents; 477 PetscContainer container; 478 Mat workB; 479 480 PetscFunctionBegin; 481 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 482 ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr); 483 if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist"); 484 ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr); 485 486 workB = *outworkB = contents->workB; 487 if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n); 488 sindices = to->indices; 489 sstarts = to->starts; 490 sprocs = to->procs; 491 swaits = contents->swaits; 492 svalues = contents->svalues; 493 494 rindices = from->indices; 495 rstarts = from->starts; 496 rprocs = from->procs; 497 rwaits = contents->rwaits; 498 rvalues = contents->rvalues; 499 500 ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr); 501 ierr = MatDenseGetArray(workB,&w);CHKERRQ(ierr); 502 503 for (i=0; i<from->n; i++) { 504 ierr = MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr); 505 } 506 507 for (i=0; i<to->n; i++) { 508 /* pack a message at a time */ 509 for (j=0; j<sstarts[i+1]-sstarts[i]; j++) { 510 for (k=0; k<ncols; k++) { 511 svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k]; 512 } 513 } 514 ierr = MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr); 515 } 516 517 nrecvs = from->n; 518 while (nrecvs) { 519 ierr = MPI_Waitany(from->n,rwaits,&imdex,&status);CHKERRQ(ierr); 520 nrecvs--; 521 /* unpack a message at a time */ 522 for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++) { 523 for (k=0; k<ncols; k++) { 524 w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k]; 525 } 526 } 527 } 528 if (to->n) {ierr = MPI_Waitall(to->n,swaits,to->sstatus);CHKERRQ(ierr);} 529 530 ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr); 531 ierr = MatDenseRestoreArray(workB,&w);CHKERRQ(ierr); 532 ierr = MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 533 ierr = MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 534 PetscFunctionReturn(0); 535 } 536 extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat); 537 538 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C) 539 { 540 PetscErrorCode ierr; 541 Mat_MPIAIJ *aij = (Mat_MPIAIJ*)A->data; 542 Mat_MPIDense *bdense = (Mat_MPIDense*)B->data; 543 Mat_MPIDense *cdense = (Mat_MPIDense*)C->data; 544 Mat workB; 545 546 PetscFunctionBegin; 547 /* diagonal block of A times all local rows of B*/ 548 ierr = MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);CHKERRQ(ierr); 549 550 /* get off processor parts of B needed to complete the product */ 551 ierr = MatMPIDenseScatter(A,B,C,&workB);CHKERRQ(ierr); 552 553 /* off-diagonal block of A times nonlocal rows of B */ 554 ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);CHKERRQ(ierr); 555 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 556 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 557 PetscFunctionReturn(0); 558 } 559 560 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C) 561 { 562 PetscErrorCode ierr; 563 Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data; 564 Mat_SeqAIJ *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data; 565 Mat_SeqAIJ *cd = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data; 566 PetscInt *adi = ad->i,*adj,*aoi=ao->i,*aoj; 567 PetscScalar *ada,*aoa,*cda=cd->a,*coa=co->a; 568 Mat_SeqAIJ *p_loc,*p_oth; 569 PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj; 570 PetscScalar *pa_loc,*pa_oth,*pa,valtmp,*ca; 571 PetscInt cm = C->rmap->n,anz,pnz; 572 Mat_PtAPMPI *ptap = c->ptap; 573 PetscScalar *apa_sparse = ptap->apa; 574 PetscInt *api,*apj,*apJ,i,j,k,row; 575 PetscInt cstart = C->cmap->rstart; 576 PetscInt cdnz,conz,k0,k1,nextp; 577 MPI_Comm comm; 578 PetscMPIInt size; 579 580 PetscFunctionBegin; 581 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 582 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 583 584 /* 1) get P_oth = ptap->P_oth and P_loc = ptap->P_loc */ 585 /*-----------------------------------------------------*/ 586 /* update numerical values of P_oth and P_loc */ 587 ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr); 588 ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr); 589 590 /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */ 591 /*----------------------------------------------------------*/ 592 /* get data from symbolic products */ 593 p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data; 594 pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a; 595 if (size >1) { 596 p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data; 597 pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a; 598 } else { 599 p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL; 600 } 601 602 api = ptap->api; 603 apj = ptap->apj; 604 for (i=0; i<cm; i++) { 605 apJ = apj + api[i]; 606 607 /* diagonal portion of A */ 608 anz = adi[i+1] - adi[i]; 609 adj = ad->j + adi[i]; 610 ada = ad->a + adi[i]; 611 for (j=0; j<anz; j++) { 612 row = adj[j]; 613 pnz = pi_loc[row+1] - pi_loc[row]; 614 pj = pj_loc + pi_loc[row]; 615 pa = pa_loc + pi_loc[row]; 616 /* perform sparse axpy */ 617 valtmp = ada[j]; 618 nextp = 0; 619 for (k=0; nextp<pnz; k++) { 620 if (apJ[k] == pj[nextp]) { /* column of AP == column of P */ 621 apa_sparse[k] += valtmp*pa[nextp++]; 622 } 623 } 624 ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr); 625 } 626 627 /* off-diagonal portion of A */ 628 anz = aoi[i+1] - aoi[i]; 629 aoj = ao->j + aoi[i]; 630 aoa = ao->a + aoi[i]; 631 for (j=0; j<anz; j++) { 632 row = aoj[j]; 633 pnz = pi_oth[row+1] - pi_oth[row]; 634 pj = pj_oth + pi_oth[row]; 635 pa = pa_oth + pi_oth[row]; 636 /* perform sparse axpy */ 637 valtmp = aoa[j]; 638 nextp = 0; 639 for (k=0; nextp<pnz; k++) { 640 if (apJ[k] == pj[nextp]) { /* column of AP == column of P */ 641 apa_sparse[k] += valtmp*pa[nextp++]; 642 } 643 } 644 ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr); 645 } 646 647 /* set values in C */ 648 cdnz = cd->i[i+1] - cd->i[i]; 649 conz = co->i[i+1] - co->i[i]; 650 651 /* 1st off-diagoanl part of C */ 652 ca = coa + co->i[i]; 653 k = 0; 654 for (k0=0; k0<conz; k0++) { 655 if (apJ[k] >= cstart) break; 656 ca[k0] = apa_sparse[k]; 657 apa_sparse[k] = 0.0; 658 k++; 659 } 660 661 /* diagonal part of C */ 662 ca = cda + cd->i[i]; 663 for (k1=0; k1<cdnz; k1++) { 664 ca[k1] = apa_sparse[k]; 665 apa_sparse[k] = 0.0; 666 k++; 667 } 668 669 /* 2nd off-diagoanl part of C */ 670 ca = coa + co->i[i]; 671 for (; k0<conz; k0++) { 672 ca[k0] = apa_sparse[k]; 673 apa_sparse[k] = 0.0; 674 k++; 675 } 676 } 677 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 678 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 679 PetscFunctionReturn(0); 680 } 681 682 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */ 683 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C) 684 { 685 PetscErrorCode ierr; 686 MPI_Comm comm; 687 PetscMPIInt size; 688 Mat Cmpi; 689 Mat_PtAPMPI *ptap; 690 PetscFreeSpaceList free_space = NULL,current_space=NULL; 691 Mat_MPIAIJ *a = (Mat_MPIAIJ*)A->data,*c; 692 Mat_SeqAIJ *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth; 693 PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz; 694 PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart; 695 PetscInt i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0; 696 PetscInt am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20; 697 PetscReal afill; 698 PetscScalar *apa; 699 MatType mtype; 700 701 PetscFunctionBegin; 702 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 703 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 704 705 /* create struct Mat_PtAPMPI and attached it to C later */ 706 ierr = PetscNew(&ptap);CHKERRQ(ierr); 707 708 /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */ 709 ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr); 710 711 /* get P_loc by taking all local rows of P */ 712 ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr); 713 714 p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data; 715 pi_loc = p_loc->i; pj_loc = p_loc->j; 716 if (size > 1) { 717 p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data; 718 pi_oth = p_oth->i; pj_oth = p_oth->j; 719 } else { 720 p_oth = NULL; 721 pi_oth = NULL; pj_oth = NULL; 722 } 723 724 /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */ 725 /*-------------------------------------------------------------------*/ 726 ierr = PetscMalloc1(am+2,&api);CHKERRQ(ierr); 727 ptap->api = api; 728 api[0] = 0; 729 730 ierr = PetscLLCondensedCreate_Scalable(lsize,&lnk);CHKERRQ(ierr); 731 732 /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */ 733 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr); 734 current_space = free_space; 735 ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr); 736 for (i=0; i<am; i++) { 737 /* diagonal portion of A */ 738 nzi = adi[i+1] - adi[i]; 739 for (j=0; j<nzi; j++) { 740 row = *adj++; 741 pnz = pi_loc[row+1] - pi_loc[row]; 742 Jptr = pj_loc + pi_loc[row]; 743 /* Expand list if it is not long enough */ 744 if (pnz+apnz_max > lsize) { 745 lsize = pnz+apnz_max; 746 ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr); 747 } 748 /* add non-zero cols of P into the sorted linked list lnk */ 749 ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr); 750 apnz = *lnk; /* The first element in the list is the number of items in the list */ 751 api[i+1] = api[i] + apnz; 752 if (apnz > apnz_max) apnz_max = apnz; 753 } 754 /* off-diagonal portion of A */ 755 nzi = aoi[i+1] - aoi[i]; 756 for (j=0; j<nzi; j++) { 757 row = *aoj++; 758 pnz = pi_oth[row+1] - pi_oth[row]; 759 Jptr = pj_oth + pi_oth[row]; 760 /* Expand list if it is not long enough */ 761 if (pnz+apnz_max > lsize) { 762 lsize = pnz + apnz_max; 763 ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr); 764 } 765 /* add non-zero cols of P into the sorted linked list lnk */ 766 ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr); 767 apnz = *lnk; /* The first element in the list is the number of items in the list */ 768 api[i+1] = api[i] + apnz; 769 if (apnz > apnz_max) apnz_max = apnz; 770 } 771 apnz = *lnk; 772 api[i+1] = api[i] + apnz; 773 if (apnz > apnz_max) apnz_max = apnz; 774 775 /* if free space is not available, double the total space in the list */ 776 if (current_space->local_remaining<apnz) { 777 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 778 nspacedouble++; 779 } 780 781 /* Copy data into free space, then initialize lnk */ 782 ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr); 783 ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr); 784 785 current_space->array += apnz; 786 current_space->local_used += apnz; 787 current_space->local_remaining -= apnz; 788 } 789 790 /* Allocate space for apj, initialize apj, and */ 791 /* destroy list of free space and other temporary array(s) */ 792 ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr); 793 apj = ptap->apj; 794 ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr); 795 ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); 796 797 /* create and assemble symbolic parallel matrix Cmpi */ 798 /*----------------------------------------------------*/ 799 ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr); 800 ierr = MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 801 ierr = MatSetBlockSizesFromMats(Cmpi,A,P);CHKERRQ(ierr); 802 ierr = MatGetType(A,&mtype);CHKERRQ(ierr); 803 ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr); 804 ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr); 805 806 /* malloc apa for assembly Cmpi */ 807 ierr = PetscCalloc1(apnz_max,&apa);CHKERRQ(ierr); 808 ptap->apa = apa; 809 810 ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Cmpi, apj, api);CHKERRQ(ierr); 811 ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 812 ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 813 ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr); 814 815 ptap->destroy = Cmpi->ops->destroy; 816 ptap->duplicate = Cmpi->ops->duplicate; 817 Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ; 818 Cmpi->ops->destroy = MatDestroy_MPIAIJ_MatMatMult; 819 820 /* attach the supporting struct to Cmpi for reuse */ 821 c = (Mat_MPIAIJ*)Cmpi->data; 822 c->ptap = ptap; 823 *C = Cmpi; 824 825 /* set MatInfo */ 826 afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5; 827 if (afill < 1.0) afill = 1.0; 828 Cmpi->info.mallocs = nspacedouble; 829 Cmpi->info.fill_ratio_given = fill; 830 Cmpi->info.fill_ratio_needed = afill; 831 832 #if defined(PETSC_USE_INFO) 833 if (api[am]) { 834 ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 835 ierr = PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 836 } else { 837 ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr); 838 } 839 #endif 840 PetscFunctionReturn(0); 841 } 842 843 /* This function is needed for the seqMPI matrix-matrix multiplication. */ 844 /* Three input arrays are merged to one output array. The size of the */ 845 /* output array is also output. Duplicate entries only show up once. */ 846 static void Merge3SortedArrays(PetscInt size1, PetscInt *in1, 847 PetscInt size2, PetscInt *in2, 848 PetscInt size3, PetscInt *in3, 849 PetscInt *size4, PetscInt *out) 850 { 851 int i = 0, j = 0, k = 0, l = 0; 852 853 /* Traverse all three arrays */ 854 while (i<size1 && j<size2 && k<size3) { 855 if (in1[i] < in2[j] && in1[i] < in3[k]) { 856 out[l++] = in1[i++]; 857 } 858 else if(in2[j] < in1[i] && in2[j] < in3[k]) { 859 out[l++] = in2[j++]; 860 } 861 else if(in3[k] < in1[i] && in3[k] < in2[j]) { 862 out[l++] = in3[k++]; 863 } 864 else if(in1[i] == in2[j] && in1[i] < in3[k]) { 865 out[l++] = in1[i]; 866 i++, j++; 867 } 868 else if(in1[i] == in3[k] && in1[i] < in2[j]) { 869 out[l++] = in1[i]; 870 i++, k++; 871 } 872 else if(in3[k] == in2[j] && in2[j] < in1[i]) { 873 out[l++] = in2[j]; 874 k++, j++; 875 } 876 else if(in1[i] == in2[j] && in1[i] == in3[k]) { 877 out[l++] = in1[i]; 878 i++, j++, k++; 879 } 880 } 881 882 /* Traverse two remaining arrays */ 883 while (i<size1 && j<size2) { 884 if (in1[i] < in2[j]) { 885 out[l++] = in1[i++]; 886 } 887 else if(in1[i] > in2[j]) { 888 out[l++] = in2[j++]; 889 } 890 else { 891 out[l++] = in1[i]; 892 i++, j++; 893 } 894 } 895 896 while (i<size1 && k<size3) { 897 if (in1[i] < in3[k]) { 898 out[l++] = in1[i++]; 899 } 900 else if(in1[i] > in3[k]) { 901 out[l++] = in3[k++]; 902 } 903 else { 904 out[l++] = in1[i]; 905 i++, k++; 906 } 907 } 908 909 while (k<size3 && j<size2) { 910 if (in3[k] < in2[j]) { 911 out[l++] = in3[k++]; 912 } 913 else if(in3[k] > in2[j]) { 914 out[l++] = in2[j++]; 915 } 916 else { 917 out[l++] = in3[k]; 918 k++, j++; 919 } 920 } 921 922 /* Traverse one remaining array */ 923 while (i<size1) out[l++] = in1[i++]; 924 while (j<size2) out[l++] = in2[j++]; 925 while (k<size3) out[l++] = in3[k++]; 926 927 *size4 = l; 928 } 929 930 /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and */ 931 /* adds up the products. Two of these three multiplications are performed with existing (sequential) */ 932 /* matrix-matrix multiplications. */ 933 #undef __FUNCT__ 934 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI" 935 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat *C) 936 { 937 PetscErrorCode ierr; 938 MPI_Comm comm; 939 PetscMPIInt size; 940 Mat Cmpi; 941 Mat_PtAPMPI *ptap; 942 PetscFreeSpaceList free_space_diag=NULL, current_space=NULL; 943 Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data; 944 Mat_SeqAIJ *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc; 945 Mat_MPIAIJ *p =(Mat_MPIAIJ*)P->data; 946 Mat_MPIAIJ *c; 947 Mat_SeqAIJ *adpd_seq, *p_off, *aopoth_seq; 948 PetscInt adponz, adpdnz; 949 PetscInt *pi_loc,*dnz,*onz; 950 PetscInt *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart; 951 PetscInt *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi, 952 *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj; 953 PetscInt am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend; 954 PetscBT lnkbt; 955 PetscScalar *apa; 956 PetscReal afill; 957 PetscMPIInt rank; 958 Mat adpd, aopoth; 959 MatType mtype; 960 961 PetscFunctionBegin; 962 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 963 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 964 ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr); 965 ierr = MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend); CHKERRQ(ierr); 966 967 /* create struct Mat_PtAPMPI and attached it to C later */ 968 ierr = PetscNew(&ptap);CHKERRQ(ierr); 969 970 /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */ 971 ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr); 972 973 /* get P_loc by taking all local rows of P */ 974 ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr); 975 976 977 p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data; 978 pi_loc = p_loc->i; 979 980 /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */ 981 ierr = PetscMalloc1(am+2,&api);CHKERRQ(ierr); 982 ierr = PetscMalloc1(am+2,&adpoi);CHKERRQ(ierr); 983 984 adpoi[0] = 0; 985 ptap->api = api; 986 api[0] = 0; 987 988 /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */ 989 ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr); 990 ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr); 991 992 /* Symbolic calc of A_loc_diag * P_loc_diag */ 993 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->A, p->A, fill, &adpd);CHKERRQ(ierr); 994 adpd_seq = (Mat_SeqAIJ*)((adpd)->data); 995 adpdi = adpd_seq->i; adpdj = adpd_seq->j; 996 p_off = (Mat_SeqAIJ*)((p->B)->data); 997 poff_i = p_off->i; poff_j = p_off->j; 998 999 /* j_temp stores indices of a result row before they are added to the linked list */ 1000 ierr = PetscMalloc1(pN+2,&j_temp);CHKERRQ(ierr); 1001 1002 1003 /* Symbolic calc of the A_diag * p_loc_off */ 1004 /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */ 1005 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);CHKERRQ(ierr); 1006 current_space = free_space_diag; 1007 1008 for (i=0; i<am; i++) { 1009 /* A_diag * P_loc_off */ 1010 nzi = adi[i+1] - adi[i]; 1011 for (j=0; j<nzi; j++) { 1012 row = *adj++; 1013 pnz = poff_i[row+1] - poff_i[row]; 1014 Jptr = poff_j + poff_i[row]; 1015 for(i1 = 0; i1 < pnz; i1++) { 1016 j_temp[i1] = p->garray[Jptr[i1]]; 1017 } 1018 /* add non-zero cols of P into the sorted linked list lnk */ 1019 ierr = PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);CHKERRQ(ierr); 1020 } 1021 1022 adponz = lnk[0]; 1023 adpoi[i+1] = adpoi[i] + adponz; 1024 1025 /* if free space is not available, double the total space in the list */ 1026 if (current_space->local_remaining<adponz) { 1027 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 1028 nspacedouble++; 1029 } 1030 1031 /* Copy data into free space, then initialize lnk */ 1032 ierr = PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);CHKERRQ(ierr); 1033 1034 current_space->array += adponz; 1035 current_space->local_used += adponz; 1036 current_space->local_remaining -= adponz; 1037 } 1038 1039 /* Symbolic calc of A_off * P_oth */ 1040 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, &aopoth);CHKERRQ(ierr); 1041 aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data); 1042 aopothi = aopoth_seq->i; aopothj = aopoth_seq->j; 1043 1044 /* Allocate space for apj, adpj, aopj, ... */ 1045 /* destroy lists of free space and other temporary array(s) */ 1046 1047 ierr = PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);CHKERRQ(ierr); 1048 ierr = PetscMalloc1(adpoi[am]+2, &adpoj);CHKERRQ(ierr); 1049 1050 /* Copy from linked list to j-array */ 1051 ierr = PetscFreeSpaceContiguous(&free_space_diag,adpoj);CHKERRQ(ierr); 1052 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1053 1054 adpoJ = adpoj; 1055 adpdJ = adpdj; 1056 aopJ = aopothj; 1057 apj = ptap->apj; 1058 apJ = apj; /* still empty */ 1059 1060 /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */ 1061 /* A_diag * P_loc_diag to get A*P */ 1062 for (i = 0; i < am; i++) { 1063 aopnz = aopothi[i+1] - aopothi[i]; 1064 adponz = adpoi[i+1] - adpoi[i]; 1065 adpdnz = adpdi[i+1] - adpdi[i]; 1066 1067 /* Correct indices from A_diag*P_diag */ 1068 for(i1 = 0; i1 < adpdnz; i1++) { 1069 adpdJ[i1] += p_colstart; 1070 } 1071 /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */ 1072 Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ); 1073 ierr = MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz); CHKERRQ(ierr); 1074 1075 aopJ += aopnz; 1076 adpoJ += adponz; 1077 adpdJ += adpdnz; 1078 apJ += apnz; 1079 api[i+1] = api[i] + apnz; 1080 } 1081 1082 /* malloc apa to store dense row A[i,:]*P */ 1083 ierr = PetscCalloc1(pN+2,&apa);CHKERRQ(ierr); 1084 1085 ptap->apa = apa; 1086 /* create and assemble symbolic parallel matrix Cmpi */ 1087 ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr); 1088 ierr = MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 1089 ierr = MatSetBlockSizesFromMats(Cmpi,A,P);CHKERRQ(ierr); 1090 ierr = MatGetType(A,&mtype);CHKERRQ(ierr); 1091 ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr); 1092 ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr); 1093 1094 1095 ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Cmpi, apj, api);CHKERRQ(ierr); 1096 ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1097 ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1098 ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr); 1099 1100 1101 ptap->destroy = Cmpi->ops->destroy; 1102 ptap->duplicate = Cmpi->ops->duplicate; 1103 Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable; 1104 Cmpi->ops->destroy = MatDestroy_MPIAIJ_MatMatMult; 1105 1106 /* attach the supporting struct to Cmpi for reuse */ 1107 c = (Mat_MPIAIJ*)Cmpi->data; 1108 c->ptap = ptap; 1109 *C = Cmpi; 1110 1111 /* set MatInfo */ 1112 afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5; 1113 if (afill < 1.0) afill = 1.0; 1114 Cmpi->info.mallocs = nspacedouble; 1115 Cmpi->info.fill_ratio_given = fill; 1116 Cmpi->info.fill_ratio_needed = afill; 1117 1118 #if defined(PETSC_USE_INFO) 1119 if (api[am]) { 1120 ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 1121 ierr = PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 1122 } else { 1123 ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr); 1124 } 1125 #endif 1126 1127 ierr = MatDestroy(&aopoth);CHKERRQ(ierr); 1128 ierr = MatDestroy(&adpd);CHKERRQ(ierr); 1129 ierr = PetscFree(j_temp);CHKERRQ(ierr); 1130 ierr = PetscFree(adpoj);CHKERRQ(ierr); 1131 ierr = PetscFree(adpoi);CHKERRQ(ierr); 1132 PetscFunctionReturn(0); 1133 } 1134 1135 1136 /*-------------------------------------------------------------------------*/ 1137 PetscErrorCode MatTransposeMatMult_MPIAIJ_MPIAIJ(Mat P,Mat A,MatReuse scall,PetscReal fill,Mat *C) 1138 { 1139 PetscErrorCode ierr; 1140 const char *algTypes[3] = {"scalable","nonscalable","matmatmult"}; 1141 PetscInt aN=A->cmap->N,alg=1; /* set default algorithm */ 1142 PetscBool flg; 1143 1144 PetscFunctionBegin; 1145 if (scall == MAT_INITIAL_MATRIX) { 1146 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 1147 PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */ 1148 ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,3,algTypes[1],&alg,&flg);CHKERRQ(ierr); 1149 ierr = PetscOptionsEnd();CHKERRQ(ierr); 1150 1151 ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,P,A,0,0);CHKERRQ(ierr); 1152 switch (alg) { 1153 case 1: 1154 if (!flg && aN > 100000) { /* may switch to scalable algorithm as default */ 1155 MatInfo Ainfo,Pinfo; 1156 PetscInt nz_local; 1157 PetscBool alg_scalable_loc=PETSC_FALSE,alg_scalable; 1158 MPI_Comm comm; 1159 1160 ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr); 1161 ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr); 1162 nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated); /* estimated local nonzero entries */ 1163 1164 if (aN > fill*nz_local) alg_scalable_loc = PETSC_TRUE; 1165 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 1166 ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr); 1167 1168 if (alg_scalable) { 1169 alg = 0; /* scalable algorithm would slower than nonscalable algorithm */ 1170 ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);CHKERRQ(ierr); 1171 break; 1172 } 1173 } 1174 ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(P,A,fill,C);CHKERRQ(ierr); 1175 break; 1176 case 2: 1177 { 1178 Mat Pt; 1179 Mat_PtAPMPI *ptap; 1180 Mat_MPIAIJ *c; 1181 ierr = MatTranspose(P,MAT_INITIAL_MATRIX,&Pt);CHKERRQ(ierr); 1182 ierr = MatMatMult(Pt,A,MAT_INITIAL_MATRIX,fill,C);CHKERRQ(ierr); 1183 c = (Mat_MPIAIJ*)(*C)->data; 1184 ptap = c->ptap; 1185 ptap->Pt = Pt; 1186 (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult; 1187 PetscFunctionReturn(0); 1188 } 1189 break; 1190 default: /* scalable algorithm */ 1191 ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);CHKERRQ(ierr); 1192 break; 1193 } 1194 ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,P,A,0,0);CHKERRQ(ierr); 1195 } 1196 ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,P,A,0,0);CHKERRQ(ierr); 1197 ierr = (*(*C)->ops->mattransposemultnumeric)(P,A,*C);CHKERRQ(ierr); 1198 ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,P,A,0,0);CHKERRQ(ierr); 1199 PetscFunctionReturn(0); 1200 } 1201 1202 /* This routine only works when scall=MAT_REUSE_MATRIX! */ 1203 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C) 1204 { 1205 PetscErrorCode ierr; 1206 Mat_MPIAIJ *c=(Mat_MPIAIJ*)C->data; 1207 Mat_PtAPMPI *ptap= c->ptap; 1208 Mat Pt=ptap->Pt; 1209 1210 PetscFunctionBegin; 1211 ierr = MatTranspose(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr); 1212 ierr = MatMatMultNumeric(Pt,A,C);CHKERRQ(ierr); 1213 PetscFunctionReturn(0); 1214 } 1215 1216 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */ 1217 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat *C) 1218 { 1219 PetscErrorCode ierr; 1220 Mat_PtAPMPI *ptap; 1221 Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data,*c; 1222 MPI_Comm comm; 1223 PetscMPIInt size,rank; 1224 Mat Cmpi; 1225 PetscFreeSpaceList free_space=NULL,current_space=NULL; 1226 PetscInt pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n; 1227 PetscInt *lnk,i,k,nsend; 1228 PetscBT lnkbt; 1229 PetscMPIInt tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv; 1230 PetscInt **buf_rj,**buf_ri,**buf_ri_k; 1231 PetscInt len,proc,*dnz,*onz,*owners,nzi; 1232 PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci; 1233 MPI_Request *swaits,*rwaits; 1234 MPI_Status *sstatus,rstatus; 1235 PetscLayout rowmap; 1236 PetscInt *owners_co,*coi,*coj; /* i and j array of (p->B)^T*A*P - used in the communication */ 1237 PetscMPIInt *len_r,*id_r; /* array of length of comm->size, store send/recv matrix values */ 1238 PetscInt *Jptr,*prmap=p->garray,con,j,Crmax; 1239 Mat_SeqAIJ *a_loc,*c_loc,*c_oth; 1240 PetscTable ta; 1241 MatType mtype; 1242 1243 PetscFunctionBegin; 1244 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 1245 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 1246 ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr); 1247 1248 /* create symbolic parallel matrix Cmpi */ 1249 ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr); 1250 ierr = MatGetType(A,&mtype);CHKERRQ(ierr); 1251 ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr); 1252 1253 Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable; 1254 1255 /* create struct Mat_PtAPMPI and attached it to C later */ 1256 ierr = PetscNew(&ptap);CHKERRQ(ierr); 1257 ptap->reuse = MAT_INITIAL_MATRIX; 1258 1259 /* (0) compute Rd = Pd^T, Ro = Po^T */ 1260 /* --------------------------------- */ 1261 ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr); 1262 ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr); 1263 1264 /* (1) compute symbolic A_loc */ 1265 /* ---------------------------*/ 1266 ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);CHKERRQ(ierr); 1267 1268 /* (2-1) compute symbolic C_oth = Ro*A_loc */ 1269 /* ------------------------------------ */ 1270 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,&ptap->C_oth);CHKERRQ(ierr); 1271 1272 /* (3) send coj of C_oth to other processors */ 1273 /* ------------------------------------------ */ 1274 /* determine row ownership */ 1275 ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr); 1276 rowmap->n = pn; 1277 rowmap->bs = 1; 1278 ierr = PetscLayoutSetUp(rowmap);CHKERRQ(ierr); 1279 owners = rowmap->range; 1280 1281 /* determine the number of messages to send, their lengths */ 1282 ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr); 1283 ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr); 1284 ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr); 1285 1286 c_oth = (Mat_SeqAIJ*)ptap->C_oth->data; 1287 coi = c_oth->i; coj = c_oth->j; 1288 con = ptap->C_oth->rmap->n; 1289 proc = 0; 1290 for (i=0; i<con; i++) { 1291 while (prmap[i] >= owners[proc+1]) proc++; 1292 len_si[proc]++; /* num of rows in Co(=Pt*A) to be sent to [proc] */ 1293 len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */ 1294 } 1295 1296 len = 0; /* max length of buf_si[], see (4) */ 1297 owners_co[0] = 0; 1298 nsend = 0; 1299 for (proc=0; proc<size; proc++) { 1300 owners_co[proc+1] = owners_co[proc] + len_si[proc]; 1301 if (len_s[proc]) { 1302 nsend++; 1303 len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */ 1304 len += len_si[proc]; 1305 } 1306 } 1307 1308 /* determine the number and length of messages to receive for coi and coj */ 1309 ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr); 1310 ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr); 1311 1312 /* post the Irecv and Isend of coj */ 1313 ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr); 1314 ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr); 1315 ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr); 1316 for (proc=0, k=0; proc<size; proc++) { 1317 if (!len_s[proc]) continue; 1318 i = owners_co[proc]; 1319 ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr); 1320 k++; 1321 } 1322 1323 /* (2-2) compute symbolic C_loc = Rd*A_loc */ 1324 /* ---------------------------------------- */ 1325 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,&ptap->C_loc);CHKERRQ(ierr); 1326 c_loc = (Mat_SeqAIJ*)ptap->C_loc->data; 1327 1328 /* receives coj are complete */ 1329 for (i=0; i<nrecv; i++) { 1330 ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr); 1331 } 1332 ierr = PetscFree(rwaits);CHKERRQ(ierr); 1333 if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);} 1334 1335 /* add received column indices into ta to update Crmax */ 1336 a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data; 1337 1338 /* create and initialize a linked list */ 1339 ierr = PetscTableCreate(an,aN,&ta);CHKERRQ(ierr); /* for compute Crmax */ 1340 MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta); 1341 1342 for (k=0; k<nrecv; k++) {/* k-th received message */ 1343 Jptr = buf_rj[k]; 1344 for (j=0; j<len_r[k]; j++) { 1345 ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr); 1346 } 1347 } 1348 ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); 1349 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 1350 1351 /* (4) send and recv coi */ 1352 /*-----------------------*/ 1353 ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr); 1354 ierr = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr); 1355 ierr = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr); 1356 buf_si = buf_s; /* points to the beginning of k-th msg to be sent */ 1357 for (proc=0,k=0; proc<size; proc++) { 1358 if (!len_s[proc]) continue; 1359 /* form outgoing message for i-structure: 1360 buf_si[0]: nrows to be sent 1361 [1:nrows]: row index (global) 1362 [nrows+1:2*nrows+1]: i-structure index 1363 */ 1364 /*-------------------------------------------*/ 1365 nrows = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */ 1366 buf_si_i = buf_si + nrows+1; 1367 buf_si[0] = nrows; 1368 buf_si_i[0] = 0; 1369 nrows = 0; 1370 for (i=owners_co[proc]; i<owners_co[proc+1]; i++) { 1371 nzi = coi[i+1] - coi[i]; 1372 buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */ 1373 buf_si[nrows+1] = prmap[i] -owners[proc]; /* local row index */ 1374 nrows++; 1375 } 1376 ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr); 1377 k++; 1378 buf_si += len_si[proc]; 1379 } 1380 for (i=0; i<nrecv; i++) { 1381 ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr); 1382 } 1383 ierr = PetscFree(rwaits);CHKERRQ(ierr); 1384 if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);} 1385 1386 ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr); 1387 ierr = PetscFree(len_ri);CHKERRQ(ierr); 1388 ierr = PetscFree(swaits);CHKERRQ(ierr); 1389 ierr = PetscFree(buf_s);CHKERRQ(ierr); 1390 1391 /* (5) compute the local portion of Cmpi */ 1392 /* ------------------------------------------ */ 1393 /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */ 1394 ierr = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr); 1395 current_space = free_space; 1396 1397 ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr); 1398 for (k=0; k<nrecv; k++) { 1399 buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */ 1400 nrows = *buf_ri_k[k]; 1401 nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */ 1402 nextci[k] = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure */ 1403 } 1404 1405 ierr = MatPreallocateInitialize(comm,pn,an,dnz,onz);CHKERRQ(ierr); 1406 ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr); 1407 for (i=0; i<pn; i++) { 1408 /* add C_loc into Cmpi */ 1409 nzi = c_loc->i[i+1] - c_loc->i[i]; 1410 Jptr = c_loc->j + c_loc->i[i]; 1411 ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr); 1412 1413 /* add received col data into lnk */ 1414 for (k=0; k<nrecv; k++) { /* k-th received message */ 1415 if (i == *nextrow[k]) { /* i-th row */ 1416 nzi = *(nextci[k]+1) - *nextci[k]; 1417 Jptr = buf_rj[k] + *nextci[k]; 1418 ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr); 1419 nextrow[k]++; nextci[k]++; 1420 } 1421 } 1422 nzi = lnk[0]; 1423 1424 /* copy data into free space, then initialize lnk */ 1425 ierr = PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr); 1426 ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr); 1427 } 1428 ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr); 1429 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1430 ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr); 1431 1432 /* local sizes and preallocation */ 1433 ierr = MatSetSizes(Cmpi,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 1434 ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr); 1435 ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr); 1436 ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr); 1437 1438 /* members in merge */ 1439 ierr = PetscFree(id_r);CHKERRQ(ierr); 1440 ierr = PetscFree(len_r);CHKERRQ(ierr); 1441 ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr); 1442 ierr = PetscFree(buf_ri);CHKERRQ(ierr); 1443 ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr); 1444 ierr = PetscFree(buf_rj);CHKERRQ(ierr); 1445 ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr); 1446 1447 /* attach the supporting struct to Cmpi for reuse */ 1448 c = (Mat_MPIAIJ*)Cmpi->data; 1449 c->ptap = ptap; 1450 ptap->destroy = Cmpi->ops->destroy; 1451 1452 /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */ 1453 Cmpi->assembled = PETSC_FALSE; 1454 Cmpi->ops->destroy = MatDestroy_MPIAIJ_PtAP; 1455 *C = Cmpi; 1456 PetscFunctionReturn(0); 1457 } 1458 1459 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C) 1460 { 1461 PetscErrorCode ierr; 1462 Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data; 1463 Mat_SeqAIJ *c_seq; 1464 Mat_PtAPMPI *ptap = c->ptap; 1465 Mat A_loc,C_loc,C_oth; 1466 PetscInt i,rstart,rend,cm,ncols,row; 1467 const PetscInt *cols; 1468 const PetscScalar *vals; 1469 1470 PetscFunctionBegin; 1471 ierr = MatZeroEntries(C);CHKERRQ(ierr); 1472 1473 if (ptap->reuse == MAT_REUSE_MATRIX) { 1474 /* These matrices are obtained in MatTransposeMatMultSymbolic() */ 1475 /* 1) get R = Pd^T, Ro = Po^T */ 1476 /*----------------------------*/ 1477 ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr); 1478 ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr); 1479 1480 /* 2) compute numeric A_loc */ 1481 /*--------------------------*/ 1482 ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);CHKERRQ(ierr); 1483 } 1484 1485 /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */ 1486 A_loc = ptap->A_loc; 1487 ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);CHKERRQ(ierr); 1488 ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);CHKERRQ(ierr); 1489 C_loc = ptap->C_loc; 1490 C_oth = ptap->C_oth; 1491 1492 /* add C_loc and Co to to C */ 1493 ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr); 1494 1495 /* C_loc -> C */ 1496 cm = C_loc->rmap->N; 1497 c_seq = (Mat_SeqAIJ*)C_loc->data; 1498 cols = c_seq->j; 1499 vals = c_seq->a; 1500 for (i=0; i<cm; i++) { 1501 ncols = c_seq->i[i+1] - c_seq->i[i]; 1502 row = rstart + i; 1503 ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr); 1504 cols += ncols; vals += ncols; 1505 } 1506 1507 /* Co -> C, off-processor part */ 1508 cm = C_oth->rmap->N; 1509 c_seq = (Mat_SeqAIJ*)C_oth->data; 1510 cols = c_seq->j; 1511 vals = c_seq->a; 1512 for (i=0; i<cm; i++) { 1513 ncols = c_seq->i[i+1] - c_seq->i[i]; 1514 row = p->garray[i]; 1515 ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr); 1516 cols += ncols; vals += ncols; 1517 } 1518 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1519 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1520 1521 ptap->reuse = MAT_REUSE_MATRIX; 1522 PetscFunctionReturn(0); 1523 } 1524 1525 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C) 1526 { 1527 PetscErrorCode ierr; 1528 Mat_Merge_SeqsToMPI *merge; 1529 Mat_MPIAIJ *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data; 1530 Mat_SeqAIJ *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data; 1531 Mat_PtAPMPI *ptap; 1532 PetscInt *adj; 1533 PetscInt i,j,k,anz,pnz,row,*cj,nexta; 1534 MatScalar *ada,*ca,valtmp; 1535 PetscInt am =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n; 1536 MPI_Comm comm; 1537 PetscMPIInt size,rank,taga,*len_s; 1538 PetscInt *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci; 1539 PetscInt **buf_ri,**buf_rj; 1540 PetscInt cnz=0,*bj_i,*bi,*bj,bnz,nextcj; /* bi,bj,ba: local array of C(mpi mat) */ 1541 MPI_Request *s_waits,*r_waits; 1542 MPI_Status *status; 1543 MatScalar **abuf_r,*ba_i,*pA,*coa,*ba; 1544 PetscInt *ai,*aj,*coi,*coj,*poJ,*pdJ; 1545 Mat A_loc; 1546 Mat_SeqAIJ *a_loc; 1547 1548 PetscFunctionBegin; 1549 ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr); 1550 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 1551 ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr); 1552 1553 ptap = c->ptap; 1554 merge = ptap->merge; 1555 1556 /* 2) compute numeric C_seq = P_loc^T*A_loc */ 1557 /*------------------------------------------*/ 1558 /* get data from symbolic products */ 1559 coi = merge->coi; coj = merge->coj; 1560 ierr = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr); 1561 bi = merge->bi; bj = merge->bj; 1562 owners = merge->rowmap->range; 1563 ierr = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr); 1564 1565 /* get A_loc by taking all local rows of A */ 1566 A_loc = ptap->A_loc; 1567 ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr); 1568 a_loc = (Mat_SeqAIJ*)(A_loc)->data; 1569 ai = a_loc->i; 1570 aj = a_loc->j; 1571 1572 for (i=0; i<am; i++) { 1573 anz = ai[i+1] - ai[i]; 1574 adj = aj + ai[i]; 1575 ada = a_loc->a + ai[i]; 1576 1577 /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */ 1578 /*-------------------------------------------------------------*/ 1579 /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */ 1580 pnz = po->i[i+1] - po->i[i]; 1581 poJ = po->j + po->i[i]; 1582 pA = po->a + po->i[i]; 1583 for (j=0; j<pnz; j++) { 1584 row = poJ[j]; 1585 cj = coj + coi[row]; 1586 ca = coa + coi[row]; 1587 /* perform sparse axpy */ 1588 nexta = 0; 1589 valtmp = pA[j]; 1590 for (k=0; nexta<anz; k++) { 1591 if (cj[k] == adj[nexta]) { 1592 ca[k] += valtmp*ada[nexta]; 1593 nexta++; 1594 } 1595 } 1596 ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr); 1597 } 1598 1599 /* put the value into Cd (diagonal part) */ 1600 pnz = pd->i[i+1] - pd->i[i]; 1601 pdJ = pd->j + pd->i[i]; 1602 pA = pd->a + pd->i[i]; 1603 for (j=0; j<pnz; j++) { 1604 row = pdJ[j]; 1605 cj = bj + bi[row]; 1606 ca = ba + bi[row]; 1607 /* perform sparse axpy */ 1608 nexta = 0; 1609 valtmp = pA[j]; 1610 for (k=0; nexta<anz; k++) { 1611 if (cj[k] == adj[nexta]) { 1612 ca[k] += valtmp*ada[nexta]; 1613 nexta++; 1614 } 1615 } 1616 ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr); 1617 } 1618 } 1619 1620 /* 3) send and recv matrix values coa */ 1621 /*------------------------------------*/ 1622 buf_ri = merge->buf_ri; 1623 buf_rj = merge->buf_rj; 1624 len_s = merge->len_s; 1625 ierr = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr); 1626 ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr); 1627 1628 ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr); 1629 for (proc=0,k=0; proc<size; proc++) { 1630 if (!len_s[proc]) continue; 1631 i = merge->owners_co[proc]; 1632 ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr); 1633 k++; 1634 } 1635 if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);} 1636 if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);} 1637 1638 ierr = PetscFree2(s_waits,status);CHKERRQ(ierr); 1639 ierr = PetscFree(r_waits);CHKERRQ(ierr); 1640 ierr = PetscFree(coa);CHKERRQ(ierr); 1641 1642 /* 4) insert local Cseq and received values into Cmpi */ 1643 /*----------------------------------------------------*/ 1644 ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr); 1645 for (k=0; k<merge->nrecv; k++) { 1646 buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */ 1647 nrows = *(buf_ri_k[k]); 1648 nextrow[k] = buf_ri_k[k]+1; /* next row number of k-th recved i-structure */ 1649 nextci[k] = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure */ 1650 } 1651 1652 for (i=0; i<cm; i++) { 1653 row = owners[rank] + i; /* global row index of C_seq */ 1654 bj_i = bj + bi[i]; /* col indices of the i-th row of C */ 1655 ba_i = ba + bi[i]; 1656 bnz = bi[i+1] - bi[i]; 1657 /* add received vals into ba */ 1658 for (k=0; k<merge->nrecv; k++) { /* k-th received message */ 1659 /* i-th row */ 1660 if (i == *nextrow[k]) { 1661 cnz = *(nextci[k]+1) - *nextci[k]; 1662 cj = buf_rj[k] + *(nextci[k]); 1663 ca = abuf_r[k] + *(nextci[k]); 1664 nextcj = 0; 1665 for (j=0; nextcj<cnz; j++) { 1666 if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */ 1667 ba_i[j] += ca[nextcj++]; 1668 } 1669 } 1670 nextrow[k]++; nextci[k]++; 1671 ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr); 1672 } 1673 } 1674 ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr); 1675 } 1676 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1677 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1678 1679 ierr = PetscFree(ba);CHKERRQ(ierr); 1680 ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr); 1681 ierr = PetscFree(abuf_r);CHKERRQ(ierr); 1682 ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr); 1683 PetscFunctionReturn(0); 1684 } 1685 1686 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat *C) 1687 { 1688 PetscErrorCode ierr; 1689 Mat Cmpi,A_loc,POt,PDt; 1690 Mat_PtAPMPI *ptap; 1691 PetscFreeSpaceList free_space=NULL,current_space=NULL; 1692 Mat_MPIAIJ *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data,*c; 1693 PetscInt *pdti,*pdtj,*poti,*potj,*ptJ; 1694 PetscInt nnz; 1695 PetscInt *lnk,*owners_co,*coi,*coj,i,k,pnz,row; 1696 PetscInt am =A->rmap->n,pn=P->cmap->n; 1697 MPI_Comm comm; 1698 PetscMPIInt size,rank,tagi,tagj,*len_si,*len_s,*len_ri; 1699 PetscInt **buf_rj,**buf_ri,**buf_ri_k; 1700 PetscInt len,proc,*dnz,*onz,*owners; 1701 PetscInt nzi,*bi,*bj; 1702 PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci; 1703 MPI_Request *swaits,*rwaits; 1704 MPI_Status *sstatus,rstatus; 1705 Mat_Merge_SeqsToMPI *merge; 1706 PetscInt *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j; 1707 PetscReal afill =1.0,afill_tmp; 1708 PetscInt rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax; 1709 PetscScalar *vals; 1710 Mat_SeqAIJ *a_loc,*pdt,*pot; 1711 PetscTable ta; 1712 MatType mtype; 1713 1714 PetscFunctionBegin; 1715 ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr); 1716 /* check if matrix local sizes are compatible */ 1717 if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend); 1718 1719 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 1720 ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr); 1721 1722 /* create struct Mat_PtAPMPI and attached it to C later */ 1723 ierr = PetscNew(&ptap);CHKERRQ(ierr); 1724 1725 /* get A_loc by taking all local rows of A */ 1726 ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr); 1727 1728 ptap->A_loc = A_loc; 1729 a_loc = (Mat_SeqAIJ*)(A_loc)->data; 1730 ai = a_loc->i; 1731 aj = a_loc->j; 1732 1733 /* determine symbolic Co=(p->B)^T*A - send to others */ 1734 /*----------------------------------------------------*/ 1735 ierr = MatTransposeSymbolic_SeqAIJ(p->A,&PDt);CHKERRQ(ierr); 1736 pdt = (Mat_SeqAIJ*)PDt->data; 1737 pdti = pdt->i; pdtj = pdt->j; 1738 1739 ierr = MatTransposeSymbolic_SeqAIJ(p->B,&POt);CHKERRQ(ierr); 1740 pot = (Mat_SeqAIJ*)POt->data; 1741 poti = pot->i; potj = pot->j; 1742 1743 /* then, compute symbolic Co = (p->B)^T*A */ 1744 pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors 1745 >= (num of nonzero rows of C_seq) - pn */ 1746 ierr = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr); 1747 coi[0] = 0; 1748 1749 /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */ 1750 nnz = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am])); 1751 ierr = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr); 1752 current_space = free_space; 1753 1754 /* create and initialize a linked list */ 1755 ierr = PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);CHKERRQ(ierr); 1756 MatRowMergeMax_SeqAIJ(a_loc,am,ta); 1757 ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr); 1758 1759 ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr); 1760 1761 for (i=0; i<pon; i++) { 1762 pnz = poti[i+1] - poti[i]; 1763 ptJ = potj + poti[i]; 1764 for (j=0; j<pnz; j++) { 1765 row = ptJ[j]; /* row of A_loc == col of Pot */ 1766 anz = ai[row+1] - ai[row]; 1767 Jptr = aj + ai[row]; 1768 /* add non-zero cols of AP into the sorted linked list lnk */ 1769 ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr); 1770 } 1771 nnz = lnk[0]; 1772 1773 /* If free space is not available, double the total space in the list */ 1774 if (current_space->local_remaining<nnz) { 1775 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 1776 nspacedouble++; 1777 } 1778 1779 /* Copy data into free space, and zero out denserows */ 1780 ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr); 1781 1782 current_space->array += nnz; 1783 current_space->local_used += nnz; 1784 current_space->local_remaining -= nnz; 1785 1786 coi[i+1] = coi[i] + nnz; 1787 } 1788 1789 ierr = PetscMalloc1(coi[pon]+1,&coj);CHKERRQ(ierr); 1790 ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr); 1791 ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); /* must destroy to get a new one for C */ 1792 1793 afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1); 1794 if (afill_tmp > afill) afill = afill_tmp; 1795 1796 /* send j-array (coj) of Co to other processors */ 1797 /*----------------------------------------------*/ 1798 /* determine row ownership */ 1799 ierr = PetscNew(&merge);CHKERRQ(ierr); 1800 ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr); 1801 1802 merge->rowmap->n = pn; 1803 merge->rowmap->bs = 1; 1804 1805 ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr); 1806 owners = merge->rowmap->range; 1807 1808 /* determine the number of messages to send, their lengths */ 1809 ierr = PetscCalloc1(size,&len_si);CHKERRQ(ierr); 1810 ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr); 1811 1812 len_s = merge->len_s; 1813 merge->nsend = 0; 1814 1815 ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr); 1816 ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr); 1817 1818 proc = 0; 1819 for (i=0; i<pon; i++) { 1820 while (prmap[i] >= owners[proc+1]) proc++; 1821 len_si[proc]++; /* num of rows in Co to be sent to [proc] */ 1822 len_s[proc] += coi[i+1] - coi[i]; 1823 } 1824 1825 len = 0; /* max length of buf_si[] */ 1826 owners_co[0] = 0; 1827 for (proc=0; proc<size; proc++) { 1828 owners_co[proc+1] = owners_co[proc] + len_si[proc]; 1829 if (len_si[proc]) { 1830 merge->nsend++; 1831 len_si[proc] = 2*(len_si[proc] + 1); 1832 len += len_si[proc]; 1833 } 1834 } 1835 1836 /* determine the number and length of messages to receive for coi and coj */ 1837 ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr); 1838 ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr); 1839 1840 /* post the Irecv and Isend of coj */ 1841 ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr); 1842 ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr); 1843 ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr); 1844 for (proc=0, k=0; proc<size; proc++) { 1845 if (!len_s[proc]) continue; 1846 i = owners_co[proc]; 1847 ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr); 1848 k++; 1849 } 1850 1851 /* receives and sends of coj are complete */ 1852 ierr = PetscMalloc1(size,&sstatus);CHKERRQ(ierr); 1853 for (i=0; i<merge->nrecv; i++) { 1854 PetscMPIInt icompleted; 1855 ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr); 1856 } 1857 ierr = PetscFree(rwaits);CHKERRQ(ierr); 1858 if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);} 1859 1860 /* add received column indices into table to update Armax */ 1861 /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/examples/tutorials/ex56.c! */ 1862 for (k=0; k<merge->nrecv; k++) {/* k-th received message */ 1863 Jptr = buf_rj[k]; 1864 for (j=0; j<merge->len_r[k]; j++) { 1865 ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr); 1866 } 1867 } 1868 ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr); 1869 /* printf("Armax %d, an %d + Bn %d = %d, aN %d\n",Armax,A->cmap->n,a->B->cmap->N,A->cmap->n+a->B->cmap->N,aN); */ 1870 1871 /* send and recv coi */ 1872 /*-------------------*/ 1873 ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr); 1874 ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr); 1875 ierr = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr); 1876 buf_si = buf_s; /* points to the beginning of k-th msg to be sent */ 1877 for (proc=0,k=0; proc<size; proc++) { 1878 if (!len_s[proc]) continue; 1879 /* form outgoing message for i-structure: 1880 buf_si[0]: nrows to be sent 1881 [1:nrows]: row index (global) 1882 [nrows+1:2*nrows+1]: i-structure index 1883 */ 1884 /*-------------------------------------------*/ 1885 nrows = len_si[proc]/2 - 1; 1886 buf_si_i = buf_si + nrows+1; 1887 buf_si[0] = nrows; 1888 buf_si_i[0] = 0; 1889 nrows = 0; 1890 for (i=owners_co[proc]; i<owners_co[proc+1]; i++) { 1891 nzi = coi[i+1] - coi[i]; 1892 buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */ 1893 buf_si[nrows+1] = prmap[i] -owners[proc]; /* local row index */ 1894 nrows++; 1895 } 1896 ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr); 1897 k++; 1898 buf_si += len_si[proc]; 1899 } 1900 i = merge->nrecv; 1901 while (i--) { 1902 PetscMPIInt icompleted; 1903 ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr); 1904 } 1905 ierr = PetscFree(rwaits);CHKERRQ(ierr); 1906 if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);} 1907 ierr = PetscFree(len_si);CHKERRQ(ierr); 1908 ierr = PetscFree(len_ri);CHKERRQ(ierr); 1909 ierr = PetscFree(swaits);CHKERRQ(ierr); 1910 ierr = PetscFree(sstatus);CHKERRQ(ierr); 1911 ierr = PetscFree(buf_s);CHKERRQ(ierr); 1912 1913 /* compute the local portion of C (mpi mat) */ 1914 /*------------------------------------------*/ 1915 /* allocate bi array and free space for accumulating nonzero column info */ 1916 ierr = PetscMalloc1(pn+1,&bi);CHKERRQ(ierr); 1917 bi[0] = 0; 1918 1919 /* set initial free space to be fill*(nnz(P) + nnz(AP)) */ 1920 nnz = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am]))); 1921 ierr = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr); 1922 current_space = free_space; 1923 1924 ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr); 1925 for (k=0; k<merge->nrecv; k++) { 1926 buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */ 1927 nrows = *buf_ri_k[k]; 1928 nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */ 1929 nextci[k] = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recieved i-structure */ 1930 } 1931 1932 ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr); 1933 ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr); 1934 rmax = 0; 1935 for (i=0; i<pn; i++) { 1936 /* add pdt[i,:]*AP into lnk */ 1937 pnz = pdti[i+1] - pdti[i]; 1938 ptJ = pdtj + pdti[i]; 1939 for (j=0; j<pnz; j++) { 1940 row = ptJ[j]; /* row of AP == col of Pt */ 1941 anz = ai[row+1] - ai[row]; 1942 Jptr = aj + ai[row]; 1943 /* add non-zero cols of AP into the sorted linked list lnk */ 1944 ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr); 1945 } 1946 1947 /* add received col data into lnk */ 1948 for (k=0; k<merge->nrecv; k++) { /* k-th received message */ 1949 if (i == *nextrow[k]) { /* i-th row */ 1950 nzi = *(nextci[k]+1) - *nextci[k]; 1951 Jptr = buf_rj[k] + *nextci[k]; 1952 ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr); 1953 nextrow[k]++; nextci[k]++; 1954 } 1955 } 1956 nnz = lnk[0]; 1957 1958 /* if free space is not available, make more free space */ 1959 if (current_space->local_remaining<nnz) { 1960 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 1961 nspacedouble++; 1962 } 1963 /* copy data into free space, then initialize lnk */ 1964 ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr); 1965 ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr); 1966 1967 current_space->array += nnz; 1968 current_space->local_used += nnz; 1969 current_space->local_remaining -= nnz; 1970 1971 bi[i+1] = bi[i] + nnz; 1972 if (nnz > rmax) rmax = nnz; 1973 } 1974 ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr); 1975 1976 ierr = PetscMalloc1(bi[pn]+1,&bj);CHKERRQ(ierr); 1977 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 1978 afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1); 1979 if (afill_tmp > afill) afill = afill_tmp; 1980 ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); 1981 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 1982 1983 ierr = MatDestroy(&POt);CHKERRQ(ierr); 1984 ierr = MatDestroy(&PDt);CHKERRQ(ierr); 1985 1986 /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part */ 1987 /*----------------------------------------------------------------------------------*/ 1988 ierr = PetscCalloc1(rmax+1,&vals);CHKERRQ(ierr); 1989 1990 ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr); 1991 ierr = MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 1992 ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));CHKERRQ(ierr); 1993 ierr = MatGetType(A,&mtype);CHKERRQ(ierr); 1994 ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr); 1995 ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr); 1996 ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr); 1997 ierr = MatSetBlockSize(Cmpi,1);CHKERRQ(ierr); 1998 for (i=0; i<pn; i++) { 1999 row = i + rstart; 2000 nnz = bi[i+1] - bi[i]; 2001 Jptr = bj + bi[i]; 2002 ierr = MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);CHKERRQ(ierr); 2003 } 2004 ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 2005 ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 2006 ierr = PetscFree(vals);CHKERRQ(ierr); 2007 2008 merge->bi = bi; 2009 merge->bj = bj; 2010 merge->coi = coi; 2011 merge->coj = coj; 2012 merge->buf_ri = buf_ri; 2013 merge->buf_rj = buf_rj; 2014 merge->owners_co = owners_co; 2015 2016 /* attach the supporting struct to Cmpi for reuse */ 2017 c = (Mat_MPIAIJ*)Cmpi->data; 2018 2019 c->ptap = ptap; 2020 ptap->api = NULL; 2021 ptap->apj = NULL; 2022 ptap->merge = merge; 2023 ptap->apa = NULL; 2024 ptap->destroy = Cmpi->ops->destroy; 2025 ptap->duplicate = Cmpi->ops->duplicate; 2026 2027 Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ; 2028 Cmpi->ops->destroy = MatDestroy_MPIAIJ_PtAP; 2029 2030 *C = Cmpi; 2031 #if defined(PETSC_USE_INFO) 2032 if (bi[pn] != 0) { 2033 ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 2034 ierr = PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr); 2035 } else { 2036 ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr); 2037 } 2038 #endif 2039 PetscFunctionReturn(0); 2040 } 2041