1 2 /* 3 Defines projective product routines where A is a SeqAIJ 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 <petscbt.h> 10 #include <petsctime.h> 11 12 #if defined(PETSC_HAVE_HYPRE) 13 PETSC_INTERN PetscErrorCode MatPtAPSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*); 14 #endif 15 16 #undef __FUNCT__ 17 #define __FUNCT__ "MatPtAP_SeqAIJ_SeqAIJ" 18 PETSC_INTERN PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C) 19 { 20 PetscErrorCode ierr; 21 #if !defined(PETSC_HAVE_HYPRE) 22 const char *algTypes[2] = {"scalable","nonscalable"}; 23 PetscInt nalg = 2; 24 #else 25 const char *algTypes[3] = {"scalable","nonscalable","hypre"}; 26 PetscInt nalg = 3; 27 #endif 28 PetscInt alg = 0; /* set default algorithm */ 29 30 PetscFunctionBegin; 31 if (scall == MAT_INITIAL_MATRIX) { 32 /* 33 Alg 'scalable' determines which implementations to be used: 34 "nonscalable": do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P; 35 "scalable": do two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P. 36 "hypre": use boomerAMGBuildCoarseOperator. 37 */ 38 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 39 ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[0],&alg,NULL);CHKERRQ(ierr); 40 ierr = PetscOptionsEnd();CHKERRQ(ierr); 41 ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 42 switch (alg) { 43 case 1: 44 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(A,P,fill,C);CHKERRQ(ierr); 45 break; 46 #if defined(PETSC_HAVE_HYPRE) 47 case 2: 48 ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr); 49 break; 50 #endif 51 default: 52 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr); 53 break; 54 } 55 ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 56 } 57 ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr); 58 ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr); 59 ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr); 60 PetscFunctionReturn(0); 61 } 62 63 #undef __FUNCT__ 64 #define __FUNCT__ "MatDestroy_SeqAIJ_PtAP" 65 PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A) 66 { 67 PetscErrorCode ierr; 68 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 69 Mat_PtAP *ptap = a->ptap; 70 71 PetscFunctionBegin; 72 ierr = PetscFree(ptap->apa);CHKERRQ(ierr); 73 ierr = PetscFree(ptap->api);CHKERRQ(ierr); 74 ierr = PetscFree(ptap->apj);CHKERRQ(ierr); 75 ierr = (ptap->destroy)(A);CHKERRQ(ierr); 76 ierr = PetscFree(ptap);CHKERRQ(ierr); 77 PetscFunctionReturn(0); 78 } 79 80 #undef __FUNCT__ 81 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy" 82 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 83 { 84 PetscErrorCode ierr; 85 PetscFreeSpaceList free_space=NULL,current_space=NULL; 86 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 87 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 88 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 89 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N; 90 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 91 MatScalar *ca; 92 PetscBT lnkbt; 93 PetscReal afill; 94 95 PetscFunctionBegin; 96 /* Get ij structure of P^T */ 97 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 98 ptJ = ptj; 99 100 /* Allocate ci array, arrays for fill computation and */ 101 /* free space for accumulating nonzero column info */ 102 ierr = PetscMalloc1(pn+1,&ci);CHKERRQ(ierr); 103 ci[0] = 0; 104 105 ierr = PetscCalloc1(2*an+1,&ptadenserow);CHKERRQ(ierr); 106 ptasparserow = ptadenserow + an; 107 108 /* create and initialize a linked list */ 109 nlnk = pn+1; 110 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 111 112 /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */ 113 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);CHKERRQ(ierr); 114 current_space = free_space; 115 116 /* Determine symbolic info for each row of C: */ 117 for (i=0; i<pn; i++) { 118 ptnzi = pti[i+1] - pti[i]; 119 ptanzi = 0; 120 /* Determine symbolic row of PtA: */ 121 for (j=0; j<ptnzi; j++) { 122 arow = *ptJ++; 123 anzj = ai[arow+1] - ai[arow]; 124 ajj = aj + ai[arow]; 125 for (k=0; k<anzj; k++) { 126 if (!ptadenserow[ajj[k]]) { 127 ptadenserow[ajj[k]] = -1; 128 ptasparserow[ptanzi++] = ajj[k]; 129 } 130 } 131 } 132 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 133 ptaj = ptasparserow; 134 cnzi = 0; 135 for (j=0; j<ptanzi; j++) { 136 prow = *ptaj++; 137 pnzj = pi[prow+1] - pi[prow]; 138 pjj = pj + pi[prow]; 139 /* add non-zero cols of P into the sorted linked list lnk */ 140 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 141 cnzi += nlnk; 142 } 143 144 /* If free space is not available, make more free space */ 145 /* Double the amount of total space in the list */ 146 if (current_space->local_remaining<cnzi) { 147 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 148 nspacedouble++; 149 } 150 151 /* Copy data into free space, and zero out denserows */ 152 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 153 154 current_space->array += cnzi; 155 current_space->local_used += cnzi; 156 current_space->local_remaining -= cnzi; 157 158 for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0; 159 160 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 161 /* For now, we will recompute what is needed. */ 162 ci[i+1] = ci[i] + cnzi; 163 } 164 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 165 /* Allocate space for cj, initialize cj, and */ 166 /* destroy list of free space and other temporary array(s) */ 167 ierr = PetscMalloc1(ci[pn]+1,&cj);CHKERRQ(ierr); 168 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 169 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 170 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 171 172 ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr); 173 174 /* put together the new matrix */ 175 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 176 ierr = MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr); 177 178 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 179 /* Since these are PETSc arrays, change flags to free them as necessary. */ 180 c = (Mat_SeqAIJ*)((*C)->data); 181 c->free_a = PETSC_TRUE; 182 c->free_ij = PETSC_TRUE; 183 c->nonew = 0; 184 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy; 185 186 /* set MatInfo */ 187 afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5); 188 if (afill < 1.0) afill = 1.0; 189 c->maxnz = ci[pn]; 190 c->nz = ci[pn]; 191 (*C)->info.mallocs = nspacedouble; 192 (*C)->info.fill_ratio_given = fill; 193 (*C)->info.fill_ratio_needed = afill; 194 195 /* Clean up. */ 196 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 197 #if defined(PETSC_USE_INFO) 198 if (ci[pn] != 0) { 199 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr); 200 ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr); 201 } else { 202 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 203 } 204 #endif 205 PetscFunctionReturn(0); 206 } 207 208 #undef __FUNCT__ 209 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy" 210 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 211 { 212 PetscErrorCode ierr; 213 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 214 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 215 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 216 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 217 PetscInt *ci=c->i,*cj=c->j,*cjj; 218 PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 219 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 220 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 221 222 PetscFunctionBegin; 223 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 224 ierr = PetscMalloc3(cn,&apa,cn,&apjdense,cn,&apj);CHKERRQ(ierr); 225 ierr = PetscMemzero(apa,cn*sizeof(MatScalar));CHKERRQ(ierr); 226 ierr = PetscMemzero(apjdense,cn*sizeof(PetscInt));CHKERRQ(ierr); 227 228 /* Clear old values in C */ 229 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 230 231 for (i=0; i<am; i++) { 232 /* Form sparse row of A*P */ 233 anzi = ai[i+1] - ai[i]; 234 apnzj = 0; 235 for (j=0; j<anzi; j++) { 236 prow = *aj++; 237 pnzj = pi[prow+1] - pi[prow]; 238 pjj = pj + pi[prow]; 239 paj = pa + pi[prow]; 240 for (k=0; k<pnzj; k++) { 241 if (!apjdense[pjj[k]]) { 242 apjdense[pjj[k]] = -1; 243 apj[apnzj++] = pjj[k]; 244 } 245 apa[pjj[k]] += (*aa)*paj[k]; 246 } 247 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 248 aa++; 249 } 250 251 /* Sort the j index array for quick sparse axpy. */ 252 /* Note: a array does not need sorting as it is in dense storage locations. */ 253 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 254 255 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 256 pnzi = pi[i+1] - pi[i]; 257 for (j=0; j<pnzi; j++) { 258 nextap = 0; 259 crow = *pJ++; 260 cjj = cj + ci[crow]; 261 caj = ca + ci[crow]; 262 /* Perform sparse axpy operation. Note cjj includes apj. */ 263 for (k=0; nextap<apnzj; k++) { 264 #if defined(PETSC_USE_DEBUG) 265 if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 266 #endif 267 if (cjj[k]==apj[nextap]) { 268 caj[k] += (*pA)*apa[apj[nextap++]]; 269 } 270 } 271 ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr); 272 pA++; 273 } 274 275 /* Zero the current row info for A*P */ 276 for (j=0; j<apnzj; j++) { 277 apa[apj[j]] = 0.; 278 apjdense[apj[j]] = 0; 279 } 280 } 281 282 /* Assemble the final matrix and clean up */ 283 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 284 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 285 286 ierr = PetscFree3(apa,apjdense,apj);CHKERRQ(ierr); 287 PetscFunctionReturn(0); 288 } 289 290 #undef __FUNCT__ 291 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy" 292 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 293 { 294 PetscErrorCode ierr; 295 Mat_SeqAIJ *ap,*c; 296 PetscInt *api,*apj,*ci,pn=P->cmap->N; 297 MatScalar *ca; 298 Mat_PtAP *ptap; 299 Mat Pt,AP; 300 301 PetscFunctionBegin; 302 /* Get symbolic Pt = P^T */ 303 ierr = MatTransposeSymbolic_SeqAIJ(P,&Pt);CHKERRQ(ierr); 304 305 /* Get symbolic AP = A*P */ 306 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);CHKERRQ(ierr); 307 308 ap = (Mat_SeqAIJ*)AP->data; 309 api = ap->i; 310 apj = ap->j; 311 ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */ 312 313 /* Get C = Pt*AP */ 314 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);CHKERRQ(ierr); 315 316 c = (Mat_SeqAIJ*)(*C)->data; 317 ci = c->i; 318 ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr); 319 c->a = ca; 320 c->free_a = PETSC_TRUE; 321 322 /* Create a supporting struct for reuse by MatPtAPNumeric() */ 323 ierr = PetscNew(&ptap);CHKERRQ(ierr); 324 325 c->ptap = ptap; 326 ptap->destroy = (*C)->ops->destroy; 327 (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP; 328 329 /* Allocate temporary array for storage of one row of A*P */ 330 ierr = PetscCalloc1(pn+1,&ptap->apa);CHKERRQ(ierr); 331 332 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ; 333 334 ptap->api = api; 335 ptap->apj = apj; 336 337 /* Clean up. */ 338 ierr = MatDestroy(&Pt);CHKERRQ(ierr); 339 ierr = MatDestroy(&AP);CHKERRQ(ierr); 340 #if defined(PETSC_USE_INFO) 341 ierr = PetscInfo1((*C),"given fill %g\n",(double)fill);CHKERRQ(ierr); 342 #endif 343 PetscFunctionReturn(0); 344 } 345 346 /* #define PROFILE_MatPtAPNumeric */ 347 #undef __FUNCT__ 348 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ" 349 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 350 { 351 PetscErrorCode ierr; 352 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 353 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 354 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 355 const PetscInt *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*ci=c->i,*cj=c->j; 356 const PetscScalar *aa=a->a,*pa=p->a,*pval; 357 const PetscInt *apj,*pcol,*cjj; 358 const PetscInt am=A->rmap->N,cm=C->rmap->N; 359 PetscInt i,j,k,anz,apnz,pnz,prow,crow,cnz; 360 PetscScalar *apa,*ca=c->a,*caj,pvalj; 361 Mat_PtAP *ptap = c->ptap; 362 #if defined(PROFILE_MatPtAPNumeric) 363 PetscLogDouble t0,tf,time_Cseq0=0.0,time_Cseq1=0.0; 364 PetscInt flops0=0,flops1=0; 365 #endif 366 367 PetscFunctionBegin; 368 /* Get temporary array for storage of one row of A*P */ 369 apa = ptap->apa; 370 371 /* Clear old values in C */ 372 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 373 374 for (i=0; i<am; i++) { 375 /* Form sparse row of AP[i,:] = A[i,:]*P */ 376 #if defined(PROFILE_MatPtAPNumeric) 377 ierr = PetscTime(&t0);CHKERRQ(ierr); 378 #endif 379 anz = ai[i+1] - ai[i]; 380 for (j=0; j<anz; j++) { 381 prow = aj[j]; 382 pnz = pi[prow+1] - pi[prow]; 383 pcol = pj + pi[prow]; 384 pval = pa + pi[prow]; 385 for (k=0; k<pnz; k++) { 386 apa[pcol[k]] += aa[j]*pval[k]; 387 } 388 ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr); 389 #if defined(PROFILE_MatPtAPNumeric) 390 flops0 += 2.0*pnz; 391 #endif 392 } 393 aj += anz; aa += anz; 394 #if defined(PROFILE_MatPtAPNumeric) 395 ierr = PetscTime(&tf);CHKERRQ(ierr); 396 397 time_Cseq0 += tf - t0; 398 #endif 399 400 /* Compute P^T*A*P using outer product P[i,:]^T*AP[i,:]. */ 401 #if defined(PROFILE_MatPtAPNumeric) 402 ierr = PetscTime(&t0);CHKERRQ(ierr); 403 #endif 404 apj = ptap->apj + ptap->api[i]; 405 apnz = ptap->api[i+1] - ptap->api[i]; 406 pnz = pi[i+1] - pi[i]; 407 pcol = pj + pi[i]; 408 pval = pa + pi[i]; 409 410 /* Perform dense axpy */ 411 for (j=0; j<pnz; j++) { 412 crow = pcol[j]; 413 cjj = cj + ci[crow]; 414 caj = ca + ci[crow]; 415 pvalj = pval[j]; 416 cnz = ci[crow+1] - ci[crow]; 417 for (k=0; k<cnz; k++) caj[k] += pvalj*apa[cjj[k]]; 418 ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr); 419 #if defined(PROFILE_MatPtAPNumeric) 420 flops1 += 2.0*cnz; 421 #endif 422 } 423 #if defined(PROFILE_MatPtAPNumeric) 424 ierr = PetscTime(&tf);CHKERRQ(ierr); 425 time_Cseq1 += tf - t0; 426 #endif 427 428 /* Zero the current row info for A*P */ 429 for (j=0; j<apnz; j++) apa[apj[j]] = 0.0; 430 } 431 432 /* Assemble the final matrix and clean up */ 433 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 434 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 435 #if defined(PROFILE_MatPtAPNumeric) 436 printf("PtAPNumeric_SeqAIJ time %g + %g, flops %d %d\n",time_Cseq0,time_Cseq1,flops0,flops1); 437 #endif 438 PetscFunctionReturn(0); 439 } 440