1 2 /* 3 Defines matrix-matrix product routines for pairs of SeqAIJ matrices 4 C = A * B 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 <petsc/private/isimpl.h> 11 #include <../src/mat/impls/dense/seq/dense.h> 12 13 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*); 14 15 #if defined(PETSC_HAVE_HYPRE) 16 PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*); 17 #endif 18 19 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 20 { 21 PetscErrorCode ierr; 22 #if !defined(PETSC_HAVE_HYPRE) 23 const char *algTypes[8] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined","rowmerge"}; 24 PetscInt nalg = 8; 25 #else 26 const char *algTypes[9] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined","rowmerge","hypre"}; 27 PetscInt nalg = 9; 28 #endif 29 PetscInt alg = 0; /* set default algorithm */ 30 PetscBool combined = PETSC_FALSE; /* Indicates whether the symbolic stage already computed the numerical values. */ 31 32 PetscFunctionBegin; 33 if (scall == MAT_INITIAL_MATRIX) { 34 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 35 PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */ 36 ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[0],&alg,NULL);CHKERRQ(ierr); 37 ierr = PetscOptionsEnd();CHKERRQ(ierr); 38 ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 39 switch (alg) { 40 case 1: 41 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr); 42 break; 43 case 2: 44 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr); 45 break; 46 case 3: 47 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr); 48 break; 49 case 4: 50 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr); 51 break; 52 case 5: 53 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr); 54 break; 55 case 6: 56 ierr = MatMatMult_SeqAIJ_SeqAIJ_Combined(A,B,fill,C);CHKERRQ(ierr); 57 combined = PETSC_TRUE; 58 break; 59 case 7: 60 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(A,B,fill,C);CHKERRQ(ierr); 61 break; 62 #if defined(PETSC_HAVE_HYPRE) 63 case 8: 64 ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr); 65 break; 66 #endif 67 default: 68 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 69 break; 70 } 71 ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 72 } 73 74 ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 75 if (!combined) { 76 ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr); 77 } 78 ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 79 PetscFunctionReturn(0); 80 } 81 82 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C) 83 { 84 PetscErrorCode ierr; 85 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 86 PetscInt *ai=a->i,*bi=b->i,*ci,*cj; 87 PetscInt am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 88 PetscReal afill; 89 PetscInt i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax; 90 PetscTable ta; 91 PetscBT lnkbt; 92 PetscFreeSpaceList free_space=NULL,current_space=NULL; 93 94 PetscFunctionBegin; 95 /* Get ci and cj */ 96 /*---------------*/ 97 /* Allocate ci array, arrays for fill computation and */ 98 /* free space for accumulating nonzero column info */ 99 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 100 ci[0] = 0; 101 102 /* create and initialize a linked list */ 103 ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr); 104 MatRowMergeMax_SeqAIJ(b,bm,ta); 105 ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); 106 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 107 108 ierr = PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);CHKERRQ(ierr); 109 110 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 111 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 112 113 current_space = free_space; 114 115 /* Determine ci and cj */ 116 for (i=0; i<am; i++) { 117 anzi = ai[i+1] - ai[i]; 118 aj = a->j + ai[i]; 119 for (j=0; j<anzi; j++) { 120 brow = aj[j]; 121 bnzj = bi[brow+1] - bi[brow]; 122 bj = b->j + bi[brow]; 123 /* add non-zero cols of B into the sorted linked list lnk */ 124 ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr); 125 } 126 cnzi = lnk[0]; 127 128 /* If free space is not available, make more free space */ 129 /* Double the amount of total space in the list */ 130 if (current_space->local_remaining<cnzi) { 131 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 132 ndouble++; 133 } 134 135 /* Copy data into free space, then initialize lnk */ 136 ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr); 137 138 current_space->array += cnzi; 139 current_space->local_used += cnzi; 140 current_space->local_remaining -= cnzi; 141 142 ci[i+1] = ci[i] + cnzi; 143 } 144 145 /* Column indices are in the list of free space */ 146 /* Allocate space for cj, initialize cj, and */ 147 /* destroy list of free space and other temporary array(s) */ 148 ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr); 149 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 150 ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr); 151 152 /* put together the new symbolic matrix */ 153 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 154 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 155 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 156 157 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 158 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 159 c = (Mat_SeqAIJ*)((*C)->data); 160 c->free_a = PETSC_FALSE; 161 c->free_ij = PETSC_TRUE; 162 c->nonew = 0; 163 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */ 164 165 /* set MatInfo */ 166 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 167 if (afill < 1.0) afill = 1.0; 168 c->maxnz = ci[am]; 169 c->nz = ci[am]; 170 (*C)->info.mallocs = ndouble; 171 (*C)->info.fill_ratio_given = fill; 172 (*C)->info.fill_ratio_needed = afill; 173 174 #if defined(PETSC_USE_INFO) 175 if (ci[am]) { 176 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 177 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 178 } else { 179 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 180 } 181 #endif 182 PetscFunctionReturn(0); 183 } 184 185 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 186 { 187 PetscErrorCode ierr; 188 PetscLogDouble flops=0.0; 189 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 190 Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data; 191 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 192 PetscInt *ai =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j; 193 PetscInt am =A->rmap->n,cm=C->rmap->n; 194 PetscInt i,j,k,anzi,bnzi,cnzi,brow; 195 PetscScalar *aa=a->a,*ba=b->a,*baj,*ca,valtmp; 196 PetscScalar *ab_dense; 197 198 PetscFunctionBegin; 199 if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */ 200 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 201 c->a = ca; 202 c->free_a = PETSC_TRUE; 203 } else { 204 ca = c->a; 205 } 206 if (!c->matmult_abdense) { 207 ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr); 208 c->matmult_abdense = ab_dense; 209 } else { 210 ab_dense = c->matmult_abdense; 211 } 212 213 /* clean old values in C */ 214 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 215 /* Traverse A row-wise. */ 216 /* Build the ith row in C by summing over nonzero columns in A, */ 217 /* the rows of B corresponding to nonzeros of A. */ 218 for (i=0; i<am; i++) { 219 anzi = ai[i+1] - ai[i]; 220 for (j=0; j<anzi; j++) { 221 brow = aj[j]; 222 bnzi = bi[brow+1] - bi[brow]; 223 bjj = bj + bi[brow]; 224 baj = ba + bi[brow]; 225 /* perform dense axpy */ 226 valtmp = aa[j]; 227 for (k=0; k<bnzi; k++) { 228 ab_dense[bjj[k]] += valtmp*baj[k]; 229 } 230 flops += 2*bnzi; 231 } 232 aj += anzi; aa += anzi; 233 234 cnzi = ci[i+1] - ci[i]; 235 for (k=0; k<cnzi; k++) { 236 ca[k] += ab_dense[cj[k]]; 237 ab_dense[cj[k]] = 0.0; /* zero ab_dense */ 238 } 239 flops += cnzi; 240 cj += cnzi; ca += cnzi; 241 } 242 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 243 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 244 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 245 PetscFunctionReturn(0); 246 } 247 248 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C) 249 { 250 PetscErrorCode ierr; 251 PetscLogDouble flops=0.0; 252 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 253 Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data; 254 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 255 PetscInt *ai = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j; 256 PetscInt am = A->rmap->N,cm=C->rmap->N; 257 PetscInt i,j,k,anzi,bnzi,cnzi,brow; 258 PetscScalar *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp; 259 PetscInt nextb; 260 261 PetscFunctionBegin; 262 if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */ 263 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 264 c->a = ca; 265 c->free_a = PETSC_TRUE; 266 } 267 268 /* clean old values in C */ 269 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 270 /* Traverse A row-wise. */ 271 /* Build the ith row in C by summing over nonzero columns in A, */ 272 /* the rows of B corresponding to nonzeros of A. */ 273 for (i=0; i<am; i++) { 274 anzi = ai[i+1] - ai[i]; 275 cnzi = ci[i+1] - ci[i]; 276 for (j=0; j<anzi; j++) { 277 brow = aj[j]; 278 bnzi = bi[brow+1] - bi[brow]; 279 bjj = bj + bi[brow]; 280 baj = ba + bi[brow]; 281 /* perform sparse axpy */ 282 valtmp = aa[j]; 283 nextb = 0; 284 for (k=0; nextb<bnzi; k++) { 285 if (cj[k] == bjj[nextb]) { /* ccol == bcol */ 286 ca[k] += valtmp*baj[nextb++]; 287 } 288 } 289 flops += 2*bnzi; 290 } 291 aj += anzi; aa += anzi; 292 cj += cnzi; ca += cnzi; 293 } 294 295 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 296 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 297 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 298 PetscFunctionReturn(0); 299 } 300 301 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C) 302 { 303 PetscErrorCode ierr; 304 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 305 PetscInt *ai = a->i,*bi=b->i,*ci,*cj; 306 PetscInt am = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 307 MatScalar *ca; 308 PetscReal afill; 309 PetscInt i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax; 310 PetscTable ta; 311 PetscFreeSpaceList free_space=NULL,current_space=NULL; 312 313 PetscFunctionBegin; 314 /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */ 315 /*-----------------------------------------------------------------------------------------*/ 316 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 317 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 318 ci[0] = 0; 319 320 /* create and initialize a linked list */ 321 ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr); 322 MatRowMergeMax_SeqAIJ(b,bm,ta); 323 ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); 324 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 325 326 ierr = PetscLLCondensedCreate_fast(Crmax,&lnk);CHKERRQ(ierr); 327 328 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 329 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 330 current_space = free_space; 331 332 /* Determine ci and cj */ 333 for (i=0; i<am; i++) { 334 anzi = ai[i+1] - ai[i]; 335 aj = a->j + ai[i]; 336 for (j=0; j<anzi; j++) { 337 brow = aj[j]; 338 bnzj = bi[brow+1] - bi[brow]; 339 bj = b->j + bi[brow]; 340 /* add non-zero cols of B into the sorted linked list lnk */ 341 ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr); 342 } 343 cnzi = lnk[1]; 344 345 /* If free space is not available, make more free space */ 346 /* Double the amount of total space in the list */ 347 if (current_space->local_remaining<cnzi) { 348 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 349 ndouble++; 350 } 351 352 /* Copy data into free space, then initialize lnk */ 353 ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr); 354 355 current_space->array += cnzi; 356 current_space->local_used += cnzi; 357 current_space->local_remaining -= cnzi; 358 359 ci[i+1] = ci[i] + cnzi; 360 } 361 362 /* Column indices are in the list of free space */ 363 /* Allocate space for cj, initialize cj, and */ 364 /* destroy list of free space and other temporary array(s) */ 365 ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr); 366 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 367 ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr); 368 369 /* Allocate space for ca */ 370 ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr); 371 ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr); 372 373 /* put together the new symbolic matrix */ 374 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr); 375 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 376 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 377 378 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 379 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 380 c = (Mat_SeqAIJ*)((*C)->data); 381 c->free_a = PETSC_TRUE; 382 c->free_ij = PETSC_TRUE; 383 c->nonew = 0; 384 385 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */ 386 387 /* set MatInfo */ 388 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 389 if (afill < 1.0) afill = 1.0; 390 c->maxnz = ci[am]; 391 c->nz = ci[am]; 392 (*C)->info.mallocs = ndouble; 393 (*C)->info.fill_ratio_given = fill; 394 (*C)->info.fill_ratio_needed = afill; 395 396 #if defined(PETSC_USE_INFO) 397 if (ci[am]) { 398 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 399 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 400 } else { 401 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 402 } 403 #endif 404 PetscFunctionReturn(0); 405 } 406 407 408 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C) 409 { 410 PetscErrorCode ierr; 411 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 412 PetscInt *ai = a->i,*bi=b->i,*ci,*cj; 413 PetscInt am = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 414 MatScalar *ca; 415 PetscReal afill; 416 PetscInt i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax; 417 PetscTable ta; 418 PetscFreeSpaceList free_space=NULL,current_space=NULL; 419 420 PetscFunctionBegin; 421 /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */ 422 /*---------------------------------------------------------------------------------------------*/ 423 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 424 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 425 ci[0] = 0; 426 427 /* create and initialize a linked list */ 428 ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr); 429 MatRowMergeMax_SeqAIJ(b,bm,ta); 430 ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); 431 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 432 ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr); 433 434 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 435 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 436 current_space = free_space; 437 438 /* Determine ci and cj */ 439 for (i=0; i<am; i++) { 440 anzi = ai[i+1] - ai[i]; 441 aj = a->j + ai[i]; 442 for (j=0; j<anzi; j++) { 443 brow = aj[j]; 444 bnzj = bi[brow+1] - bi[brow]; 445 bj = b->j + bi[brow]; 446 /* add non-zero cols of B into the sorted linked list lnk */ 447 ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr); 448 } 449 cnzi = lnk[0]; 450 451 /* If free space is not available, make more free space */ 452 /* Double the amount of total space in the list */ 453 if (current_space->local_remaining<cnzi) { 454 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 455 ndouble++; 456 } 457 458 /* Copy data into free space, then initialize lnk */ 459 ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr); 460 461 current_space->array += cnzi; 462 current_space->local_used += cnzi; 463 current_space->local_remaining -= cnzi; 464 465 ci[i+1] = ci[i] + cnzi; 466 } 467 468 /* Column indices are in the list of free space */ 469 /* Allocate space for cj, initialize cj, and */ 470 /* destroy list of free space and other temporary array(s) */ 471 ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr); 472 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 473 ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); 474 475 /* Allocate space for ca */ 476 /*-----------------------*/ 477 ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr); 478 ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr); 479 480 /* put together the new symbolic matrix */ 481 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr); 482 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 483 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 484 485 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 486 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 487 c = (Mat_SeqAIJ*)((*C)->data); 488 c->free_a = PETSC_TRUE; 489 c->free_ij = PETSC_TRUE; 490 c->nonew = 0; 491 492 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */ 493 494 /* set MatInfo */ 495 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 496 if (afill < 1.0) afill = 1.0; 497 c->maxnz = ci[am]; 498 c->nz = ci[am]; 499 (*C)->info.mallocs = ndouble; 500 (*C)->info.fill_ratio_given = fill; 501 (*C)->info.fill_ratio_needed = afill; 502 503 #if defined(PETSC_USE_INFO) 504 if (ci[am]) { 505 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 506 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 507 } else { 508 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 509 } 510 #endif 511 PetscFunctionReturn(0); 512 } 513 514 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C) 515 { 516 PetscErrorCode ierr; 517 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 518 const PetscInt *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j; 519 PetscInt *ci,*cj,*bb; 520 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 521 PetscReal afill; 522 PetscInt i,j,col,ndouble = 0; 523 PetscFreeSpaceList free_space=NULL,current_space=NULL; 524 PetscHeap h; 525 526 PetscFunctionBegin; 527 /* Get ci and cj - by merging sorted rows using a heap */ 528 /*---------------------------------------------------------------------------------------------*/ 529 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 530 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 531 ci[0] = 0; 532 533 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 534 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 535 current_space = free_space; 536 537 ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr); 538 ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr); 539 540 /* Determine ci and cj */ 541 for (i=0; i<am; i++) { 542 const PetscInt anzi = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */ 543 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 544 ci[i+1] = ci[i]; 545 /* Populate the min heap */ 546 for (j=0; j<anzi; j++) { 547 bb[j] = bi[acol[j]]; /* bb points at the start of the row */ 548 if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */ 549 ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr); 550 } 551 } 552 /* Pick off the min element, adding it to free space */ 553 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 554 while (j >= 0) { 555 if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */ 556 ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),¤t_space);CHKERRQ(ierr); 557 ndouble++; 558 } 559 *(current_space->array++) = col; 560 current_space->local_used++; 561 current_space->local_remaining--; 562 ci[i+1]++; 563 564 /* stash if anything else remains in this row of B */ 565 if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);} 566 while (1) { /* pop and stash any other rows of B that also had an entry in this column */ 567 PetscInt j2,col2; 568 ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr); 569 if (col2 != col) break; 570 ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr); 571 if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);} 572 } 573 /* Put any stashed elements back into the min heap */ 574 ierr = PetscHeapUnstash(h);CHKERRQ(ierr); 575 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 576 } 577 } 578 ierr = PetscFree(bb);CHKERRQ(ierr); 579 ierr = PetscHeapDestroy(&h);CHKERRQ(ierr); 580 581 /* Column indices are in the list of free space */ 582 /* Allocate space for cj, initialize cj, and */ 583 /* destroy list of free space and other temporary array(s) */ 584 ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr); 585 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 586 587 /* put together the new symbolic matrix */ 588 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 589 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 590 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 591 592 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 593 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 594 c = (Mat_SeqAIJ*)((*C)->data); 595 c->free_a = PETSC_TRUE; 596 c->free_ij = PETSC_TRUE; 597 c->nonew = 0; 598 599 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; 600 601 /* set MatInfo */ 602 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 603 if (afill < 1.0) afill = 1.0; 604 c->maxnz = ci[am]; 605 c->nz = ci[am]; 606 (*C)->info.mallocs = ndouble; 607 (*C)->info.fill_ratio_given = fill; 608 (*C)->info.fill_ratio_needed = afill; 609 610 #if defined(PETSC_USE_INFO) 611 if (ci[am]) { 612 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 613 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 614 } else { 615 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 616 } 617 #endif 618 PetscFunctionReturn(0); 619 } 620 621 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C) 622 { 623 PetscErrorCode ierr; 624 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 625 const PetscInt *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j; 626 PetscInt *ci,*cj,*bb; 627 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 628 PetscReal afill; 629 PetscInt i,j,col,ndouble = 0; 630 PetscFreeSpaceList free_space=NULL,current_space=NULL; 631 PetscHeap h; 632 PetscBT bt; 633 634 PetscFunctionBegin; 635 /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */ 636 /*---------------------------------------------------------------------------------------------*/ 637 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 638 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 639 ci[0] = 0; 640 641 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 642 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 643 644 current_space = free_space; 645 646 ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr); 647 ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr); 648 ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr); 649 650 /* Determine ci and cj */ 651 for (i=0; i<am; i++) { 652 const PetscInt anzi = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */ 653 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 654 const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */ 655 ci[i+1] = ci[i]; 656 /* Populate the min heap */ 657 for (j=0; j<anzi; j++) { 658 PetscInt brow = acol[j]; 659 for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) { 660 PetscInt bcol = bj[bb[j]]; 661 if (!PetscBTLookupSet(bt,bcol)) { /* new entry */ 662 ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr); 663 bb[j]++; 664 break; 665 } 666 } 667 } 668 /* Pick off the min element, adding it to free space */ 669 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 670 while (j >= 0) { 671 if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */ 672 fptr = NULL; /* need PetscBTMemzero */ 673 ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),¤t_space);CHKERRQ(ierr); 674 ndouble++; 675 } 676 *(current_space->array++) = col; 677 current_space->local_used++; 678 current_space->local_remaining--; 679 ci[i+1]++; 680 681 /* stash if anything else remains in this row of B */ 682 for (; bb[j] < bi[acol[j]+1]; bb[j]++) { 683 PetscInt bcol = bj[bb[j]]; 684 if (!PetscBTLookupSet(bt,bcol)) { /* new entry */ 685 ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr); 686 bb[j]++; 687 break; 688 } 689 } 690 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 691 } 692 if (fptr) { /* Clear the bits for this row */ 693 for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);} 694 } else { /* We reallocated so we don't remember (easily) how to clear only the bits we changed */ 695 ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr); 696 } 697 } 698 ierr = PetscFree(bb);CHKERRQ(ierr); 699 ierr = PetscHeapDestroy(&h);CHKERRQ(ierr); 700 ierr = PetscBTDestroy(&bt);CHKERRQ(ierr); 701 702 /* Column indices are in the list of free space */ 703 /* Allocate space for cj, initialize cj, and */ 704 /* destroy list of free space and other temporary array(s) */ 705 ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr); 706 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 707 708 /* put together the new symbolic matrix */ 709 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 710 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 711 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 712 713 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 714 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 715 c = (Mat_SeqAIJ*)((*C)->data); 716 c->free_a = PETSC_TRUE; 717 c->free_ij = PETSC_TRUE; 718 c->nonew = 0; 719 720 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; 721 722 /* set MatInfo */ 723 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 724 if (afill < 1.0) afill = 1.0; 725 c->maxnz = ci[am]; 726 c->nz = ci[am]; 727 (*C)->info.mallocs = ndouble; 728 (*C)->info.fill_ratio_given = fill; 729 (*C)->info.fill_ratio_needed = afill; 730 731 #if defined(PETSC_USE_INFO) 732 if (ci[am]) { 733 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 734 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 735 } else { 736 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 737 } 738 #endif 739 PetscFunctionReturn(0); 740 } 741 742 743 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A,Mat B,PetscReal fill,Mat *C) 744 { 745 PetscErrorCode ierr; 746 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 747 const PetscInt *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j,*inputi,*inputj,*inputcol,*inputcol_L1; 748 PetscInt *ci,*cj,*outputj,worki_L1[9],worki_L2[9]; 749 PetscInt c_maxmem,a_maxrownnz=0,a_rownnz; 750 const PetscInt workcol[8]={0,1,2,3,4,5,6,7}; 751 const PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 752 const PetscInt *brow_ptr[8],*brow_end[8]; 753 PetscInt window[8]; 754 PetscInt window_min,old_window_min,ci_nnz,outputi_nnz=0,L1_nrows,L2_nrows; 755 PetscInt i,k,ndouble=0,L1_rowsleft,rowsleft; 756 PetscReal afill; 757 PetscInt *workj_L1,*workj_L2,*workj_L3; 758 PetscInt L1_nnz,L2_nnz; 759 760 /* Step 1: Get upper bound on memory required for allocation. 761 Because of the way virtual memory works, 762 only the memory pages that are actually needed will be physically allocated. */ 763 PetscFunctionBegin; 764 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 765 for (i=0; i<am; i++) { 766 const PetscInt anzi = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */ 767 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 768 a_rownnz = 0; 769 for (k=0; k<anzi; ++k) { 770 a_rownnz += bi[acol[k]+1] - bi[acol[k]]; 771 if (a_rownnz > bn) { 772 a_rownnz = bn; 773 break; 774 } 775 } 776 a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz); 777 } 778 /* temporary work areas for merging rows */ 779 ierr = PetscMalloc1(a_maxrownnz*8,&workj_L1);CHKERRQ(ierr); 780 ierr = PetscMalloc1(a_maxrownnz*8,&workj_L2);CHKERRQ(ierr); 781 ierr = PetscMalloc1(a_maxrownnz,&workj_L3);CHKERRQ(ierr); 782 783 /* This should be enough for almost all matrices. If not, memory is reallocated later. */ 784 c_maxmem = 8*(ai[am]+bi[bm]); 785 /* Step 2: Populate pattern for C */ 786 ierr = PetscMalloc1(c_maxmem,&cj);CHKERRQ(ierr); 787 788 ci_nnz = 0; 789 ci[0] = 0; 790 worki_L1[0] = 0; 791 worki_L2[0] = 0; 792 for (i=0; i<am; i++) { 793 const PetscInt anzi = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */ 794 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 795 rowsleft = anzi; 796 inputcol_L1 = acol; 797 L2_nnz = 0; 798 L2_nrows = 1; /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1 */ 799 worki_L2[1] = 0; 800 801 /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem -> allocate more memory */ 802 while (ci_nnz+a_maxrownnz > c_maxmem) { 803 c_maxmem *= 2; 804 ndouble++; 805 ierr = PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);CHKERRQ(ierr); 806 } 807 808 while (rowsleft) { 809 L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */ 810 L1_nrows = 0; 811 L1_nnz = 0; 812 inputcol = inputcol_L1; 813 inputi = bi; 814 inputj = bj; 815 816 /* The following macro is used to specialize for small rows in A. 817 This helps with compiler unrolling, improving performance substantially. 818 Input: inputj inputi inputcol bn 819 Output: outputj outputi_nnz */ 820 #define MatMatMultSymbolic_RowMergeMacro(ANNZ) \ 821 window_min = bn; \ 822 outputi_nnz = 0; \ 823 for (k=0; k<ANNZ; ++k) { \ 824 brow_ptr[k] = inputj + inputi[inputcol[k]]; \ 825 brow_end[k] = inputj + inputi[inputcol[k]+1]; \ 826 window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \ 827 window_min = PetscMin(window[k], window_min); \ 828 } \ 829 while (window_min < bn) { \ 830 outputj[outputi_nnz++] = window_min; \ 831 /* advance front and compute new minimum */ \ 832 old_window_min = window_min; \ 833 window_min = bn; \ 834 for (k=0; k<ANNZ; ++k) { \ 835 if (window[k] == old_window_min) { \ 836 brow_ptr[k]++; \ 837 window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \ 838 } \ 839 window_min = PetscMin(window[k], window_min); \ 840 } \ 841 } 842 843 /************** L E V E L 1 ***************/ 844 /* Merge up to 8 rows of B to L1 work array*/ 845 while (L1_rowsleft) { 846 outputi_nnz = 0; 847 if (anzi > 8) outputj = workj_L1 + L1_nnz; /* Level 1 rowmerge*/ 848 else outputj = cj + ci_nnz; /* Merge directly to C */ 849 850 switch (L1_rowsleft) { 851 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 852 brow_end[0] = inputj + inputi[inputcol[0]+1]; 853 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 854 inputcol += L1_rowsleft; 855 rowsleft -= L1_rowsleft; 856 L1_rowsleft = 0; 857 break; 858 case 2: MatMatMultSymbolic_RowMergeMacro(2); 859 inputcol += L1_rowsleft; 860 rowsleft -= L1_rowsleft; 861 L1_rowsleft = 0; 862 break; 863 case 3: MatMatMultSymbolic_RowMergeMacro(3); 864 inputcol += L1_rowsleft; 865 rowsleft -= L1_rowsleft; 866 L1_rowsleft = 0; 867 break; 868 case 4: MatMatMultSymbolic_RowMergeMacro(4); 869 inputcol += L1_rowsleft; 870 rowsleft -= L1_rowsleft; 871 L1_rowsleft = 0; 872 break; 873 case 5: MatMatMultSymbolic_RowMergeMacro(5); 874 inputcol += L1_rowsleft; 875 rowsleft -= L1_rowsleft; 876 L1_rowsleft = 0; 877 break; 878 case 6: MatMatMultSymbolic_RowMergeMacro(6); 879 inputcol += L1_rowsleft; 880 rowsleft -= L1_rowsleft; 881 L1_rowsleft = 0; 882 break; 883 case 7: MatMatMultSymbolic_RowMergeMacro(7); 884 inputcol += L1_rowsleft; 885 rowsleft -= L1_rowsleft; 886 L1_rowsleft = 0; 887 break; 888 default: MatMatMultSymbolic_RowMergeMacro(8); 889 inputcol += 8; 890 rowsleft -= 8; 891 L1_rowsleft -= 8; 892 break; 893 } 894 inputcol_L1 = inputcol; 895 L1_nnz += outputi_nnz; 896 worki_L1[++L1_nrows] = L1_nnz; 897 } 898 899 /********************** L E V E L 2 ************************/ 900 /* Merge from L1 work array to either C or to L2 work array */ 901 if (anzi > 8) { 902 inputi = worki_L1; 903 inputj = workj_L1; 904 inputcol = workcol; 905 outputi_nnz = 0; 906 907 if (anzi <= 64) outputj = cj + ci_nnz; /* Merge from L1 work array to C */ 908 else outputj = workj_L2 + L2_nnz; /* Merge from L1 work array to L2 work array */ 909 910 switch (L1_nrows) { 911 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 912 brow_end[0] = inputj + inputi[inputcol[0]+1]; 913 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 914 break; 915 case 2: MatMatMultSymbolic_RowMergeMacro(2); break; 916 case 3: MatMatMultSymbolic_RowMergeMacro(3); break; 917 case 4: MatMatMultSymbolic_RowMergeMacro(4); break; 918 case 5: MatMatMultSymbolic_RowMergeMacro(5); break; 919 case 6: MatMatMultSymbolic_RowMergeMacro(6); break; 920 case 7: MatMatMultSymbolic_RowMergeMacro(7); break; 921 case 8: MatMatMultSymbolic_RowMergeMacro(8); break; 922 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L1 work array!"); 923 } 924 L2_nnz += outputi_nnz; 925 worki_L2[++L2_nrows] = L2_nnz; 926 927 /************************ L E V E L 3 **********************/ 928 /* Merge from L2 work array to either C or to L2 work array */ 929 if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) { 930 inputi = worki_L2; 931 inputj = workj_L2; 932 inputcol = workcol; 933 outputi_nnz = 0; 934 if (rowsleft) outputj = workj_L3; 935 else outputj = cj + ci_nnz; 936 switch (L2_nrows) { 937 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 938 brow_end[0] = inputj + inputi[inputcol[0]+1]; 939 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 940 break; 941 case 2: MatMatMultSymbolic_RowMergeMacro(2); break; 942 case 3: MatMatMultSymbolic_RowMergeMacro(3); break; 943 case 4: MatMatMultSymbolic_RowMergeMacro(4); break; 944 case 5: MatMatMultSymbolic_RowMergeMacro(5); break; 945 case 6: MatMatMultSymbolic_RowMergeMacro(6); break; 946 case 7: MatMatMultSymbolic_RowMergeMacro(7); break; 947 case 8: MatMatMultSymbolic_RowMergeMacro(8); break; 948 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L2 work array!"); 949 } 950 L2_nrows = 1; 951 L2_nnz = outputi_nnz; 952 worki_L2[1] = outputi_nnz; 953 /* Copy to workj_L2 */ 954 if (rowsleft) { 955 for (k=0; k<outputi_nnz; ++k) workj_L2[k] = outputj[k]; 956 } 957 } 958 } 959 } /* while (rowsleft) */ 960 #undef MatMatMultSymbolic_RowMergeMacro 961 962 /* terminate current row */ 963 ci_nnz += outputi_nnz; 964 ci[i+1] = ci_nnz; 965 } 966 967 /* Step 3: Create the new symbolic matrix */ 968 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 969 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 970 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 971 972 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 973 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 974 c = (Mat_SeqAIJ*)((*C)->data); 975 c->free_a = PETSC_TRUE; 976 c->free_ij = PETSC_TRUE; 977 c->nonew = 0; 978 979 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; 980 981 /* set MatInfo */ 982 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 983 if (afill < 1.0) afill = 1.0; 984 c->maxnz = ci[am]; 985 c->nz = ci[am]; 986 (*C)->info.mallocs = ndouble; 987 (*C)->info.fill_ratio_given = fill; 988 (*C)->info.fill_ratio_needed = afill; 989 990 #if defined(PETSC_USE_INFO) 991 if (ci[am]) { 992 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 993 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 994 } else { 995 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 996 } 997 #endif 998 999 /* Step 4: Free temporary work areas */ 1000 ierr = PetscFree(workj_L1);CHKERRQ(ierr); 1001 ierr = PetscFree(workj_L2);CHKERRQ(ierr); 1002 ierr = PetscFree(workj_L3);CHKERRQ(ierr); 1003 PetscFunctionReturn(0); 1004 } 1005 1006 /* concatenate unique entries and then sort */ 1007 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1008 { 1009 PetscErrorCode ierr; 1010 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 1011 const PetscInt *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j; 1012 PetscInt *ci,*cj; 1013 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 1014 PetscReal afill; 1015 PetscInt i,j,ndouble = 0; 1016 PetscSegBuffer seg,segrow; 1017 char *seen; 1018 1019 PetscFunctionBegin; 1020 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 1021 ci[0] = 0; 1022 1023 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 1024 ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr); 1025 ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr); 1026 ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr); 1027 ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr); 1028 1029 /* Determine ci and cj */ 1030 for (i=0; i<am; i++) { 1031 const PetscInt anzi = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */ 1032 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 1033 PetscInt packlen = 0,*PETSC_RESTRICT crow; 1034 /* Pack segrow */ 1035 for (j=0; j<anzi; j++) { 1036 PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k; 1037 for (k=bjstart; k<bjend; k++) { 1038 PetscInt bcol = bj[k]; 1039 if (!seen[bcol]) { /* new entry */ 1040 PetscInt *PETSC_RESTRICT slot; 1041 ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr); 1042 *slot = bcol; 1043 seen[bcol] = 1; 1044 packlen++; 1045 } 1046 } 1047 } 1048 ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr); 1049 ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr); 1050 ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr); 1051 ci[i+1] = ci[i] + packlen; 1052 for (j=0; j<packlen; j++) seen[crow[j]] = 0; 1053 } 1054 ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr); 1055 ierr = PetscFree(seen);CHKERRQ(ierr); 1056 1057 /* Column indices are in the segmented buffer */ 1058 ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr); 1059 ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr); 1060 1061 /* put together the new symbolic matrix */ 1062 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 1063 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 1064 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 1065 1066 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 1067 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 1068 c = (Mat_SeqAIJ*)((*C)->data); 1069 c->free_a = PETSC_TRUE; 1070 c->free_ij = PETSC_TRUE; 1071 c->nonew = 0; 1072 1073 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; 1074 1075 /* set MatInfo */ 1076 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 1077 if (afill < 1.0) afill = 1.0; 1078 c->maxnz = ci[am]; 1079 c->nz = ci[am]; 1080 (*C)->info.mallocs = ndouble; 1081 (*C)->info.fill_ratio_given = fill; 1082 (*C)->info.fill_ratio_needed = afill; 1083 1084 #if defined(PETSC_USE_INFO) 1085 if (ci[am]) { 1086 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 1087 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 1088 } else { 1089 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 1090 } 1091 #endif 1092 PetscFunctionReturn(0); 1093 } 1094 1095 /* This routine is not used. Should be removed! */ 1096 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1097 { 1098 PetscErrorCode ierr; 1099 1100 PetscFunctionBegin; 1101 if (scall == MAT_INITIAL_MATRIX) { 1102 ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1103 ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 1104 ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1105 } 1106 ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr); 1107 ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr); 1108 ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr); 1109 PetscFunctionReturn(0); 1110 } 1111 1112 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A) 1113 { 1114 PetscErrorCode ierr; 1115 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1116 Mat_MatMatTransMult *abt=a->abt; 1117 1118 PetscFunctionBegin; 1119 ierr = (abt->destroy)(A);CHKERRQ(ierr); 1120 ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr); 1121 ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr); 1122 ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr); 1123 ierr = PetscFree(abt);CHKERRQ(ierr); 1124 PetscFunctionReturn(0); 1125 } 1126 1127 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1128 { 1129 PetscErrorCode ierr; 1130 Mat Bt; 1131 PetscInt *bti,*btj; 1132 Mat_MatMatTransMult *abt; 1133 Mat_SeqAIJ *c; 1134 1135 PetscFunctionBegin; 1136 /* create symbolic Bt */ 1137 ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr); 1138 ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr); 1139 ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr); 1140 ierr = MatSetType(Bt,((PetscObject)A)->type_name);CHKERRQ(ierr); 1141 1142 /* get symbolic C=A*Bt */ 1143 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr); 1144 1145 /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */ 1146 ierr = PetscNew(&abt);CHKERRQ(ierr); 1147 c = (Mat_SeqAIJ*)(*C)->data; 1148 c->abt = abt; 1149 1150 abt->usecoloring = PETSC_FALSE; 1151 abt->destroy = (*C)->ops->destroy; 1152 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans; 1153 1154 ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr); 1155 if (abt->usecoloring) { 1156 /* Create MatTransposeColoring from symbolic C=A*B^T */ 1157 MatTransposeColoring matcoloring; 1158 MatColoring coloring; 1159 ISColoring iscoloring; 1160 Mat Bt_dense,C_dense; 1161 Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data; 1162 /* inode causes memory problem, don't know why */ 1163 if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'"); 1164 1165 ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr); 1166 ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr); 1167 ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr); 1168 ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr); 1169 ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr); 1170 ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr); 1171 ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr); 1172 1173 abt->matcoloring = matcoloring; 1174 1175 ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr); 1176 1177 /* Create Bt_dense and C_dense = A*Bt_dense */ 1178 ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr); 1179 ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr); 1180 ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr); 1181 ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr); 1182 1183 Bt_dense->assembled = PETSC_TRUE; 1184 abt->Bt_den = Bt_dense; 1185 1186 ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr); 1187 ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr); 1188 ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr); 1189 ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr); 1190 1191 Bt_dense->assembled = PETSC_TRUE; 1192 abt->ABt_den = C_dense; 1193 1194 #if defined(PETSC_USE_INFO) 1195 { 1196 Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data; 1197 ierr = PetscInfo7(*C,"Use coloring of C=A*B^T; B^T: %D %D, Bt_dense: %D,%D; Cnz %D / (cm*ncolors %D) = %g\n",B->cmap->n,B->rmap->n,Bt_dense->rmap->n,Bt_dense->cmap->n,c->nz,A->rmap->n*matcoloring->ncolors,(PetscReal)(c->nz)/(A->rmap->n*matcoloring->ncolors));CHKERRQ(ierr); 1198 } 1199 #endif 1200 } 1201 /* clean up */ 1202 ierr = MatDestroy(&Bt);CHKERRQ(ierr); 1203 ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr); 1204 PetscFunctionReturn(0); 1205 } 1206 1207 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 1208 { 1209 PetscErrorCode ierr; 1210 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data; 1211 PetscInt *ai =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow; 1212 PetscInt cm =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol; 1213 PetscLogDouble flops=0.0; 1214 MatScalar *aa =a->a,*aval,*ba=b->a,*bval,*ca,*cval; 1215 Mat_MatMatTransMult *abt = c->abt; 1216 1217 PetscFunctionBegin; 1218 /* clear old values in C */ 1219 if (!c->a) { 1220 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 1221 c->a = ca; 1222 c->free_a = PETSC_TRUE; 1223 } else { 1224 ca = c->a; 1225 } 1226 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 1227 1228 if (abt->usecoloring) { 1229 MatTransposeColoring matcoloring = abt->matcoloring; 1230 Mat Bt_dense,C_dense = abt->ABt_den; 1231 1232 /* Get Bt_dense by Apply MatTransposeColoring to B */ 1233 Bt_dense = abt->Bt_den; 1234 ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr); 1235 1236 /* C_dense = A*Bt_dense */ 1237 ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr); 1238 1239 /* Recover C from C_dense */ 1240 ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr); 1241 PetscFunctionReturn(0); 1242 } 1243 1244 for (i=0; i<cm; i++) { 1245 anzi = ai[i+1] - ai[i]; 1246 acol = aj + ai[i]; 1247 aval = aa + ai[i]; 1248 cnzi = ci[i+1] - ci[i]; 1249 ccol = cj + ci[i]; 1250 cval = ca + ci[i]; 1251 for (j=0; j<cnzi; j++) { 1252 brow = ccol[j]; 1253 bnzj = bi[brow+1] - bi[brow]; 1254 bcol = bj + bi[brow]; 1255 bval = ba + bi[brow]; 1256 1257 /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */ 1258 nexta = 0; nextb = 0; 1259 while (nexta<anzi && nextb<bnzj) { 1260 while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++; 1261 if (nexta == anzi) break; 1262 while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++; 1263 if (nextb == bnzj) break; 1264 if (acol[nexta] == bcol[nextb]) { 1265 cval[j] += aval[nexta]*bval[nextb]; 1266 nexta++; nextb++; 1267 flops += 2; 1268 } 1269 } 1270 } 1271 } 1272 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1273 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1274 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1275 PetscFunctionReturn(0); 1276 } 1277 1278 PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(Mat A) 1279 { 1280 PetscErrorCode ierr; 1281 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1282 Mat_MatTransMatMult *atb = a->atb; 1283 1284 PetscFunctionBegin; 1285 ierr = MatDestroy(&atb->At);CHKERRQ(ierr); 1286 ierr = (atb->destroy)(A);CHKERRQ(ierr); 1287 ierr = PetscFree(atb);CHKERRQ(ierr); 1288 PetscFunctionReturn(0); 1289 } 1290 1291 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1292 { 1293 PetscErrorCode ierr; 1294 const char *algTypes[2] = {"matmatmult","outerproduct"}; 1295 PetscInt alg=0; /* set default algorithm */ 1296 Mat At; 1297 Mat_MatTransMatMult *atb; 1298 Mat_SeqAIJ *c; 1299 1300 PetscFunctionBegin; 1301 if (scall == MAT_INITIAL_MATRIX) { 1302 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 1303 PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */ 1304 ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,2,algTypes[0],&alg,NULL);CHKERRQ(ierr); 1305 ierr = PetscOptionsEnd();CHKERRQ(ierr); 1306 1307 switch (alg) { 1308 case 1: 1309 ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 1310 break; 1311 default: 1312 ierr = PetscNew(&atb);CHKERRQ(ierr); 1313 ierr = MatTranspose_SeqAIJ(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr); 1314 ierr = MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_INITIAL_MATRIX,fill,C);CHKERRQ(ierr); 1315 1316 c = (Mat_SeqAIJ*)(*C)->data; 1317 c->atb = atb; 1318 atb->At = At; 1319 atb->destroy = (*C)->ops->destroy; 1320 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult; 1321 1322 break; 1323 } 1324 } 1325 if (alg) { 1326 ierr = (*(*C)->ops->mattransposemultnumeric)(A,B,*C);CHKERRQ(ierr); 1327 } else if (!alg && scall == MAT_REUSE_MATRIX) { 1328 c = (Mat_SeqAIJ*)(*C)->data; 1329 atb = c->atb; 1330 At = atb->At; 1331 ierr = MatTranspose_SeqAIJ(A,MAT_REUSE_MATRIX,&At);CHKERRQ(ierr); 1332 ierr = MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_REUSE_MATRIX,fill,C);CHKERRQ(ierr); 1333 } 1334 PetscFunctionReturn(0); 1335 } 1336 1337 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1338 { 1339 PetscErrorCode ierr; 1340 Mat At; 1341 PetscInt *ati,*atj; 1342 1343 PetscFunctionBegin; 1344 /* create symbolic At */ 1345 ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr); 1346 ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr); 1347 ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr); 1348 ierr = MatSetType(At,((PetscObject)A)->type_name);CHKERRQ(ierr); 1349 1350 /* get symbolic C=At*B */ 1351 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr); 1352 1353 /* clean up */ 1354 ierr = MatDestroy(&At);CHKERRQ(ierr); 1355 ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr); 1356 1357 (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; 1358 PetscFunctionReturn(0); 1359 } 1360 1361 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 1362 { 1363 PetscErrorCode ierr; 1364 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data; 1365 PetscInt am =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb; 1366 PetscInt cm =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k; 1367 PetscLogDouble flops=0.0; 1368 MatScalar *aa =a->a,*ba,*ca,*caj; 1369 1370 PetscFunctionBegin; 1371 if (!c->a) { 1372 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 1373 1374 c->a = ca; 1375 c->free_a = PETSC_TRUE; 1376 } else { 1377 ca = c->a; 1378 } 1379 /* clear old values in C */ 1380 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 1381 1382 /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */ 1383 for (i=0; i<am; i++) { 1384 bj = b->j + bi[i]; 1385 ba = b->a + bi[i]; 1386 bnzi = bi[i+1] - bi[i]; 1387 anzi = ai[i+1] - ai[i]; 1388 for (j=0; j<anzi; j++) { 1389 nextb = 0; 1390 crow = *aj++; 1391 cjj = cj + ci[crow]; 1392 caj = ca + ci[crow]; 1393 /* perform sparse axpy operation. Note cjj includes bj. */ 1394 for (k=0; nextb<bnzi; k++) { 1395 if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */ 1396 caj[k] += (*aa)*(*(ba+nextb)); 1397 nextb++; 1398 } 1399 } 1400 flops += 2*bnzi; 1401 aa++; 1402 } 1403 } 1404 1405 /* Assemble the final matrix and clean up */ 1406 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1407 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1408 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1409 PetscFunctionReturn(0); 1410 } 1411 1412 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1413 { 1414 PetscErrorCode ierr; 1415 1416 PetscFunctionBegin; 1417 if (scall == MAT_INITIAL_MATRIX) { 1418 ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1419 ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr); 1420 ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1421 } 1422 ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 1423 ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr); 1424 ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 1425 PetscFunctionReturn(0); 1426 } 1427 1428 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C) 1429 { 1430 PetscErrorCode ierr; 1431 1432 PetscFunctionBegin; 1433 ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr); 1434 1435 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense; 1436 PetscFunctionReturn(0); 1437 } 1438 1439 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C) 1440 { 1441 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1442 Mat_SeqDense *bd = (Mat_SeqDense*)B->data; 1443 PetscErrorCode ierr; 1444 PetscScalar *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp; 1445 const PetscScalar *aa,*b1,*b2,*b3,*b4; 1446 const PetscInt *aj; 1447 PetscInt cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n; 1448 PetscInt am4=4*am,bm4=4*bm,col,i,j,n,ajtmp; 1449 1450 PetscFunctionBegin; 1451 if (!cm || !cn) PetscFunctionReturn(0); 1452 if (B->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,B->rmap->n); 1453 if (A->rmap->n != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in C %D not equal rows in A %D\n",C->rmap->n,A->rmap->n); 1454 if (B->cmap->n != C->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in B %D not equal columns in C %D\n",B->cmap->n,C->cmap->n); 1455 b = bd->v; 1456 ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr); 1457 b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm; 1458 c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am; 1459 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1460 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1461 r1 = r2 = r3 = r4 = 0.0; 1462 n = a->i[i+1] - a->i[i]; 1463 aj = a->j + a->i[i]; 1464 aa = a->a + a->i[i]; 1465 for (j=0; j<n; j++) { 1466 aatmp = aa[j]; ajtmp = aj[j]; 1467 r1 += aatmp*b1[ajtmp]; 1468 r2 += aatmp*b2[ajtmp]; 1469 r3 += aatmp*b3[ajtmp]; 1470 r4 += aatmp*b4[ajtmp]; 1471 } 1472 c1[i] = r1; 1473 c2[i] = r2; 1474 c3[i] = r3; 1475 c4[i] = r4; 1476 } 1477 b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4; 1478 c1 += am4; c2 += am4; c3 += am4; c4 += am4; 1479 } 1480 for (; col<cn; col++) { /* over extra columns of C */ 1481 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1482 r1 = 0.0; 1483 n = a->i[i+1] - a->i[i]; 1484 aj = a->j + a->i[i]; 1485 aa = a->a + a->i[i]; 1486 for (j=0; j<n; j++) { 1487 r1 += aa[j]*b1[aj[j]]; 1488 } 1489 c1[i] = r1; 1490 } 1491 b1 += bm; 1492 c1 += am; 1493 } 1494 ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr); 1495 ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr); 1496 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1497 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1498 PetscFunctionReturn(0); 1499 } 1500 1501 /* 1502 Note very similar to MatMult_SeqAIJ(), should generate both codes from same base 1503 */ 1504 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C) 1505 { 1506 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1507 Mat_SeqDense *bd = (Mat_SeqDense*)B->data; 1508 PetscErrorCode ierr; 1509 PetscScalar *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4; 1510 MatScalar *aa; 1511 PetscInt cm = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm; 1512 PetscInt am2 = 2*am, am3 = 3*am, bm4 = 4*bm,colam,*ridx; 1513 1514 PetscFunctionBegin; 1515 if (!cm || !cn) PetscFunctionReturn(0); 1516 b = bd->v; 1517 ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr); 1518 b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm; 1519 1520 if (a->compressedrow.use) { /* use compressed row format */ 1521 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1522 colam = col*am; 1523 arm = a->compressedrow.nrows; 1524 ii = a->compressedrow.i; 1525 ridx = a->compressedrow.rindex; 1526 for (i=0; i<arm; i++) { /* over rows of C in those columns */ 1527 r1 = r2 = r3 = r4 = 0.0; 1528 n = ii[i+1] - ii[i]; 1529 aj = a->j + ii[i]; 1530 aa = a->a + ii[i]; 1531 for (j=0; j<n; j++) { 1532 r1 += (*aa)*b1[*aj]; 1533 r2 += (*aa)*b2[*aj]; 1534 r3 += (*aa)*b3[*aj]; 1535 r4 += (*aa++)*b4[*aj++]; 1536 } 1537 c[colam + ridx[i]] += r1; 1538 c[colam + am + ridx[i]] += r2; 1539 c[colam + am2 + ridx[i]] += r3; 1540 c[colam + am3 + ridx[i]] += r4; 1541 } 1542 b1 += bm4; 1543 b2 += bm4; 1544 b3 += bm4; 1545 b4 += bm4; 1546 } 1547 for (; col<cn; col++) { /* over extra columns of C */ 1548 colam = col*am; 1549 arm = a->compressedrow.nrows; 1550 ii = a->compressedrow.i; 1551 ridx = a->compressedrow.rindex; 1552 for (i=0; i<arm; i++) { /* over rows of C in those columns */ 1553 r1 = 0.0; 1554 n = ii[i+1] - ii[i]; 1555 aj = a->j + ii[i]; 1556 aa = a->a + ii[i]; 1557 1558 for (j=0; j<n; j++) { 1559 r1 += (*aa++)*b1[*aj++]; 1560 } 1561 c[colam + ridx[i]] += r1; 1562 } 1563 b1 += bm; 1564 } 1565 } else { 1566 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1567 colam = col*am; 1568 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1569 r1 = r2 = r3 = r4 = 0.0; 1570 n = a->i[i+1] - a->i[i]; 1571 aj = a->j + a->i[i]; 1572 aa = a->a + a->i[i]; 1573 for (j=0; j<n; j++) { 1574 r1 += (*aa)*b1[*aj]; 1575 r2 += (*aa)*b2[*aj]; 1576 r3 += (*aa)*b3[*aj]; 1577 r4 += (*aa++)*b4[*aj++]; 1578 } 1579 c[colam + i] += r1; 1580 c[colam + am + i] += r2; 1581 c[colam + am2 + i] += r3; 1582 c[colam + am3 + i] += r4; 1583 } 1584 b1 += bm4; 1585 b2 += bm4; 1586 b3 += bm4; 1587 b4 += bm4; 1588 } 1589 for (; col<cn; col++) { /* over extra columns of C */ 1590 colam = col*am; 1591 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1592 r1 = 0.0; 1593 n = a->i[i+1] - a->i[i]; 1594 aj = a->j + a->i[i]; 1595 aa = a->a + a->i[i]; 1596 1597 for (j=0; j<n; j++) { 1598 r1 += (*aa++)*b1[*aj++]; 1599 } 1600 c[colam + i] += r1; 1601 } 1602 b1 += bm; 1603 } 1604 } 1605 ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr); 1606 ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr); 1607 PetscFunctionReturn(0); 1608 } 1609 1610 PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense) 1611 { 1612 PetscErrorCode ierr; 1613 Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data; 1614 Mat_SeqDense *btdense = (Mat_SeqDense*)Btdense->data; 1615 PetscInt *bi = b->i,*bj=b->j; 1616 PetscInt m = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns; 1617 MatScalar *btval,*btval_den,*ba=b->a; 1618 PetscInt *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors; 1619 1620 PetscFunctionBegin; 1621 btval_den=btdense->v; 1622 ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr); 1623 for (k=0; k<ncolors; k++) { 1624 ncolumns = coloring->ncolumns[k]; 1625 for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */ 1626 col = *(columns + colorforcol[k] + l); 1627 btcol = bj + bi[col]; 1628 btval = ba + bi[col]; 1629 anz = bi[col+1] - bi[col]; 1630 for (j=0; j<anz; j++) { 1631 brow = btcol[j]; 1632 btval_den[brow] = btval[j]; 1633 } 1634 } 1635 btval_den += m; 1636 } 1637 PetscFunctionReturn(0); 1638 } 1639 1640 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp) 1641 { 1642 PetscErrorCode ierr; 1643 Mat_SeqAIJ *csp = (Mat_SeqAIJ*)Csp->data; 1644 PetscScalar *ca_den,*ca_den_ptr,*ca=csp->a; 1645 PetscInt k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors; 1646 PetscInt brows=matcoloring->brows,*den2sp=matcoloring->den2sp; 1647 PetscInt nrows,*row,*idx; 1648 PetscInt *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow; 1649 1650 PetscFunctionBegin; 1651 ierr = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr); 1652 1653 if (brows > 0) { 1654 PetscInt *lstart,row_end,row_start; 1655 lstart = matcoloring->lstart; 1656 ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr); 1657 1658 row_end = brows; 1659 if (row_end > m) row_end = m; 1660 for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */ 1661 ca_den_ptr = ca_den; 1662 for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */ 1663 nrows = matcoloring->nrows[k]; 1664 row = rows + colorforrow[k]; 1665 idx = den2sp + colorforrow[k]; 1666 for (l=lstart[k]; l<nrows; l++) { 1667 if (row[l] >= row_end) { 1668 lstart[k] = l; 1669 break; 1670 } else { 1671 ca[idx[l]] = ca_den_ptr[row[l]]; 1672 } 1673 } 1674 ca_den_ptr += m; 1675 } 1676 row_end += brows; 1677 if (row_end > m) row_end = m; 1678 } 1679 } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */ 1680 ca_den_ptr = ca_den; 1681 for (k=0; k<ncolors; k++) { 1682 nrows = matcoloring->nrows[k]; 1683 row = rows + colorforrow[k]; 1684 idx = den2sp + colorforrow[k]; 1685 for (l=0; l<nrows; l++) { 1686 ca[idx[l]] = ca_den_ptr[row[l]]; 1687 } 1688 ca_den_ptr += m; 1689 } 1690 } 1691 1692 ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr); 1693 #if defined(PETSC_USE_INFO) 1694 if (matcoloring->brows > 0) { 1695 ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr); 1696 } else { 1697 ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr); 1698 } 1699 #endif 1700 PetscFunctionReturn(0); 1701 } 1702 1703 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c) 1704 { 1705 PetscErrorCode ierr; 1706 PetscInt i,n,nrows,Nbs,j,k,m,ncols,col,cm; 1707 const PetscInt *is,*ci,*cj,*row_idx; 1708 PetscInt nis = iscoloring->n,*rowhit,bs = 1; 1709 IS *isa; 1710 Mat_SeqAIJ *csp = (Mat_SeqAIJ*)mat->data; 1711 PetscInt *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i; 1712 PetscInt *colorforcol,*columns,*columns_i,brows; 1713 PetscBool flg; 1714 1715 PetscFunctionBegin; 1716 ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr); 1717 1718 /* bs >1 is not being tested yet! */ 1719 Nbs = mat->cmap->N/bs; 1720 c->M = mat->rmap->N/bs; /* set total rows, columns and local rows */ 1721 c->N = Nbs; 1722 c->m = c->M; 1723 c->rstart = 0; 1724 c->brows = 100; 1725 1726 c->ncolors = nis; 1727 ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr); 1728 ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr); 1729 ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr); 1730 1731 brows = c->brows; 1732 ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr); 1733 if (flg) c->brows = brows; 1734 if (brows > 0) { 1735 ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr); 1736 } 1737 1738 colorforrow[0] = 0; 1739 rows_i = rows; 1740 den2sp_i = den2sp; 1741 1742 ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr); 1743 ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr); 1744 1745 colorforcol[0] = 0; 1746 columns_i = columns; 1747 1748 /* get column-wise storage of mat */ 1749 ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); 1750 1751 cm = c->m; 1752 ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr); 1753 ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr); 1754 for (i=0; i<nis; i++) { /* loop over color */ 1755 ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr); 1756 ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr); 1757 1758 c->ncolumns[i] = n; 1759 if (n) { 1760 ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr); 1761 } 1762 colorforcol[i+1] = colorforcol[i] + n; 1763 columns_i += n; 1764 1765 /* fast, crude version requires O(N*N) work */ 1766 ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr); 1767 1768 for (j=0; j<n; j++) { /* loop over columns*/ 1769 col = is[j]; 1770 row_idx = cj + ci[col]; 1771 m = ci[col+1] - ci[col]; 1772 for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */ 1773 idxhit[*row_idx] = spidx[ci[col] + k]; 1774 rowhit[*row_idx++] = col + 1; 1775 } 1776 } 1777 /* count the number of hits */ 1778 nrows = 0; 1779 for (j=0; j<cm; j++) { 1780 if (rowhit[j]) nrows++; 1781 } 1782 c->nrows[i] = nrows; 1783 colorforrow[i+1] = colorforrow[i] + nrows; 1784 1785 nrows = 0; 1786 for (j=0; j<cm; j++) { /* loop over rows */ 1787 if (rowhit[j]) { 1788 rows_i[nrows] = j; 1789 den2sp_i[nrows] = idxhit[j]; 1790 nrows++; 1791 } 1792 } 1793 den2sp_i += nrows; 1794 1795 ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr); 1796 rows_i += nrows; 1797 } 1798 ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); 1799 ierr = PetscFree(rowhit);CHKERRQ(ierr); 1800 ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr); 1801 if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]); 1802 1803 c->colorforrow = colorforrow; 1804 c->rows = rows; 1805 c->den2sp = den2sp; 1806 c->colorforcol = colorforcol; 1807 c->columns = columns; 1808 1809 ierr = PetscFree(idxhit);CHKERRQ(ierr); 1810 PetscFunctionReturn(0); 1811 } 1812 1813 /* This algorithm combines the symbolic and numeric phase of matrix-matrix multiplication. */ 1814 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ_Combined(Mat A,Mat B,PetscReal fill,Mat *C) 1815 { 1816 PetscErrorCode ierr; 1817 PetscLogDouble flops=0.0; 1818 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 1819 const PetscInt *ai=a->i,*bi=b->i; 1820 PetscInt *ci,*cj,*cj_i; 1821 PetscScalar *ca,*ca_i; 1822 PetscInt b_maxmemrow,c_maxmem,a_col; 1823 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 1824 PetscInt i,k,ndouble=0; 1825 PetscReal afill; 1826 PetscScalar *c_row_val_dense; 1827 PetscBool *c_row_idx_flags; 1828 PetscInt *aj_i=a->j; 1829 PetscScalar *aa_i=a->a; 1830 1831 PetscFunctionBegin; 1832 1833 /* Step 1: Determine upper bounds on memory for C and allocate memory */ 1834 /* This should be enough for almost all matrices. If still more memory is needed, it is reallocated later. */ 1835 c_maxmem = 8*(ai[am]+bi[bm]); 1836 b_maxmemrow = PetscMin(bi[bm],bn); 1837 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 1838 ierr = PetscMalloc1(bn,&c_row_val_dense);CHKERRQ(ierr); 1839 ierr = PetscMalloc1(bn,&c_row_idx_flags);CHKERRQ(ierr); 1840 ierr = PetscMalloc1(c_maxmem,&cj);CHKERRQ(ierr); 1841 ierr = PetscMalloc1(c_maxmem,&ca);CHKERRQ(ierr); 1842 ca_i = ca; 1843 cj_i = cj; 1844 ci[0] = 0; 1845 ierr = PetscMemzero(c_row_val_dense,bn*sizeof(PetscScalar));CHKERRQ(ierr); 1846 ierr = PetscMemzero(c_row_idx_flags,bn*sizeof(PetscBool));CHKERRQ(ierr); 1847 for (i=0; i<am; i++) { 1848 /* Step 2: Initialize the dense row vector for C */ 1849 const PetscInt anzi = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */ 1850 PetscInt cnzi = 0; 1851 PetscInt *bj_i; 1852 PetscScalar *ba_i; 1853 /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem -> allocate more memory 1854 Usually, there is enough memory in the first place, so this is not executed. */ 1855 while (ci[i] + b_maxmemrow > c_maxmem) { 1856 c_maxmem *= 2; 1857 ndouble++; 1858 ierr = PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj); 1859 ierr = PetscRealloc(sizeof(PetscScalar)*c_maxmem,&ca); 1860 } 1861 1862 /* Step 3: Do the numerical calculations */ 1863 for (a_col=0; a_col<anzi; a_col++) { /* iterate over all non zero values in a row of A */ 1864 PetscInt a_col_index = aj_i[a_col]; 1865 const PetscInt bnzi = bi[a_col_index+1] - bi[a_col_index]; 1866 flops += 2*bnzi; 1867 bj_i = b->j + bi[a_col_index]; /* points to the current row in bj */ 1868 ba_i = b->a + bi[a_col_index]; /* points to the current row in ba */ 1869 for (k=0; k<bnzi; ++k) { /* iterate over all non zeros of this row in B */ 1870 if (c_row_idx_flags[bj_i[k]] == PETSC_FALSE) { 1871 cj_i[cnzi++] = bj_i[k]; 1872 c_row_idx_flags[bj_i[k]] = PETSC_TRUE; 1873 } 1874 c_row_val_dense[bj_i[k]] += aa_i[a_col] * ba_i[k]; 1875 } 1876 } 1877 1878 /* Sort array */ 1879 ierr = PetscSortInt(cnzi,cj_i);CHKERRQ(ierr); 1880 /* Step 4 */ 1881 for (k=0; k<cnzi; k++) { 1882 ca_i[k] = c_row_val_dense[cj_i[k]]; 1883 c_row_val_dense[cj_i[k]] = 0.; 1884 c_row_idx_flags[cj_i[k]] = PETSC_FALSE; 1885 } 1886 /* terminate current row */ 1887 aa_i += anzi; 1888 aj_i += anzi; 1889 ca_i += cnzi; 1890 cj_i += cnzi; 1891 ci[i+1] = ci[i] + cnzi; 1892 flops += cnzi; 1893 } 1894 1895 /* Step 5 */ 1896 /* Create the new matrix */ 1897 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 1898 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 1899 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 1900 1901 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 1902 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 1903 c = (Mat_SeqAIJ*)((*C)->data); 1904 c->a = ca; 1905 c->free_a = PETSC_TRUE; 1906 c->free_ij = PETSC_TRUE; 1907 c->nonew = 0; 1908 1909 /* set MatInfo */ 1910 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 1911 if (afill < 1.0) afill = 1.0; 1912 c->maxnz = ci[am]; 1913 c->nz = ci[am]; 1914 (*C)->info.mallocs = ndouble; 1915 (*C)->info.fill_ratio_given = fill; 1916 (*C)->info.fill_ratio_needed = afill; 1917 1918 ierr = PetscFree(c_row_val_dense);CHKERRQ(ierr); 1919 ierr = PetscFree(c_row_idx_flags);CHKERRQ(ierr); 1920 1921 ierr = MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1922 ierr = MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1923 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1924 PetscFunctionReturn(0); 1925 } 1926