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 outputi_nnz = 0; 801 802 /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem -> allocate more memory */ 803 while (ci_nnz+a_maxrownnz > c_maxmem) { 804 c_maxmem *= 2; 805 ndouble++; 806 ierr = PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);CHKERRQ(ierr); 807 } 808 809 while (rowsleft) { 810 L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */ 811 L1_nrows = 0; 812 L1_nnz = 0; 813 inputcol = inputcol_L1; 814 inputi = bi; 815 inputj = bj; 816 817 /* The following macro is used to specialize for small rows in A. 818 This helps with compiler unrolling, improving performance substantially. 819 Input: inputj inputi inputcol bn 820 Output: outputj outputi_nnz */ 821 #define MatMatMultSymbolic_RowMergeMacro(ANNZ) \ 822 window_min = bn; \ 823 outputi_nnz = 0; \ 824 for (k=0; k<ANNZ; ++k) { \ 825 brow_ptr[k] = inputj + inputi[inputcol[k]]; \ 826 brow_end[k] = inputj + inputi[inputcol[k]+1]; \ 827 window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \ 828 window_min = PetscMin(window[k], window_min); \ 829 } \ 830 while (window_min < bn) { \ 831 outputj[outputi_nnz++] = window_min; \ 832 /* advance front and compute new minimum */ \ 833 old_window_min = window_min; \ 834 window_min = bn; \ 835 for (k=0; k<ANNZ; ++k) { \ 836 if (window[k] == old_window_min) { \ 837 brow_ptr[k]++; \ 838 window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \ 839 } \ 840 window_min = PetscMin(window[k], window_min); \ 841 } \ 842 } 843 844 /************** L E V E L 1 ***************/ 845 /* Merge up to 8 rows of B to L1 work array*/ 846 while (L1_rowsleft) { 847 outputi_nnz = 0; 848 if (anzi > 8) outputj = workj_L1 + L1_nnz; /* Level 1 rowmerge*/ 849 else outputj = cj + ci_nnz; /* Merge directly to C */ 850 851 switch (L1_rowsleft) { 852 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 853 brow_end[0] = inputj + inputi[inputcol[0]+1]; 854 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 855 inputcol += L1_rowsleft; 856 rowsleft -= L1_rowsleft; 857 L1_rowsleft = 0; 858 break; 859 case 2: MatMatMultSymbolic_RowMergeMacro(2); 860 inputcol += L1_rowsleft; 861 rowsleft -= L1_rowsleft; 862 L1_rowsleft = 0; 863 break; 864 case 3: MatMatMultSymbolic_RowMergeMacro(3); 865 inputcol += L1_rowsleft; 866 rowsleft -= L1_rowsleft; 867 L1_rowsleft = 0; 868 break; 869 case 4: MatMatMultSymbolic_RowMergeMacro(4); 870 inputcol += L1_rowsleft; 871 rowsleft -= L1_rowsleft; 872 L1_rowsleft = 0; 873 break; 874 case 5: MatMatMultSymbolic_RowMergeMacro(5); 875 inputcol += L1_rowsleft; 876 rowsleft -= L1_rowsleft; 877 L1_rowsleft = 0; 878 break; 879 case 6: MatMatMultSymbolic_RowMergeMacro(6); 880 inputcol += L1_rowsleft; 881 rowsleft -= L1_rowsleft; 882 L1_rowsleft = 0; 883 break; 884 case 7: MatMatMultSymbolic_RowMergeMacro(7); 885 inputcol += L1_rowsleft; 886 rowsleft -= L1_rowsleft; 887 L1_rowsleft = 0; 888 break; 889 default: MatMatMultSymbolic_RowMergeMacro(8); 890 inputcol += 8; 891 rowsleft -= 8; 892 L1_rowsleft -= 8; 893 break; 894 } 895 inputcol_L1 = inputcol; 896 L1_nnz += outputi_nnz; 897 worki_L1[++L1_nrows] = L1_nnz; 898 } 899 900 /********************** L E V E L 2 ************************/ 901 /* Merge from L1 work array to either C or to L2 work array */ 902 if (anzi > 8) { 903 inputi = worki_L1; 904 inputj = workj_L1; 905 inputcol = workcol; 906 outputi_nnz = 0; 907 908 if (anzi <= 64) outputj = cj + ci_nnz; /* Merge from L1 work array to C */ 909 else outputj = workj_L2 + L2_nnz; /* Merge from L1 work array to L2 work array */ 910 911 switch (L1_nrows) { 912 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 913 brow_end[0] = inputj + inputi[inputcol[0]+1]; 914 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 915 break; 916 case 2: MatMatMultSymbolic_RowMergeMacro(2); break; 917 case 3: MatMatMultSymbolic_RowMergeMacro(3); break; 918 case 4: MatMatMultSymbolic_RowMergeMacro(4); break; 919 case 5: MatMatMultSymbolic_RowMergeMacro(5); break; 920 case 6: MatMatMultSymbolic_RowMergeMacro(6); break; 921 case 7: MatMatMultSymbolic_RowMergeMacro(7); break; 922 case 8: MatMatMultSymbolic_RowMergeMacro(8); break; 923 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L1 work array!"); 924 } 925 L2_nnz += outputi_nnz; 926 worki_L2[++L2_nrows] = L2_nnz; 927 928 /************************ L E V E L 3 **********************/ 929 /* Merge from L2 work array to either C or to L2 work array */ 930 if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) { 931 inputi = worki_L2; 932 inputj = workj_L2; 933 inputcol = workcol; 934 outputi_nnz = 0; 935 if (rowsleft) outputj = workj_L3; 936 else outputj = cj + ci_nnz; 937 switch (L2_nrows) { 938 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 939 brow_end[0] = inputj + inputi[inputcol[0]+1]; 940 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 941 break; 942 case 2: MatMatMultSymbolic_RowMergeMacro(2); break; 943 case 3: MatMatMultSymbolic_RowMergeMacro(3); break; 944 case 4: MatMatMultSymbolic_RowMergeMacro(4); break; 945 case 5: MatMatMultSymbolic_RowMergeMacro(5); break; 946 case 6: MatMatMultSymbolic_RowMergeMacro(6); break; 947 case 7: MatMatMultSymbolic_RowMergeMacro(7); break; 948 case 8: MatMatMultSymbolic_RowMergeMacro(8); break; 949 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L2 work array!"); 950 } 951 L2_nrows = 1; 952 L2_nnz = outputi_nnz; 953 worki_L2[1] = outputi_nnz; 954 /* Copy to workj_L2 */ 955 if (rowsleft) { 956 for (k=0; k<outputi_nnz; ++k) workj_L2[k] = outputj[k]; 957 } 958 } 959 } 960 } /* while (rowsleft) */ 961 #undef MatMatMultSymbolic_RowMergeMacro 962 963 /* terminate current row */ 964 ci_nnz += outputi_nnz; 965 ci[i+1] = ci_nnz; 966 } 967 968 /* Step 3: Create the new symbolic matrix */ 969 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 970 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 971 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 972 973 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 974 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 975 c = (Mat_SeqAIJ*)((*C)->data); 976 c->free_a = PETSC_TRUE; 977 c->free_ij = PETSC_TRUE; 978 c->nonew = 0; 979 980 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; 981 982 /* set MatInfo */ 983 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 984 if (afill < 1.0) afill = 1.0; 985 c->maxnz = ci[am]; 986 c->nz = ci[am]; 987 (*C)->info.mallocs = ndouble; 988 (*C)->info.fill_ratio_given = fill; 989 (*C)->info.fill_ratio_needed = afill; 990 991 #if defined(PETSC_USE_INFO) 992 if (ci[am]) { 993 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 994 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 995 } else { 996 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 997 } 998 #endif 999 1000 /* Step 4: Free temporary work areas */ 1001 ierr = PetscFree(workj_L1);CHKERRQ(ierr); 1002 ierr = PetscFree(workj_L2);CHKERRQ(ierr); 1003 ierr = PetscFree(workj_L3);CHKERRQ(ierr); 1004 PetscFunctionReturn(0); 1005 } 1006 1007 /* concatenate unique entries and then sort */ 1008 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1009 { 1010 PetscErrorCode ierr; 1011 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 1012 const PetscInt *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j; 1013 PetscInt *ci,*cj; 1014 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 1015 PetscReal afill; 1016 PetscInt i,j,ndouble = 0; 1017 PetscSegBuffer seg,segrow; 1018 char *seen; 1019 1020 PetscFunctionBegin; 1021 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 1022 ci[0] = 0; 1023 1024 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 1025 ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr); 1026 ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr); 1027 ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr); 1028 ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr); 1029 1030 /* Determine ci and cj */ 1031 for (i=0; i<am; i++) { 1032 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 */ 1033 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 1034 PetscInt packlen = 0,*PETSC_RESTRICT crow; 1035 /* Pack segrow */ 1036 for (j=0; j<anzi; j++) { 1037 PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k; 1038 for (k=bjstart; k<bjend; k++) { 1039 PetscInt bcol = bj[k]; 1040 if (!seen[bcol]) { /* new entry */ 1041 PetscInt *PETSC_RESTRICT slot; 1042 ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr); 1043 *slot = bcol; 1044 seen[bcol] = 1; 1045 packlen++; 1046 } 1047 } 1048 } 1049 ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr); 1050 ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr); 1051 ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr); 1052 ci[i+1] = ci[i] + packlen; 1053 for (j=0; j<packlen; j++) seen[crow[j]] = 0; 1054 } 1055 ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr); 1056 ierr = PetscFree(seen);CHKERRQ(ierr); 1057 1058 /* Column indices are in the segmented buffer */ 1059 ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr); 1060 ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr); 1061 1062 /* put together the new symbolic matrix */ 1063 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 1064 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 1065 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 1066 1067 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 1068 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 1069 c = (Mat_SeqAIJ*)((*C)->data); 1070 c->free_a = PETSC_TRUE; 1071 c->free_ij = PETSC_TRUE; 1072 c->nonew = 0; 1073 1074 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; 1075 1076 /* set MatInfo */ 1077 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 1078 if (afill < 1.0) afill = 1.0; 1079 c->maxnz = ci[am]; 1080 c->nz = ci[am]; 1081 (*C)->info.mallocs = ndouble; 1082 (*C)->info.fill_ratio_given = fill; 1083 (*C)->info.fill_ratio_needed = afill; 1084 1085 #if defined(PETSC_USE_INFO) 1086 if (ci[am]) { 1087 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 1088 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 1089 } else { 1090 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 1091 } 1092 #endif 1093 PetscFunctionReturn(0); 1094 } 1095 1096 /* This routine is not used. Should be removed! */ 1097 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1098 { 1099 PetscErrorCode ierr; 1100 1101 PetscFunctionBegin; 1102 if (scall == MAT_INITIAL_MATRIX) { 1103 ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1104 ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 1105 ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1106 } 1107 ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr); 1108 ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr); 1109 ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr); 1110 PetscFunctionReturn(0); 1111 } 1112 1113 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A) 1114 { 1115 PetscErrorCode ierr; 1116 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1117 Mat_MatMatTransMult *abt=a->abt; 1118 1119 PetscFunctionBegin; 1120 ierr = (abt->destroy)(A);CHKERRQ(ierr); 1121 ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr); 1122 ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr); 1123 ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr); 1124 ierr = PetscFree(abt);CHKERRQ(ierr); 1125 PetscFunctionReturn(0); 1126 } 1127 1128 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1129 { 1130 PetscErrorCode ierr; 1131 Mat Bt; 1132 PetscInt *bti,*btj; 1133 Mat_MatMatTransMult *abt; 1134 Mat_SeqAIJ *c; 1135 1136 PetscFunctionBegin; 1137 /* create symbolic Bt */ 1138 ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr); 1139 ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr); 1140 ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr); 1141 ierr = MatSetType(Bt,((PetscObject)A)->type_name);CHKERRQ(ierr); 1142 1143 /* get symbolic C=A*Bt */ 1144 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr); 1145 1146 /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */ 1147 ierr = PetscNew(&abt);CHKERRQ(ierr); 1148 c = (Mat_SeqAIJ*)(*C)->data; 1149 c->abt = abt; 1150 1151 abt->usecoloring = PETSC_FALSE; 1152 abt->destroy = (*C)->ops->destroy; 1153 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans; 1154 1155 ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr); 1156 if (abt->usecoloring) { 1157 /* Create MatTransposeColoring from symbolic C=A*B^T */ 1158 MatTransposeColoring matcoloring; 1159 MatColoring coloring; 1160 ISColoring iscoloring; 1161 Mat Bt_dense,C_dense; 1162 Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data; 1163 /* inode causes memory problem, don't know why */ 1164 if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'"); 1165 1166 ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr); 1167 ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr); 1168 ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr); 1169 ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr); 1170 ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr); 1171 ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr); 1172 ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr); 1173 1174 abt->matcoloring = matcoloring; 1175 1176 ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr); 1177 1178 /* Create Bt_dense and C_dense = A*Bt_dense */ 1179 ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr); 1180 ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr); 1181 ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr); 1182 ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr); 1183 1184 Bt_dense->assembled = PETSC_TRUE; 1185 abt->Bt_den = Bt_dense; 1186 1187 ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr); 1188 ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr); 1189 ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr); 1190 ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr); 1191 1192 Bt_dense->assembled = PETSC_TRUE; 1193 abt->ABt_den = C_dense; 1194 1195 #if defined(PETSC_USE_INFO) 1196 { 1197 Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data; 1198 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); 1199 } 1200 #endif 1201 } 1202 /* clean up */ 1203 ierr = MatDestroy(&Bt);CHKERRQ(ierr); 1204 ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr); 1205 PetscFunctionReturn(0); 1206 } 1207 1208 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 1209 { 1210 PetscErrorCode ierr; 1211 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data; 1212 PetscInt *ai =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow; 1213 PetscInt cm =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol; 1214 PetscLogDouble flops=0.0; 1215 MatScalar *aa =a->a,*aval,*ba=b->a,*bval,*ca,*cval; 1216 Mat_MatMatTransMult *abt = c->abt; 1217 1218 PetscFunctionBegin; 1219 /* clear old values in C */ 1220 if (!c->a) { 1221 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 1222 c->a = ca; 1223 c->free_a = PETSC_TRUE; 1224 } else { 1225 ca = c->a; 1226 } 1227 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 1228 1229 if (abt->usecoloring) { 1230 MatTransposeColoring matcoloring = abt->matcoloring; 1231 Mat Bt_dense,C_dense = abt->ABt_den; 1232 1233 /* Get Bt_dense by Apply MatTransposeColoring to B */ 1234 Bt_dense = abt->Bt_den; 1235 ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr); 1236 1237 /* C_dense = A*Bt_dense */ 1238 ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr); 1239 1240 /* Recover C from C_dense */ 1241 ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr); 1242 PetscFunctionReturn(0); 1243 } 1244 1245 for (i=0; i<cm; i++) { 1246 anzi = ai[i+1] - ai[i]; 1247 acol = aj + ai[i]; 1248 aval = aa + ai[i]; 1249 cnzi = ci[i+1] - ci[i]; 1250 ccol = cj + ci[i]; 1251 cval = ca + ci[i]; 1252 for (j=0; j<cnzi; j++) { 1253 brow = ccol[j]; 1254 bnzj = bi[brow+1] - bi[brow]; 1255 bcol = bj + bi[brow]; 1256 bval = ba + bi[brow]; 1257 1258 /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */ 1259 nexta = 0; nextb = 0; 1260 while (nexta<anzi && nextb<bnzj) { 1261 while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++; 1262 if (nexta == anzi) break; 1263 while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++; 1264 if (nextb == bnzj) break; 1265 if (acol[nexta] == bcol[nextb]) { 1266 cval[j] += aval[nexta]*bval[nextb]; 1267 nexta++; nextb++; 1268 flops += 2; 1269 } 1270 } 1271 } 1272 } 1273 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1274 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1275 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1276 PetscFunctionReturn(0); 1277 } 1278 1279 PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(Mat A) 1280 { 1281 PetscErrorCode ierr; 1282 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1283 Mat_MatTransMatMult *atb = a->atb; 1284 1285 PetscFunctionBegin; 1286 ierr = MatDestroy(&atb->At);CHKERRQ(ierr); 1287 ierr = (atb->destroy)(A);CHKERRQ(ierr); 1288 ierr = PetscFree(atb);CHKERRQ(ierr); 1289 PetscFunctionReturn(0); 1290 } 1291 1292 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1293 { 1294 PetscErrorCode ierr; 1295 const char *algTypes[2] = {"matmatmult","outerproduct"}; 1296 PetscInt alg=0; /* set default algorithm */ 1297 Mat At; 1298 Mat_MatTransMatMult *atb; 1299 Mat_SeqAIJ *c; 1300 1301 PetscFunctionBegin; 1302 if (scall == MAT_INITIAL_MATRIX) { 1303 ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr); 1304 PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */ 1305 ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,2,algTypes[0],&alg,NULL);CHKERRQ(ierr); 1306 ierr = PetscOptionsEnd();CHKERRQ(ierr); 1307 1308 switch (alg) { 1309 case 1: 1310 ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 1311 break; 1312 default: 1313 ierr = PetscNew(&atb);CHKERRQ(ierr); 1314 ierr = MatTranspose_SeqAIJ(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr); 1315 ierr = MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_INITIAL_MATRIX,fill,C);CHKERRQ(ierr); 1316 1317 c = (Mat_SeqAIJ*)(*C)->data; 1318 c->atb = atb; 1319 atb->At = At; 1320 atb->destroy = (*C)->ops->destroy; 1321 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult; 1322 1323 break; 1324 } 1325 } 1326 if (alg) { 1327 ierr = (*(*C)->ops->mattransposemultnumeric)(A,B,*C);CHKERRQ(ierr); 1328 } else if (!alg && scall == MAT_REUSE_MATRIX) { 1329 c = (Mat_SeqAIJ*)(*C)->data; 1330 atb = c->atb; 1331 At = atb->At; 1332 ierr = MatTranspose_SeqAIJ(A,MAT_REUSE_MATRIX,&At);CHKERRQ(ierr); 1333 ierr = MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_REUSE_MATRIX,fill,C);CHKERRQ(ierr); 1334 } 1335 PetscFunctionReturn(0); 1336 } 1337 1338 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1339 { 1340 PetscErrorCode ierr; 1341 Mat At; 1342 PetscInt *ati,*atj; 1343 1344 PetscFunctionBegin; 1345 /* create symbolic At */ 1346 ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr); 1347 ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr); 1348 ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr); 1349 ierr = MatSetType(At,((PetscObject)A)->type_name);CHKERRQ(ierr); 1350 1351 /* get symbolic C=At*B */ 1352 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr); 1353 1354 /* clean up */ 1355 ierr = MatDestroy(&At);CHKERRQ(ierr); 1356 ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr); 1357 1358 (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; 1359 PetscFunctionReturn(0); 1360 } 1361 1362 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 1363 { 1364 PetscErrorCode ierr; 1365 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data; 1366 PetscInt am =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb; 1367 PetscInt cm =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k; 1368 PetscLogDouble flops=0.0; 1369 MatScalar *aa =a->a,*ba,*ca,*caj; 1370 1371 PetscFunctionBegin; 1372 if (!c->a) { 1373 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 1374 1375 c->a = ca; 1376 c->free_a = PETSC_TRUE; 1377 } else { 1378 ca = c->a; 1379 } 1380 /* clear old values in C */ 1381 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 1382 1383 /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */ 1384 for (i=0; i<am; i++) { 1385 bj = b->j + bi[i]; 1386 ba = b->a + bi[i]; 1387 bnzi = bi[i+1] - bi[i]; 1388 anzi = ai[i+1] - ai[i]; 1389 for (j=0; j<anzi; j++) { 1390 nextb = 0; 1391 crow = *aj++; 1392 cjj = cj + ci[crow]; 1393 caj = ca + ci[crow]; 1394 /* perform sparse axpy operation. Note cjj includes bj. */ 1395 for (k=0; nextb<bnzi; k++) { 1396 if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */ 1397 caj[k] += (*aa)*(*(ba+nextb)); 1398 nextb++; 1399 } 1400 } 1401 flops += 2*bnzi; 1402 aa++; 1403 } 1404 } 1405 1406 /* Assemble the final matrix and clean up */ 1407 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1408 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1409 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1410 PetscFunctionReturn(0); 1411 } 1412 1413 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1414 { 1415 PetscErrorCode ierr; 1416 1417 PetscFunctionBegin; 1418 if (scall == MAT_INITIAL_MATRIX) { 1419 ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1420 ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr); 1421 ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1422 } 1423 ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 1424 ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr); 1425 ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 1426 PetscFunctionReturn(0); 1427 } 1428 1429 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C) 1430 { 1431 PetscErrorCode ierr; 1432 1433 PetscFunctionBegin; 1434 ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr); 1435 1436 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense; 1437 PetscFunctionReturn(0); 1438 } 1439 1440 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C) 1441 { 1442 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1443 Mat_SeqDense *bd = (Mat_SeqDense*)B->data; 1444 PetscErrorCode ierr; 1445 PetscScalar *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp; 1446 const PetscScalar *aa,*b1,*b2,*b3,*b4; 1447 const PetscInt *aj; 1448 PetscInt cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n; 1449 PetscInt am4=4*am,bm4=4*bm,col,i,j,n,ajtmp; 1450 1451 PetscFunctionBegin; 1452 if (!cm || !cn) PetscFunctionReturn(0); 1453 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); 1454 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); 1455 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); 1456 b = bd->v; 1457 ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr); 1458 b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm; 1459 c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am; 1460 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1461 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1462 r1 = r2 = r3 = r4 = 0.0; 1463 n = a->i[i+1] - a->i[i]; 1464 aj = a->j + a->i[i]; 1465 aa = a->a + a->i[i]; 1466 for (j=0; j<n; j++) { 1467 aatmp = aa[j]; ajtmp = aj[j]; 1468 r1 += aatmp*b1[ajtmp]; 1469 r2 += aatmp*b2[ajtmp]; 1470 r3 += aatmp*b3[ajtmp]; 1471 r4 += aatmp*b4[ajtmp]; 1472 } 1473 c1[i] = r1; 1474 c2[i] = r2; 1475 c3[i] = r3; 1476 c4[i] = r4; 1477 } 1478 b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4; 1479 c1 += am4; c2 += am4; c3 += am4; c4 += am4; 1480 } 1481 for (; col<cn; col++) { /* over extra columns of C */ 1482 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1483 r1 = 0.0; 1484 n = a->i[i+1] - a->i[i]; 1485 aj = a->j + a->i[i]; 1486 aa = a->a + a->i[i]; 1487 for (j=0; j<n; j++) { 1488 r1 += aa[j]*b1[aj[j]]; 1489 } 1490 c1[i] = r1; 1491 } 1492 b1 += bm; 1493 c1 += am; 1494 } 1495 ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr); 1496 ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr); 1497 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1498 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1499 PetscFunctionReturn(0); 1500 } 1501 1502 /* 1503 Note very similar to MatMult_SeqAIJ(), should generate both codes from same base 1504 */ 1505 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C) 1506 { 1507 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1508 Mat_SeqDense *bd = (Mat_SeqDense*)B->data; 1509 PetscErrorCode ierr; 1510 PetscScalar *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4; 1511 MatScalar *aa; 1512 PetscInt cm = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm; 1513 PetscInt am2 = 2*am, am3 = 3*am, bm4 = 4*bm,colam,*ridx; 1514 1515 PetscFunctionBegin; 1516 if (!cm || !cn) PetscFunctionReturn(0); 1517 b = bd->v; 1518 ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr); 1519 b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm; 1520 1521 if (a->compressedrow.use) { /* use compressed row format */ 1522 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1523 colam = col*am; 1524 arm = a->compressedrow.nrows; 1525 ii = a->compressedrow.i; 1526 ridx = a->compressedrow.rindex; 1527 for (i=0; i<arm; i++) { /* over rows of C in those columns */ 1528 r1 = r2 = r3 = r4 = 0.0; 1529 n = ii[i+1] - ii[i]; 1530 aj = a->j + ii[i]; 1531 aa = a->a + ii[i]; 1532 for (j=0; j<n; j++) { 1533 r1 += (*aa)*b1[*aj]; 1534 r2 += (*aa)*b2[*aj]; 1535 r3 += (*aa)*b3[*aj]; 1536 r4 += (*aa++)*b4[*aj++]; 1537 } 1538 c[colam + ridx[i]] += r1; 1539 c[colam + am + ridx[i]] += r2; 1540 c[colam + am2 + ridx[i]] += r3; 1541 c[colam + am3 + ridx[i]] += r4; 1542 } 1543 b1 += bm4; 1544 b2 += bm4; 1545 b3 += bm4; 1546 b4 += bm4; 1547 } 1548 for (; col<cn; col++) { /* over extra columns of C */ 1549 colam = col*am; 1550 arm = a->compressedrow.nrows; 1551 ii = a->compressedrow.i; 1552 ridx = a->compressedrow.rindex; 1553 for (i=0; i<arm; i++) { /* over rows of C in those columns */ 1554 r1 = 0.0; 1555 n = ii[i+1] - ii[i]; 1556 aj = a->j + ii[i]; 1557 aa = a->a + ii[i]; 1558 1559 for (j=0; j<n; j++) { 1560 r1 += (*aa++)*b1[*aj++]; 1561 } 1562 c[colam + ridx[i]] += r1; 1563 } 1564 b1 += bm; 1565 } 1566 } else { 1567 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1568 colam = col*am; 1569 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1570 r1 = r2 = r3 = r4 = 0.0; 1571 n = a->i[i+1] - a->i[i]; 1572 aj = a->j + a->i[i]; 1573 aa = a->a + a->i[i]; 1574 for (j=0; j<n; j++) { 1575 r1 += (*aa)*b1[*aj]; 1576 r2 += (*aa)*b2[*aj]; 1577 r3 += (*aa)*b3[*aj]; 1578 r4 += (*aa++)*b4[*aj++]; 1579 } 1580 c[colam + i] += r1; 1581 c[colam + am + i] += r2; 1582 c[colam + am2 + i] += r3; 1583 c[colam + am3 + i] += r4; 1584 } 1585 b1 += bm4; 1586 b2 += bm4; 1587 b3 += bm4; 1588 b4 += bm4; 1589 } 1590 for (; col<cn; col++) { /* over extra columns of C */ 1591 colam = col*am; 1592 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1593 r1 = 0.0; 1594 n = a->i[i+1] - a->i[i]; 1595 aj = a->j + a->i[i]; 1596 aa = a->a + a->i[i]; 1597 1598 for (j=0; j<n; j++) { 1599 r1 += (*aa++)*b1[*aj++]; 1600 } 1601 c[colam + i] += r1; 1602 } 1603 b1 += bm; 1604 } 1605 } 1606 ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr); 1607 ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr); 1608 PetscFunctionReturn(0); 1609 } 1610 1611 PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense) 1612 { 1613 PetscErrorCode ierr; 1614 Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data; 1615 Mat_SeqDense *btdense = (Mat_SeqDense*)Btdense->data; 1616 PetscInt *bi = b->i,*bj=b->j; 1617 PetscInt m = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns; 1618 MatScalar *btval,*btval_den,*ba=b->a; 1619 PetscInt *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors; 1620 1621 PetscFunctionBegin; 1622 btval_den=btdense->v; 1623 ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr); 1624 for (k=0; k<ncolors; k++) { 1625 ncolumns = coloring->ncolumns[k]; 1626 for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */ 1627 col = *(columns + colorforcol[k] + l); 1628 btcol = bj + bi[col]; 1629 btval = ba + bi[col]; 1630 anz = bi[col+1] - bi[col]; 1631 for (j=0; j<anz; j++) { 1632 brow = btcol[j]; 1633 btval_den[brow] = btval[j]; 1634 } 1635 } 1636 btval_den += m; 1637 } 1638 PetscFunctionReturn(0); 1639 } 1640 1641 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp) 1642 { 1643 PetscErrorCode ierr; 1644 Mat_SeqAIJ *csp = (Mat_SeqAIJ*)Csp->data; 1645 PetscScalar *ca_den,*ca_den_ptr,*ca=csp->a; 1646 PetscInt k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors; 1647 PetscInt brows=matcoloring->brows,*den2sp=matcoloring->den2sp; 1648 PetscInt nrows,*row,*idx; 1649 PetscInt *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow; 1650 1651 PetscFunctionBegin; 1652 ierr = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr); 1653 1654 if (brows > 0) { 1655 PetscInt *lstart,row_end,row_start; 1656 lstart = matcoloring->lstart; 1657 ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr); 1658 1659 row_end = brows; 1660 if (row_end > m) row_end = m; 1661 for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */ 1662 ca_den_ptr = ca_den; 1663 for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */ 1664 nrows = matcoloring->nrows[k]; 1665 row = rows + colorforrow[k]; 1666 idx = den2sp + colorforrow[k]; 1667 for (l=lstart[k]; l<nrows; l++) { 1668 if (row[l] >= row_end) { 1669 lstart[k] = l; 1670 break; 1671 } else { 1672 ca[idx[l]] = ca_den_ptr[row[l]]; 1673 } 1674 } 1675 ca_den_ptr += m; 1676 } 1677 row_end += brows; 1678 if (row_end > m) row_end = m; 1679 } 1680 } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */ 1681 ca_den_ptr = ca_den; 1682 for (k=0; k<ncolors; k++) { 1683 nrows = matcoloring->nrows[k]; 1684 row = rows + colorforrow[k]; 1685 idx = den2sp + colorforrow[k]; 1686 for (l=0; l<nrows; l++) { 1687 ca[idx[l]] = ca_den_ptr[row[l]]; 1688 } 1689 ca_den_ptr += m; 1690 } 1691 } 1692 1693 ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr); 1694 #if defined(PETSC_USE_INFO) 1695 if (matcoloring->brows > 0) { 1696 ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr); 1697 } else { 1698 ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr); 1699 } 1700 #endif 1701 PetscFunctionReturn(0); 1702 } 1703 1704 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c) 1705 { 1706 PetscErrorCode ierr; 1707 PetscInt i,n,nrows,Nbs,j,k,m,ncols,col,cm; 1708 const PetscInt *is,*ci,*cj,*row_idx; 1709 PetscInt nis = iscoloring->n,*rowhit,bs = 1; 1710 IS *isa; 1711 Mat_SeqAIJ *csp = (Mat_SeqAIJ*)mat->data; 1712 PetscInt *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i; 1713 PetscInt *colorforcol,*columns,*columns_i,brows; 1714 PetscBool flg; 1715 1716 PetscFunctionBegin; 1717 ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr); 1718 1719 /* bs >1 is not being tested yet! */ 1720 Nbs = mat->cmap->N/bs; 1721 c->M = mat->rmap->N/bs; /* set total rows, columns and local rows */ 1722 c->N = Nbs; 1723 c->m = c->M; 1724 c->rstart = 0; 1725 c->brows = 100; 1726 1727 c->ncolors = nis; 1728 ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr); 1729 ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr); 1730 ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr); 1731 1732 brows = c->brows; 1733 ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr); 1734 if (flg) c->brows = brows; 1735 if (brows > 0) { 1736 ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr); 1737 } 1738 1739 colorforrow[0] = 0; 1740 rows_i = rows; 1741 den2sp_i = den2sp; 1742 1743 ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr); 1744 ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr); 1745 1746 colorforcol[0] = 0; 1747 columns_i = columns; 1748 1749 /* get column-wise storage of mat */ 1750 ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); 1751 1752 cm = c->m; 1753 ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr); 1754 ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr); 1755 for (i=0; i<nis; i++) { /* loop over color */ 1756 ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr); 1757 ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr); 1758 1759 c->ncolumns[i] = n; 1760 if (n) { 1761 ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr); 1762 } 1763 colorforcol[i+1] = colorforcol[i] + n; 1764 columns_i += n; 1765 1766 /* fast, crude version requires O(N*N) work */ 1767 ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr); 1768 1769 for (j=0; j<n; j++) { /* loop over columns*/ 1770 col = is[j]; 1771 row_idx = cj + ci[col]; 1772 m = ci[col+1] - ci[col]; 1773 for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */ 1774 idxhit[*row_idx] = spidx[ci[col] + k]; 1775 rowhit[*row_idx++] = col + 1; 1776 } 1777 } 1778 /* count the number of hits */ 1779 nrows = 0; 1780 for (j=0; j<cm; j++) { 1781 if (rowhit[j]) nrows++; 1782 } 1783 c->nrows[i] = nrows; 1784 colorforrow[i+1] = colorforrow[i] + nrows; 1785 1786 nrows = 0; 1787 for (j=0; j<cm; j++) { /* loop over rows */ 1788 if (rowhit[j]) { 1789 rows_i[nrows] = j; 1790 den2sp_i[nrows] = idxhit[j]; 1791 nrows++; 1792 } 1793 } 1794 den2sp_i += nrows; 1795 1796 ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr); 1797 rows_i += nrows; 1798 } 1799 ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); 1800 ierr = PetscFree(rowhit);CHKERRQ(ierr); 1801 ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr); 1802 if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]); 1803 1804 c->colorforrow = colorforrow; 1805 c->rows = rows; 1806 c->den2sp = den2sp; 1807 c->colorforcol = colorforcol; 1808 c->columns = columns; 1809 1810 ierr = PetscFree(idxhit);CHKERRQ(ierr); 1811 PetscFunctionReturn(0); 1812 } 1813 1814 /* This algorithm combines the symbolic and numeric phase of matrix-matrix multiplication. */ 1815 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ_Combined(Mat A,Mat B,PetscReal fill,Mat *C) 1816 { 1817 PetscErrorCode ierr; 1818 PetscLogDouble flops=0.0; 1819 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 1820 const PetscInt *ai=a->i,*bi=b->i; 1821 PetscInt *ci,*cj,*cj_i; 1822 PetscScalar *ca,*ca_i; 1823 PetscInt b_maxmemrow,c_maxmem,a_col; 1824 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 1825 PetscInt i,k,ndouble=0; 1826 PetscReal afill; 1827 PetscScalar *c_row_val_dense; 1828 PetscBool *c_row_idx_flags; 1829 PetscInt *aj_i=a->j; 1830 PetscScalar *aa_i=a->a; 1831 1832 PetscFunctionBegin; 1833 1834 /* Step 1: Determine upper bounds on memory for C and allocate memory */ 1835 /* This should be enough for almost all matrices. If still more memory is needed, it is reallocated later. */ 1836 c_maxmem = 8*(ai[am]+bi[bm]); 1837 b_maxmemrow = PetscMin(bi[bm],bn); 1838 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 1839 ierr = PetscMalloc1(bn,&c_row_val_dense);CHKERRQ(ierr); 1840 ierr = PetscMalloc1(bn,&c_row_idx_flags);CHKERRQ(ierr); 1841 ierr = PetscMalloc1(c_maxmem,&cj);CHKERRQ(ierr); 1842 ierr = PetscMalloc1(c_maxmem,&ca);CHKERRQ(ierr); 1843 ca_i = ca; 1844 cj_i = cj; 1845 ci[0] = 0; 1846 ierr = PetscMemzero(c_row_val_dense,bn*sizeof(PetscScalar));CHKERRQ(ierr); 1847 ierr = PetscMemzero(c_row_idx_flags,bn*sizeof(PetscBool));CHKERRQ(ierr); 1848 for (i=0; i<am; i++) { 1849 /* Step 2: Initialize the dense row vector for C */ 1850 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 */ 1851 PetscInt cnzi = 0; 1852 PetscInt *bj_i; 1853 PetscScalar *ba_i; 1854 /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem -> allocate more memory 1855 Usually, there is enough memory in the first place, so this is not executed. */ 1856 while (ci[i] + b_maxmemrow > c_maxmem) { 1857 c_maxmem *= 2; 1858 ndouble++; 1859 ierr = PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);CHKERRQ(ierr); 1860 ierr = PetscRealloc(sizeof(PetscScalar)*c_maxmem,&ca);CHKERRQ(ierr); 1861 } 1862 1863 /* Step 3: Do the numerical calculations */ 1864 for (a_col=0; a_col<anzi; a_col++) { /* iterate over all non zero values in a row of A */ 1865 PetscInt a_col_index = aj_i[a_col]; 1866 const PetscInt bnzi = bi[a_col_index+1] - bi[a_col_index]; 1867 flops += 2*bnzi; 1868 bj_i = b->j + bi[a_col_index]; /* points to the current row in bj */ 1869 ba_i = b->a + bi[a_col_index]; /* points to the current row in ba */ 1870 for (k=0; k<bnzi; ++k) { /* iterate over all non zeros of this row in B */ 1871 if (c_row_idx_flags[bj_i[k]] == PETSC_FALSE) { 1872 cj_i[cnzi++] = bj_i[k]; 1873 c_row_idx_flags[bj_i[k]] = PETSC_TRUE; 1874 } 1875 c_row_val_dense[bj_i[k]] += aa_i[a_col] * ba_i[k]; 1876 } 1877 } 1878 1879 /* Sort array */ 1880 ierr = PetscSortInt(cnzi,cj_i);CHKERRQ(ierr); 1881 /* Step 4 */ 1882 for (k=0; k<cnzi; k++) { 1883 ca_i[k] = c_row_val_dense[cj_i[k]]; 1884 c_row_val_dense[cj_i[k]] = 0.; 1885 c_row_idx_flags[cj_i[k]] = PETSC_FALSE; 1886 } 1887 /* terminate current row */ 1888 aa_i += anzi; 1889 aj_i += anzi; 1890 ca_i += cnzi; 1891 cj_i += cnzi; 1892 ci[i+1] = ci[i] + cnzi; 1893 flops += cnzi; 1894 } 1895 1896 /* Step 5 */ 1897 /* Create the new matrix */ 1898 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 1899 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 1900 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 1901 1902 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 1903 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 1904 c = (Mat_SeqAIJ*)((*C)->data); 1905 c->a = ca; 1906 c->free_a = PETSC_TRUE; 1907 c->free_ij = PETSC_TRUE; 1908 c->nonew = 0; 1909 1910 /* set MatInfo */ 1911 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 1912 if (afill < 1.0) afill = 1.0; 1913 c->maxnz = ci[am]; 1914 c->nz = ci[am]; 1915 (*C)->info.mallocs = ndouble; 1916 (*C)->info.fill_ratio_given = fill; 1917 (*C)->info.fill_ratio_needed = afill; 1918 1919 ierr = PetscFree(c_row_val_dense);CHKERRQ(ierr); 1920 ierr = PetscFree(c_row_idx_flags);CHKERRQ(ierr); 1921 1922 ierr = MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1923 ierr = MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1924 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1925 PetscFunctionReturn(0); 1926 } 1927