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 #undef __FUNCT__ 13 #define __FUNCT__ "MatPtAP_SeqAIJ_SeqAIJ" 14 PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C) 15 { 16 PetscErrorCode ierr; 17 18 PetscFunctionBegin; 19 if (scall == MAT_INITIAL_MATRIX) { 20 ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 21 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ(A,P,fill,C);CHKERRQ(ierr); 22 ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 23 } 24 ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr); 25 ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr); 26 ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr); 27 PetscFunctionReturn(0); 28 } 29 30 #undef __FUNCT__ 31 #define __FUNCT__ "MatDestroy_SeqAIJ_PtAP" 32 PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A) 33 { 34 PetscErrorCode ierr; 35 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 36 Mat_PtAP *ptap = a->ptap; 37 38 PetscFunctionBegin; 39 ierr = PetscFree(ptap->apa);CHKERRQ(ierr); 40 ierr = PetscFree(ptap->api);CHKERRQ(ierr); 41 ierr = PetscFree(ptap->apj);CHKERRQ(ierr); 42 ierr = (ptap->destroy)(A);CHKERRQ(ierr); 43 ierr = PetscFree(ptap);CHKERRQ(ierr); 44 PetscFunctionReturn(0); 45 } 46 47 #undef __FUNCT__ 48 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy" 49 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 50 { 51 PetscErrorCode ierr; 52 PetscFreeSpaceList free_space=NULL,current_space=NULL; 53 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 54 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 55 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 56 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N; 57 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 58 MatScalar *ca; 59 PetscBT lnkbt; 60 PetscReal afill; 61 62 PetscFunctionBegin; 63 /* Get ij structure of P^T */ 64 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 65 ptJ = ptj; 66 67 /* Allocate ci array, arrays for fill computation and */ 68 /* free space for accumulating nonzero column info */ 69 ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr); 70 ci[0] = 0; 71 72 ierr = PetscMalloc((2*an+1)*sizeof(PetscInt),&ptadenserow);CHKERRQ(ierr); 73 ierr = PetscMemzero(ptadenserow,(2*an+1)*sizeof(PetscInt));CHKERRQ(ierr); 74 ptasparserow = ptadenserow + an; 75 76 /* create and initialize a linked list */ 77 nlnk = pn+1; 78 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 79 80 /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */ 81 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+pi[pm])),&free_space);CHKERRQ(ierr); 82 current_space = free_space; 83 84 /* Determine symbolic info for each row of C: */ 85 for (i=0; i<pn; i++) { 86 ptnzi = pti[i+1] - pti[i]; 87 ptanzi = 0; 88 /* Determine symbolic row of PtA: */ 89 for (j=0; j<ptnzi; j++) { 90 arow = *ptJ++; 91 anzj = ai[arow+1] - ai[arow]; 92 ajj = aj + ai[arow]; 93 for (k=0; k<anzj; k++) { 94 if (!ptadenserow[ajj[k]]) { 95 ptadenserow[ajj[k]] = -1; 96 ptasparserow[ptanzi++] = ajj[k]; 97 } 98 } 99 } 100 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 101 ptaj = ptasparserow; 102 cnzi = 0; 103 for (j=0; j<ptanzi; j++) { 104 prow = *ptaj++; 105 pnzj = pi[prow+1] - pi[prow]; 106 pjj = pj + pi[prow]; 107 /* add non-zero cols of P into the sorted linked list lnk */ 108 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 109 cnzi += nlnk; 110 } 111 112 /* If free space is not available, make more free space */ 113 /* Double the amount of total space in the list */ 114 if (current_space->local_remaining<cnzi) { 115 ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,¤t_space);CHKERRQ(ierr); 116 nspacedouble++; 117 } 118 119 /* Copy data into free space, and zero out denserows */ 120 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 121 122 current_space->array += cnzi; 123 current_space->local_used += cnzi; 124 current_space->local_remaining -= cnzi; 125 126 for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0; 127 128 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 129 /* For now, we will recompute what is needed. */ 130 ci[i+1] = ci[i] + cnzi; 131 } 132 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 133 /* Allocate space for cj, initialize cj, and */ 134 /* destroy list of free space and other temporary array(s) */ 135 ierr = PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr); 136 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 137 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 138 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 139 140 /* Allocate space for ca */ 141 ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr); 142 ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr); 143 144 /* put together the new matrix */ 145 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 146 147 (*C)->rmap->bs = P->cmap->bs; 148 (*C)->cmap->bs = P->cmap->bs; 149 150 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 151 /* Since these are PETSc arrays, change flags to free them as necessary. */ 152 c = (Mat_SeqAIJ*)((*C)->data); 153 c->free_a = PETSC_TRUE; 154 c->free_ij = PETSC_TRUE; 155 c->nonew = 0; 156 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy; 157 158 /* set MatInfo */ 159 afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5); 160 if (afill < 1.0) afill = 1.0; 161 c->maxnz = ci[pn]; 162 c->nz = ci[pn]; 163 (*C)->info.mallocs = nspacedouble; 164 (*C)->info.fill_ratio_given = fill; 165 (*C)->info.fill_ratio_needed = afill; 166 167 /* Clean up. */ 168 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 169 #if defined(PETSC_USE_INFO) 170 if (ci[pn] != 0) { 171 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr); 172 ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr); 173 } else { 174 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 175 } 176 #endif 177 PetscFunctionReturn(0); 178 } 179 180 #undef __FUNCT__ 181 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy" 182 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 183 { 184 PetscErrorCode ierr; 185 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 186 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 187 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 188 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 189 PetscInt *ci=c->i,*cj=c->j,*cjj; 190 PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 191 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 192 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 193 194 PetscFunctionBegin; 195 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 196 ierr = PetscMalloc(cn*(sizeof(MatScalar)+sizeof(PetscInt))+c->rmax*sizeof(PetscInt),&apa);CHKERRQ(ierr); 197 198 apjdense = (PetscInt*)(apa + cn); 199 apj = apjdense + cn; 200 ierr = PetscMemzero(apa,cn*(sizeof(MatScalar)+sizeof(PetscInt)));CHKERRQ(ierr); 201 202 /* Clear old values in C */ 203 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 204 205 for (i=0; i<am; i++) { 206 /* Form sparse row of A*P */ 207 anzi = ai[i+1] - ai[i]; 208 apnzj = 0; 209 for (j=0; j<anzi; j++) { 210 prow = *aj++; 211 pnzj = pi[prow+1] - pi[prow]; 212 pjj = pj + pi[prow]; 213 paj = pa + pi[prow]; 214 for (k=0; k<pnzj; k++) { 215 if (!apjdense[pjj[k]]) { 216 apjdense[pjj[k]] = -1; 217 apj[apnzj++] = pjj[k]; 218 } 219 apa[pjj[k]] += (*aa)*paj[k]; 220 } 221 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 222 aa++; 223 } 224 225 /* Sort the j index array for quick sparse axpy. */ 226 /* Note: a array does not need sorting as it is in dense storage locations. */ 227 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 228 229 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 230 pnzi = pi[i+1] - pi[i]; 231 for (j=0; j<pnzi; j++) { 232 nextap = 0; 233 crow = *pJ++; 234 cjj = cj + ci[crow]; 235 caj = ca + ci[crow]; 236 /* Perform sparse axpy operation. Note cjj includes apj. */ 237 for (k=0; nextap<apnzj; k++) { 238 #if defined(PETSC_USE_DEBUG) 239 if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 240 #endif 241 if (cjj[k]==apj[nextap]) { 242 caj[k] += (*pA)*apa[apj[nextap++]]; 243 } 244 } 245 ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr); 246 pA++; 247 } 248 249 /* Zero the current row info for A*P */ 250 for (j=0; j<apnzj; j++) { 251 apa[apj[j]] = 0.; 252 apjdense[apj[j]] = 0; 253 } 254 } 255 256 /* Assemble the final matrix and clean up */ 257 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 258 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 259 260 ierr = PetscFree(apa);CHKERRQ(ierr); 261 PetscFunctionReturn(0); 262 } 263 264 #undef __FUNCT__ 265 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ" 266 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C) 267 { 268 PetscErrorCode ierr; 269 Mat_SeqAIJ *ap,*c; 270 PetscInt *api,*apj,*ci,pn=P->cmap->N; 271 MatScalar *ca; 272 Mat_PtAP *ptap; 273 Mat Pt,AP; 274 PetscBool sparse_axpy=PETSC_TRUE; 275 276 PetscFunctionBegin; 277 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 278 /* flag 'sparse_axpy' determines which implementations to be used: 279 0: do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P; 280 1: do two sparse axpy in MatPtAPNumeric() - slowest, does not store structure of A*P. */ 281 ierr = PetscOptionsBool("-matptap_scalable","Use sparse axpy but slower MatPtAPNumeric()","",sparse_axpy,&sparse_axpy,NULL);CHKERRQ(ierr); 282 ierr = PetscOptionsEnd();CHKERRQ(ierr); 283 if (sparse_axpy) { 284 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr); 285 PetscFunctionReturn(0); 286 } 287 288 /* Get symbolic Pt = P^T */ 289 ierr = MatTransposeSymbolic_SeqAIJ(P,&Pt);CHKERRQ(ierr); 290 291 /* Get symbolic AP = A*P */ 292 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);CHKERRQ(ierr); 293 294 ap = (Mat_SeqAIJ*)AP->data; 295 api = ap->i; 296 apj = ap->j; 297 ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */ 298 299 /* Get C = Pt*AP */ 300 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);CHKERRQ(ierr); 301 302 c = (Mat_SeqAIJ*)(*C)->data; 303 ci = c->i; 304 ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr); 305 ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr); 306 c->a = ca; 307 c->free_a = PETSC_TRUE; 308 309 /* Create a supporting struct for reuse by MatPtAPNumeric() */ 310 ierr = PetscNew(Mat_PtAP,&ptap);CHKERRQ(ierr); 311 312 c->ptap = ptap; 313 ptap->destroy = (*C)->ops->destroy; 314 (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP; 315 316 /* Allocate temporary array for storage of one row of A*P */ 317 ierr = PetscMalloc((pn+1)*sizeof(PetscScalar),&ptap->apa);CHKERRQ(ierr); 318 ierr = PetscMemzero(ptap->apa,(pn+1)*sizeof(PetscScalar));CHKERRQ(ierr); 319 320 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ; 321 322 ptap->api = api; 323 ptap->apj = apj; 324 325 /* Clean up. */ 326 ierr = MatDestroy(&Pt);CHKERRQ(ierr); 327 ierr = MatDestroy(&AP);CHKERRQ(ierr); 328 #if defined(PETSC_USE_INFO) 329 ierr = PetscInfo2((*C),"given fill %G, use scalable %d\n",fill,sparse_axpy);CHKERRQ(ierr); 330 #endif 331 PetscFunctionReturn(0); 332 } 333 334 /* #define PROFILE_MatPtAPNumeric */ 335 #undef __FUNCT__ 336 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ" 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 apnz = 0; 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