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