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 = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 20 ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ(A,P,fill,C);CHKERRQ(ierr); 21 ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr); 22 } 23 ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr); 24 //ierr = (*(A)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr); /* should use matrix *C, not A! */ 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 /* free ptap, then A */ 40 ierr = PetscFree(ptap->apa);CHKERRQ(ierr); 41 ierr = PetscFree(ptap->api);CHKERRQ(ierr); 42 ierr = PetscFree(ptap->apj);CHKERRQ(ierr); 43 ierr = (ptap->destroy)(A);CHKERRQ(ierr); 44 ierr = PetscFree(ptap);CHKERRQ(ierr); 45 PetscFunctionReturn(0); 46 } 47 48 #undef __FUNCT__ 49 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy" 50 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C) 51 { 52 PetscErrorCode ierr; 53 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 54 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c; 55 PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj; 56 PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0; 57 PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N; 58 PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk; 59 MatScalar *ca; 60 PetscBT lnkbt; 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). */ 81 /* This should be reasonable if sparsity of PtAP is similar to that of A. */ 82 ierr = PetscFreeSpaceGet((PetscInt)(fill*ai[am]),&free_space); 83 current_space = free_space; 84 85 /* Determine symbolic info for each row of C: */ 86 for (i=0;i<pn;i++) { 87 ptnzi = pti[i+1] - pti[i]; 88 ptanzi = 0; 89 /* Determine symbolic row of PtA: */ 90 for (j=0;j<ptnzi;j++) { 91 arow = *ptJ++; 92 anzj = ai[arow+1] - ai[arow]; 93 ajj = aj + ai[arow]; 94 for (k=0;k<anzj;k++) { 95 if (!ptadenserow[ajj[k]]) { 96 ptadenserow[ajj[k]] = -1; 97 ptasparserow[ptanzi++] = ajj[k]; 98 } 99 } 100 } 101 /* Using symbolic info for row of PtA, determine symbolic info for row of C: */ 102 ptaj = ptasparserow; 103 cnzi = 0; 104 for (j=0;j<ptanzi;j++) { 105 prow = *ptaj++; 106 pnzj = pi[prow+1] - pi[prow]; 107 pjj = pj + pi[prow]; 108 /* add non-zero cols of P into the sorted linked list lnk */ 109 ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr); 110 cnzi += nlnk; 111 } 112 113 /* If free space is not available, make more free space */ 114 /* Double the amount of total space in the list */ 115 if (current_space->local_remaining<cnzi) { 116 ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,¤t_space);CHKERRQ(ierr); 117 nspacedouble++; 118 } 119 120 /* Copy data into free space, and zero out denserows */ 121 ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 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++) { 127 ptadenserow[ptasparserow[j]] = 0; 128 } 129 /* Aside: Perhaps we should save the pta info for the numerical factorization. */ 130 /* For now, we will recompute what is needed. */ 131 ci[i+1] = ci[i] + cnzi; 132 } 133 /* nnz is now stored in ci[ptm], column indices are in the list of free space */ 134 /* Allocate space for cj, initialize cj, and */ 135 /* destroy list of free space and other temporary array(s) */ 136 ierr = PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr); 137 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 138 ierr = PetscFree(ptadenserow);CHKERRQ(ierr); 139 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 140 141 /* Allocate space for ca */ 142 ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr); 143 ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr); 144 145 /* put together the new matrix */ 146 ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,pn,pn,ci,cj,ca,C);CHKERRQ(ierr); 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; /* should use *C->ops until PtAP insterface is updated to double dispatch as MatMatMult() */ 157 158 /* Clean up. */ 159 ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr); 160 #if defined(PETSC_USE_INFO) 161 if (ci[pn] != 0) { 162 PetscReal afill = ((PetscReal)ci[pn])/ai[am]; 163 if (afill < 1.0) afill = 1.0; 164 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr); 165 ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr); 166 } else { 167 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 168 } 169 #endif 170 PetscFunctionReturn(0); 171 } 172 173 #undef __FUNCT__ 174 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy" 175 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C) 176 { 177 PetscErrorCode ierr; 178 Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data; 179 Mat_SeqAIJ *p = (Mat_SeqAIJ *) P->data; 180 Mat_SeqAIJ *c = (Mat_SeqAIJ *) C->data; 181 PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj; 182 PetscInt *ci=c->i,*cj=c->j,*cjj; 183 PetscInt am=A->rmap->N,cn=C->cmap->N,cm=C->rmap->N; 184 PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow; 185 MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj; 186 187 PetscFunctionBegin; 188 /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */ 189 ierr = PetscMalloc(cn*(sizeof(MatScalar)+sizeof(PetscInt))+c->rmax*sizeof(PetscInt),&apa);CHKERRQ(ierr); 190 191 apjdense = (PetscInt *)(apa + cn); 192 apj = apjdense + cn; 193 ierr = PetscMemzero(apa,cn*(sizeof(MatScalar)+sizeof(PetscInt)));CHKERRQ(ierr); 194 195 /* Clear old values in C */ 196 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 197 198 for (i=0; i<am; i++) { 199 /* Form sparse row of A*P */ 200 anzi = ai[i+1] - ai[i]; 201 apnzj = 0; 202 for (j=0; j<anzi; j++) { 203 prow = *aj++; 204 pnzj = pi[prow+1] - pi[prow]; 205 pjj = pj + pi[prow]; 206 paj = pa + pi[prow]; 207 for (k=0;k<pnzj;k++) { 208 if (!apjdense[pjj[k]]) { 209 apjdense[pjj[k]] = -1; 210 apj[apnzj++] = pjj[k]; 211 } 212 apa[pjj[k]] += (*aa)*paj[k]; 213 } 214 ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr); 215 aa++; 216 } 217 218 /* Sort the j index array for quick sparse axpy. */ 219 /* Note: a array does not need sorting as it is in dense storage locations. */ 220 ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr); 221 222 /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */ 223 pnzi = pi[i+1] - pi[i]; 224 for (j=0; j<pnzi; j++) { 225 nextap = 0; 226 crow = *pJ++; 227 cjj = cj + ci[crow]; 228 caj = ca + ci[crow]; 229 /* Perform sparse axpy operation. Note cjj includes apj. */ 230 for (k=0;nextap<apnzj;k++) { 231 #if defined(PETSC_USE_DEBUG) 232 if (k >= ci[crow+1] - ci[crow]) { 233 SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow); 234 } 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,PETSC_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 c->ptap = ptap; 307 ptap->destroy = (*C)->ops->destroy; 308 (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP; 309 310 /* Allocate temporary array for storage of one row of A*P */ 311 ierr = PetscMalloc((pn+1)*sizeof(PetscScalar),&ptap->apa);CHKERRQ(ierr); 312 ierr = PetscMemzero(ptap->apa,(pn+1)*sizeof(PetscScalar));CHKERRQ(ierr); 313 (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ; 314 315 ptap->api = api; 316 ptap->apj = apj; 317 318 /* Clean up. */ 319 ierr = MatDestroy(&Pt);CHKERRQ(ierr); 320 ierr = MatDestroy(&AP);CHKERRQ(ierr); 321 #if defined(PETSC_USE_INFO) 322 ierr = PetscInfo2((*C),"given fill %G, use scalable %d\n",fill,sparse_axpy);CHKERRQ(ierr); 323 #endif 324 PetscFunctionReturn(0); 325 } 326 327 /* #define PROFILE_MatPtAPNumeric */ 328 #undef __FUNCT__ 329 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ" 330 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C) 331 { 332 PetscErrorCode ierr; 333 Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data; 334 Mat_SeqAIJ *p = (Mat_SeqAIJ *) P->data; 335 Mat_SeqAIJ *c = (Mat_SeqAIJ *) C->data; 336 const PetscInt *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*ci=c->i,*cj=c->j; 337 const PetscScalar *aa=a->a,*pa=p->a,*pval; 338 const PetscInt *apj,*pcol,*cjj; 339 const PetscInt am=A->rmap->N,cm=C->rmap->N; 340 PetscInt i,j,k,anz,apnz,pnz,prow,crow,cnz; 341 PetscScalar *apa,*ca=c->a,*caj,pvalj; 342 Mat_PtAP *ptap = c->ptap; 343 #if defined(PROFILE_MatPtAPNumeric) 344 PetscLogDouble t0,tf,time_Cseq0=0.0,time_Cseq1=0.0; 345 PetscInt flops0=0,flops1=0; 346 #endif 347 348 PetscFunctionBegin; 349 /* Get temporary array for storage of one row of A*P */ 350 apa = ptap->apa; 351 352 /* Clear old values in C */ 353 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 354 355 for (i=0;i<am;i++) { 356 /* Form sparse row of AP[i,:] = A[i,:]*P */ 357 #if defined(PROFILE_MatPtAPNumeric) 358 ierr = PetscGetTime(&t0);CHKERRQ(ierr); 359 #endif 360 anz = ai[i+1] - ai[i]; 361 apnz = 0; 362 for (j=0; j<anz; j++) { 363 prow = aj[j]; 364 pnz = pi[prow+1] - pi[prow]; 365 pcol = pj + pi[prow]; 366 pval = pa + pi[prow]; 367 for (k=0; k<pnz; k++) { 368 apa[pcol[k]] += aa[j]*pval[k]; 369 } 370 ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr); 371 #if defined(PROFILE_MatPtAPNumeric) 372 flops0 += 2.0*pnz; 373 #endif 374 } 375 aj += anz; aa += anz; 376 #if defined(PROFILE_MatPtAPNumeric) 377 ierr = PetscGetTime(&tf);CHKERRQ(ierr); 378 time_Cseq0 += tf - t0; 379 #endif 380 381 /* Compute P^T*A*P using outer product P[i,:]^T*AP[i,:]. */ 382 #if defined(PROFILE_MatPtAPNumeric) 383 ierr = PetscGetTime(&t0);CHKERRQ(ierr); 384 #endif 385 apj = ptap->apj + ptap->api[i]; 386 apnz = ptap->api[i+1] - ptap->api[i]; 387 pnz = pi[i+1] - pi[i]; 388 pcol = pj + pi[i]; 389 pval = pa + pi[i]; 390 391 /* Perform dense axpy */ 392 for (j=0; j<pnz; j++) { 393 crow = pcol[j]; 394 cjj = cj + ci[crow]; 395 caj = ca + ci[crow]; 396 pvalj = pval[j]; 397 cnz = ci[crow+1] - ci[crow]; 398 for (k=0; k<cnz; k++){ 399 caj[k] += pvalj*apa[cjj[k]]; 400 } 401 ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr); 402 #if defined(PROFILE_MatPtAPNumeric) 403 flops1 += 2.0*cnz; 404 #endif 405 } 406 #if defined(PROFILE_MatPtAPNumeric) 407 ierr = PetscGetTime(&tf);CHKERRQ(ierr); 408 time_Cseq1 += tf - t0; 409 #endif 410 411 /* Zero the current row info for A*P */ 412 for (j=0; j<apnz; j++) apa[apj[j]] = 0.0; 413 } 414 415 /* Assemble the final matrix and clean up */ 416 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 417 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 418 #if defined(PROFILE_MatPtAPNumeric) 419 printf("PtAPNumeric_SeqAIJ time %g + %g, flops %d %d\n",time_Cseq0,time_Cseq1,flops0,flops1); 420 #endif 421 PetscFunctionReturn(0); 422 } 423