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 11 #undef __FUNCT__ 12 #define __FUNCT__ "MatPtAP_SeqAIJ_SeqAIJ" 13 PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C) 14 { 15 PetscErrorCode ierr; 16 17 PetscFunctionBegin; 18 if (scall == MAT_INITIAL_MATRIX) { 19 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ(A,P,fill,C);CHKERRQ(ierr); 20 } 21 ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr); 22 PetscFunctionReturn(0); 23 } 24 25 #undef __FUNCT__ 26 #define __FUNCT__ "MatDestroy_SeqAIJ_PtAP" 27 PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A) 28 { 29 PetscErrorCode ierr; 30 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 31 Mat_PtAP *ptap = a->ptap; 32 33 PetscFunctionBegin; 34 ierr = PetscFree(ptap->apa);CHKERRQ(ierr); 35 ierr = PetscFree(ptap->api);CHKERRQ(ierr); 36 ierr = PetscFree(ptap->apj);CHKERRQ(ierr); 37 ierr = (ptap->destroy)(A);CHKERRQ(ierr); 38 ierr = PetscFree(ptap);CHKERRQ(ierr); 39 PetscFunctionReturn(0); 40 } 41 42 #undef __FUNCT__ 43 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy" 44 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 45 { 46 PetscErrorCode ierr; 47 PetscFreeSpaceList free_space=NULL,current_space=NULL; 48 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 49 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 50 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 51 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N; 52 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 53 MatScalar *ca; 54 PetscBT lnkbt; 55 PetscReal afill; 56 57 PetscFunctionBegin; 58 /* Get ij structure of P^T */ 59 ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 60 ptJ = ptj; 61 62 /* Allocate ci array, arrays for fill computation and */ 63 /* free space for accumulating nonzero column info */ 64 ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr); 65 ci[0] = 0; 66 67 ierr = PetscMalloc((2*an+1)*sizeof(PetscInt),&ptadenserow);CHKERRQ(ierr); 68 ierr = PetscMemzero(ptadenserow,(2*an+1)*sizeof(PetscInt));CHKERRQ(ierr); 69 ptasparserow = ptadenserow + an; 70 71 /* create and initialize a linked list */ 72 nlnk = pn+1; 73 ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 74 75 /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */ 76 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+pi[pm])),&free_space);CHKERRQ(ierr); 77 current_space = free_space; 78 79 /* Determine symbolic info for each row of C: */ 80 for (i=0; i<pn; i++) { 81 ptnzi = pti[i+1] - pti[i]; 82 ptanzi = 0; 83 /* Determine symbolic row of PtA: */ 84 for (j=0; j<ptnzi; j++) { 85 arow = *ptJ++; 86 anzj = ai[arow+1] - ai[arow]; 87 ajj = aj + ai[arow]; 88 for (k=0; k<anzj; k++) { 89 if (!ptadenserow[ajj[k]]) { 90 ptadenserow[ajj[k]] = -1; 91 ptasparserow[ptanzi++] = ajj[k]; 92 } 93 } 94 } 95 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 96 ptaj = ptasparserow; 97 cnzi = 0; 98 for (j=0; j<ptanzi; j++) { 99 prow = *ptaj++; 100 pnzj = pi[prow+1] - pi[prow]; 101 pjj = pj + pi[prow]; 102 /* add non-zero cols of P into the sorted linked list lnk */ 103 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 104 cnzi += nlnk; 105 } 106 107 /* If free space is not available, make more free space */ 108 /* Double the amount of total space in the list */ 109 if (current_space->local_remaining<cnzi) { 110 ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,¤t_space);CHKERRQ(ierr); 111 nspacedouble++; 112 } 113 114 /* Copy data into free space, and zero out denserows */ 115 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 116 117 current_space->array += cnzi; 118 current_space->local_used += cnzi; 119 current_space->local_remaining -= cnzi; 120 121 for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0; 122 123 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 124 /* For now, we will recompute what is needed. */ 125 ci[i+1] = ci[i] + cnzi; 126 } 127 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 128 /* Allocate space for cj, initialize cj, and */ 129 /* destroy list of free space and other temporary array(s) */ 130 ierr = PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr); 131 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 132 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 133 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 134 135 /* Allocate space for ca */ 136 ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr); 137 ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr); 138 139 /* put together the new matrix */ 140 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 141 142 (*C)->rmap->bs = P->cmap->bs; 143 (*C)->cmap->bs = P->cmap->bs; 144 145 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 146 /* Since these are PETSc arrays, change flags to free them as necessary. */ 147 c = (Mat_SeqAIJ*)((*C)->data); 148 c->free_a = PETSC_TRUE; 149 c->free_ij = PETSC_TRUE; 150 c->nonew = 0; 151 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy; 152 153 /* set MatInfo */ 154 afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5); 155 if (afill < 1.0) afill = 1.0; 156 c->maxnz = ci[pn]; 157 c->nz = ci[pn]; 158 (*C)->info.mallocs = nspacedouble; 159 (*C)->info.fill_ratio_given = fill; 160 (*C)->info.fill_ratio_needed = afill; 161 162 /* Clean up. */ 163 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 164 #if defined(PETSC_USE_INFO) 165 if (ci[pn] != 0) { 166 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr); 167 ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr); 168 } else { 169 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 170 } 171 #endif 172 PetscFunctionReturn(0); 173 } 174 175 #undef __FUNCT__ 176 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy" 177 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 178 { 179 PetscErrorCode ierr; 180 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 181 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 182 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 183 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 184 PetscInt *ci=c->i,*cj=c->j,*cjj; 185 PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 186 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 187 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 188 189 PetscFunctionBegin; 190 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 191 ierr = PetscMalloc(cn*(sizeof(MatScalar)+sizeof(PetscInt))+c->rmax*sizeof(PetscInt),&apa);CHKERRQ(ierr); 192 193 apjdense = (PetscInt*)(apa + cn); 194 apj = apjdense + cn; 195 ierr = PetscMemzero(apa,cn*(sizeof(MatScalar)+sizeof(PetscInt)));CHKERRQ(ierr); 196 197 /* Clear old values in C */ 198 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 199 200 for (i=0; i<am; i++) { 201 /* Form sparse row of A*P */ 202 anzi = ai[i+1] - ai[i]; 203 apnzj = 0; 204 for (j=0; j<anzi; j++) { 205 prow = *aj++; 206 pnzj = pi[prow+1] - pi[prow]; 207 pjj = pj + pi[prow]; 208 paj = pa + pi[prow]; 209 for (k=0; k<pnzj; k++) { 210 if (!apjdense[pjj[k]]) { 211 apjdense[pjj[k]] = -1; 212 apj[apnzj++] = pjj[k]; 213 } 214 apa[pjj[k]] += (*aa)*paj[k]; 215 } 216 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 217 aa++; 218 } 219 220 /* Sort the j index array for quick sparse axpy. */ 221 /* Note: a array does not need sorting as it is in dense storage locations. */ 222 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 223 224 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 225 pnzi = pi[i+1] - pi[i]; 226 for (j=0; j<pnzi; j++) { 227 nextap = 0; 228 crow = *pJ++; 229 cjj = cj + ci[crow]; 230 caj = ca + ci[crow]; 231 /* Perform sparse axpy operation. Note cjj includes apj. */ 232 for (k=0; nextap<apnzj; k++) { 233 #if defined(PETSC_USE_DEBUG) 234 if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 235 #endif 236 if (cjj[k]==apj[nextap]) { 237 caj[k] += (*pA)*apa[apj[nextap++]]; 238 } 239 } 240 ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr); 241 pA++; 242 } 243 244 /* Zero the current row info for A*P */ 245 for (j=0; j<apnzj; j++) { 246 apa[apj[j]] = 0.; 247 apjdense[apj[j]] = 0; 248 } 249 } 250 251 /* Assemble the final matrix and clean up */ 252 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 253 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 254 255 ierr = PetscFree(apa);CHKERRQ(ierr); 256 PetscFunctionReturn(0); 257 } 258 259 #undef __FUNCT__ 260 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ" 261 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C) 262 { 263 PetscErrorCode ierr; 264 Mat_SeqAIJ *ap,*c; 265 PetscInt *api,*apj,*ci,pn=P->cmap->N; 266 MatScalar *ca; 267 Mat_PtAP *ptap; 268 Mat Pt,AP; 269 PetscBool sparse_axpy=PETSC_TRUE; 270 271 PetscFunctionBegin; 272 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 273 /* flag 'sparse_axpy' determines which implementations to be used: 274 0: do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P; 275 1: do two sparse axpy in MatPtAPNumeric() - slowest, does not store structure of A*P. */ 276 ierr = PetscOptionsBool("-matptap_scalable","Use sparse axpy but slower MatPtAPNumeric()","",sparse_axpy,&sparse_axpy,NULL);CHKERRQ(ierr); 277 ierr = PetscOptionsEnd();CHKERRQ(ierr); 278 if (sparse_axpy) { 279 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr); 280 PetscFunctionReturn(0); 281 } 282 283 /* Get symbolic Pt = P^T */ 284 ierr = MatTransposeSymbolic_SeqAIJ(P,&Pt);CHKERRQ(ierr); 285 286 /* Get symbolic AP = A*P */ 287 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);CHKERRQ(ierr); 288 289 ap = (Mat_SeqAIJ*)AP->data; 290 api = ap->i; 291 apj = ap->j; 292 ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */ 293 294 /* Get C = Pt*AP */ 295 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);CHKERRQ(ierr); 296 297 c = (Mat_SeqAIJ*)(*C)->data; 298 ci = c->i; 299 ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr); 300 ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr); 301 c->a = ca; 302 c->free_a = PETSC_TRUE; 303 304 /* Create a supporting struct for reuse by MatPtAPNumeric() */ 305 ierr = PetscNew(Mat_PtAP,&ptap);CHKERRQ(ierr); 306 307 c->ptap = ptap; 308 ptap->destroy = (*C)->ops->destroy; 309 (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP; 310 311 /* Allocate temporary array for storage of one row of A*P */ 312 ierr = PetscMalloc((pn+1)*sizeof(PetscScalar),&ptap->apa);CHKERRQ(ierr); 313 ierr = PetscMemzero(ptap->apa,(pn+1)*sizeof(PetscScalar));CHKERRQ(ierr); 314 315 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ; 316 317 ptap->api = api; 318 ptap->apj = apj; 319 320 /* Clean up. */ 321 ierr = MatDestroy(&Pt);CHKERRQ(ierr); 322 ierr = MatDestroy(&AP);CHKERRQ(ierr); 323 #if defined(PETSC_USE_INFO) 324 ierr = PetscInfo2((*C),"given fill %G, use scalable %d\n",fill,sparse_axpy);CHKERRQ(ierr); 325 #endif 326 PetscFunctionReturn(0); 327 } 328 329 /* #define PROFILE_MatPtAPNumeric */ 330 #undef __FUNCT__ 331 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ" 332 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 333 { 334 PetscErrorCode ierr; 335 Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data; 336 Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data; 337 Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data; 338 const PetscInt *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*ci=c->i,*cj=c->j; 339 const PetscScalar *aa=a->a,*pa=p->a,*pval; 340 const PetscInt *apj,*pcol,*cjj; 341 const PetscInt am=A->rmap->N,cm=C->rmap->N; 342 PetscInt i,j,k,anz,apnz,pnz,prow,crow,cnz; 343 PetscScalar *apa,*ca=c->a,*caj,pvalj; 344 Mat_PtAP *ptap = c->ptap; 345 #if defined(PROFILE_MatPtAPNumeric) 346 PetscLogDouble t0,tf,time_Cseq0=0.0,time_Cseq1=0.0; 347 PetscInt flops0=0,flops1=0; 348 #endif 349 350 PetscFunctionBegin; 351 /* Get temporary array for storage of one row of A*P */ 352 apa = ptap->apa; 353 354 /* Clear old values in C */ 355 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 356 357 for (i=0; i<am; i++) { 358 /* Form sparse row of AP[i,:] = A[i,:]*P */ 359 #if defined(PROFILE_MatPtAPNumeric) 360 ierr = PetscGetTime(&t0);CHKERRQ(ierr); 361 #endif 362 anz = ai[i+1] - ai[i]; 363 apnz = 0; 364 for (j=0; j<anz; j++) { 365 prow = aj[j]; 366 pnz = pi[prow+1] - pi[prow]; 367 pcol = pj + pi[prow]; 368 pval = pa + pi[prow]; 369 for (k=0; k<pnz; k++) { 370 apa[pcol[k]] += aa[j]*pval[k]; 371 } 372 ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr); 373 #if defined(PROFILE_MatPtAPNumeric) 374 flops0 += 2.0*pnz; 375 #endif 376 } 377 aj += anz; aa += anz; 378 #if defined(PROFILE_MatPtAPNumeric) 379 ierr = PetscGetTime(&tf);CHKERRQ(ierr); 380 381 time_Cseq0 += tf - t0; 382 #endif 383 384 /* Compute P^T*A*P using outer product P[i,:]^T*AP[i,:]. */ 385 #if defined(PROFILE_MatPtAPNumeric) 386 ierr = PetscGetTime(&t0);CHKERRQ(ierr); 387 #endif 388 apj = ptap->apj + ptap->api[i]; 389 apnz = ptap->api[i+1] - ptap->api[i]; 390 pnz = pi[i+1] - pi[i]; 391 pcol = pj + pi[i]; 392 pval = pa + pi[i]; 393 394 /* Perform dense axpy */ 395 for (j=0; j<pnz; j++) { 396 crow = pcol[j]; 397 cjj = cj + ci[crow]; 398 caj = ca + ci[crow]; 399 pvalj = pval[j]; 400 cnz = ci[crow+1] - ci[crow]; 401 for (k=0; k<cnz; k++) caj[k] += pvalj*apa[cjj[k]]; 402 ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr); 403 #if defined(PROFILE_MatPtAPNumeric) 404 flops1 += 2.0*cnz; 405 #endif 406 } 407 #if defined(PROFILE_MatPtAPNumeric) 408 ierr = PetscGetTime(&tf);CHKERRQ(ierr); 409 time_Cseq1 += tf - t0; 410 #endif 411 412 /* Zero the current row info for A*P */ 413 for (j=0; j<apnz; j++) apa[apj[j]] = 0.0; 414 } 415 416 /* Assemble the final matrix and clean up */ 417 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 418 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 419 #if defined(PROFILE_MatPtAPNumeric) 420 printf("PtAPNumeric_SeqAIJ time %g + %g, flops %d %d\n",time_Cseq0,time_Cseq1,flops0,flops1); 421 #endif 422 PetscFunctionReturn(0); 423 } 424