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