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