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 14 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 15 { 16 PetscErrorCode ierr; 17 18 PetscFunctionBegin; 19 if (scall == MAT_INITIAL_MATRIX) { 20 ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 21 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 22 ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 23 } 24 25 ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 26 ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr); 27 ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 28 PetscFunctionReturn(0); 29 } 30 31 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 32 { 33 PetscErrorCode ierr; 34 35 PetscFunctionBegin; 36 if (C->ops->matmultnumeric) { 37 ierr = (*C->ops->matmultnumeric)(A,B,C);CHKERRQ(ierr); 38 } else { 39 ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(A,B,C);CHKERRQ(ierr); 40 } 41 PetscFunctionReturn(0); 42 } 43 44 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 45 { 46 PetscErrorCode ierr; 47 #if !defined(PETSC_HAVE_HYPRE) 48 const char *algTypes[8] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined","rowmerge"}; 49 PetscInt nalg = 8; 50 #else 51 const char *algTypes[9] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","combined","rowmerge","hypre"}; 52 PetscInt nalg = 9; 53 #endif 54 PetscInt alg = 0; /* set default algorithm */ 55 56 PetscFunctionBegin; 57 ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatMatMult","Mat");CHKERRQ(ierr); 58 ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[0],&alg,NULL);CHKERRQ(ierr); 59 ierr = PetscOptionsEnd();CHKERRQ(ierr); 60 switch (alg) { 61 case 1: 62 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr); 63 break; 64 case 2: 65 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr); 66 break; 67 case 3: 68 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr); 69 break; 70 case 4: 71 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr); 72 break; 73 case 5: 74 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr); 75 break; 76 case 6: 77 ierr = MatMatMult_SeqAIJ_SeqAIJ_Combined(A,B,fill,C);CHKERRQ(ierr); 78 break; 79 case 7: 80 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(A,B,fill,C);CHKERRQ(ierr); 81 break; 82 #if defined(PETSC_HAVE_HYPRE) 83 case 8: 84 ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr); 85 break; 86 #endif 87 default: 88 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(A,B,fill,C);CHKERRQ(ierr); 89 break; 90 } 91 PetscFunctionReturn(0); 92 } 93 94 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C) 95 { 96 PetscErrorCode ierr; 97 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 98 PetscInt *ai=a->i,*bi=b->i,*ci,*cj; 99 PetscInt am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 100 PetscReal afill; 101 PetscInt i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax; 102 PetscTable ta; 103 PetscBT lnkbt; 104 PetscFreeSpaceList free_space=NULL,current_space=NULL; 105 106 PetscFunctionBegin; 107 /* Get ci and cj */ 108 /*---------------*/ 109 /* Allocate ci array, arrays for fill computation and */ 110 /* free space for accumulating nonzero column info */ 111 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 112 ci[0] = 0; 113 114 /* create and initialize a linked list */ 115 ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr); 116 MatRowMergeMax_SeqAIJ(b,bm,ta); 117 ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); 118 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 119 120 ierr = PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);CHKERRQ(ierr); 121 122 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 123 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 124 125 current_space = free_space; 126 127 /* Determine ci and cj */ 128 for (i=0; i<am; i++) { 129 anzi = ai[i+1] - ai[i]; 130 aj = a->j + ai[i]; 131 for (j=0; j<anzi; j++) { 132 brow = aj[j]; 133 bnzj = bi[brow+1] - bi[brow]; 134 bj = b->j + bi[brow]; 135 /* add non-zero cols of B into the sorted linked list lnk */ 136 ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr); 137 } 138 cnzi = lnk[0]; 139 140 /* If free space is not available, make more free space */ 141 /* Double the amount of total space in the list */ 142 if (current_space->local_remaining<cnzi) { 143 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 144 ndouble++; 145 } 146 147 /* Copy data into free space, then initialize lnk */ 148 ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr); 149 150 current_space->array += cnzi; 151 current_space->local_used += cnzi; 152 current_space->local_remaining -= cnzi; 153 154 ci[i+1] = ci[i] + cnzi; 155 } 156 157 /* Column indices are in the list of free space */ 158 /* Allocate space for cj, initialize cj, and */ 159 /* destroy list of free space and other temporary array(s) */ 160 ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr); 161 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 162 ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr); 163 164 /* put together the new symbolic matrix */ 165 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 166 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 167 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 168 169 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 170 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 171 c = (Mat_SeqAIJ*)((*C)->data); 172 c->free_a = PETSC_FALSE; 173 c->free_ij = PETSC_TRUE; 174 c->nonew = 0; 175 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted; /* fast, needs non-scalable O(bn) array 'abdense' */ 176 177 /* set MatInfo */ 178 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 179 if (afill < 1.0) afill = 1.0; 180 c->maxnz = ci[am]; 181 c->nz = ci[am]; 182 (*C)->info.mallocs = ndouble; 183 (*C)->info.fill_ratio_given = fill; 184 (*C)->info.fill_ratio_needed = afill; 185 186 #if defined(PETSC_USE_INFO) 187 if (ci[am]) { 188 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 189 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 190 } else { 191 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 192 } 193 #endif 194 PetscFunctionReturn(0); 195 } 196 197 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat A,Mat B,Mat C) 198 { 199 PetscErrorCode ierr; 200 PetscLogDouble flops=0.0; 201 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 202 Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data; 203 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 204 PetscInt *ai =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j; 205 PetscInt am =A->rmap->n,cm=C->rmap->n; 206 PetscInt i,j,k,anzi,bnzi,cnzi,brow; 207 PetscScalar *aa=a->a,*ba=b->a,*baj,*ca,valtmp; 208 PetscScalar *ab_dense; 209 210 PetscFunctionBegin; 211 if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */ 212 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 213 c->a = ca; 214 c->free_a = PETSC_TRUE; 215 } else { 216 ca = c->a; 217 } 218 if (!c->matmult_abdense) { 219 ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr); 220 c->matmult_abdense = ab_dense; 221 } else { 222 ab_dense = c->matmult_abdense; 223 } 224 225 /* clean old values in C */ 226 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 227 /* Traverse A row-wise. */ 228 /* Build the ith row in C by summing over nonzero columns in A, */ 229 /* the rows of B corresponding to nonzeros of A. */ 230 for (i=0; i<am; i++) { 231 anzi = ai[i+1] - ai[i]; 232 for (j=0; j<anzi; j++) { 233 brow = aj[j]; 234 bnzi = bi[brow+1] - bi[brow]; 235 bjj = bj + bi[brow]; 236 baj = ba + bi[brow]; 237 /* perform dense axpy */ 238 valtmp = aa[j]; 239 for (k=0; k<bnzi; k++) { 240 ab_dense[bjj[k]] += valtmp*baj[k]; 241 } 242 flops += 2*bnzi; 243 } 244 aj += anzi; aa += anzi; 245 246 cnzi = ci[i+1] - ci[i]; 247 for (k=0; k<cnzi; k++) { 248 ca[k] += ab_dense[cj[k]]; 249 ab_dense[cj[k]] = 0.0; /* zero ab_dense */ 250 } 251 flops += cnzi; 252 cj += cnzi; ca += cnzi; 253 } 254 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 255 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 256 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 257 PetscFunctionReturn(0); 258 } 259 260 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C) 261 { 262 PetscErrorCode ierr; 263 PetscLogDouble flops=0.0; 264 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 265 Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data; 266 Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data; 267 PetscInt *ai = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j; 268 PetscInt am = A->rmap->N,cm=C->rmap->N; 269 PetscInt i,j,k,anzi,bnzi,cnzi,brow; 270 PetscScalar *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp; 271 PetscInt nextb; 272 273 PetscFunctionBegin; 274 if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */ 275 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 276 c->a = ca; 277 c->free_a = PETSC_TRUE; 278 } 279 280 /* clean old values in C */ 281 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 282 /* Traverse A row-wise. */ 283 /* Build the ith row in C by summing over nonzero columns in A, */ 284 /* the rows of B corresponding to nonzeros of A. */ 285 for (i=0; i<am; i++) { 286 anzi = ai[i+1] - ai[i]; 287 cnzi = ci[i+1] - ci[i]; 288 for (j=0; j<anzi; j++) { 289 brow = aj[j]; 290 bnzi = bi[brow+1] - bi[brow]; 291 bjj = bj + bi[brow]; 292 baj = ba + bi[brow]; 293 /* perform sparse axpy */ 294 valtmp = aa[j]; 295 nextb = 0; 296 for (k=0; nextb<bnzi; k++) { 297 if (cj[k] == bjj[nextb]) { /* ccol == bcol */ 298 ca[k] += valtmp*baj[nextb++]; 299 } 300 } 301 flops += 2*bnzi; 302 } 303 aj += anzi; aa += anzi; 304 cj += cnzi; ca += cnzi; 305 } 306 307 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 308 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 309 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 310 PetscFunctionReturn(0); 311 } 312 313 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C) 314 { 315 PetscErrorCode ierr; 316 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 317 PetscInt *ai = a->i,*bi=b->i,*ci,*cj; 318 PetscInt am = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 319 MatScalar *ca; 320 PetscReal afill; 321 PetscInt i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax; 322 PetscTable ta; 323 PetscFreeSpaceList free_space=NULL,current_space=NULL; 324 325 PetscFunctionBegin; 326 /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */ 327 /*-----------------------------------------------------------------------------------------*/ 328 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 329 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 330 ci[0] = 0; 331 332 /* create and initialize a linked list */ 333 ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr); 334 MatRowMergeMax_SeqAIJ(b,bm,ta); 335 ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); 336 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 337 338 ierr = PetscLLCondensedCreate_fast(Crmax,&lnk);CHKERRQ(ierr); 339 340 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 341 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 342 current_space = free_space; 343 344 /* Determine ci and cj */ 345 for (i=0; i<am; i++) { 346 anzi = ai[i+1] - ai[i]; 347 aj = a->j + ai[i]; 348 for (j=0; j<anzi; j++) { 349 brow = aj[j]; 350 bnzj = bi[brow+1] - bi[brow]; 351 bj = b->j + bi[brow]; 352 /* add non-zero cols of B into the sorted linked list lnk */ 353 ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr); 354 } 355 cnzi = lnk[1]; 356 357 /* If free space is not available, make more free space */ 358 /* Double the amount of total space in the list */ 359 if (current_space->local_remaining<cnzi) { 360 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 361 ndouble++; 362 } 363 364 /* Copy data into free space, then initialize lnk */ 365 ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr); 366 367 current_space->array += cnzi; 368 current_space->local_used += cnzi; 369 current_space->local_remaining -= cnzi; 370 371 ci[i+1] = ci[i] + cnzi; 372 } 373 374 /* Column indices are in the list of free space */ 375 /* Allocate space for cj, initialize cj, and */ 376 /* destroy list of free space and other temporary array(s) */ 377 ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr); 378 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 379 ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr); 380 381 /* Allocate space for ca */ 382 ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr); 383 ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr); 384 385 /* put together the new symbolic matrix */ 386 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr); 387 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 388 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 389 390 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 391 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 392 c = (Mat_SeqAIJ*)((*C)->data); 393 c->free_a = PETSC_TRUE; 394 c->free_ij = PETSC_TRUE; 395 c->nonew = 0; 396 397 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */ 398 399 /* set MatInfo */ 400 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 401 if (afill < 1.0) afill = 1.0; 402 c->maxnz = ci[am]; 403 c->nz = ci[am]; 404 (*C)->info.mallocs = ndouble; 405 (*C)->info.fill_ratio_given = fill; 406 (*C)->info.fill_ratio_needed = afill; 407 408 #if defined(PETSC_USE_INFO) 409 if (ci[am]) { 410 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 411 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 412 } else { 413 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 414 } 415 #endif 416 PetscFunctionReturn(0); 417 } 418 419 420 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C) 421 { 422 PetscErrorCode ierr; 423 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 424 PetscInt *ai = a->i,*bi=b->i,*ci,*cj; 425 PetscInt am = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 426 MatScalar *ca; 427 PetscReal afill; 428 PetscInt i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax; 429 PetscTable ta; 430 PetscFreeSpaceList free_space=NULL,current_space=NULL; 431 432 PetscFunctionBegin; 433 /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */ 434 /*---------------------------------------------------------------------------------------------*/ 435 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 436 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 437 ci[0] = 0; 438 439 /* create and initialize a linked list */ 440 ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr); 441 MatRowMergeMax_SeqAIJ(b,bm,ta); 442 ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); 443 ierr = PetscTableDestroy(&ta);CHKERRQ(ierr); 444 ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr); 445 446 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 447 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 448 current_space = free_space; 449 450 /* Determine ci and cj */ 451 for (i=0; i<am; i++) { 452 anzi = ai[i+1] - ai[i]; 453 aj = a->j + ai[i]; 454 for (j=0; j<anzi; j++) { 455 brow = aj[j]; 456 bnzj = bi[brow+1] - bi[brow]; 457 bj = b->j + bi[brow]; 458 /* add non-zero cols of B into the sorted linked list lnk */ 459 ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr); 460 } 461 cnzi = lnk[0]; 462 463 /* If free space is not available, make more free space */ 464 /* Double the amount of total space in the list */ 465 if (current_space->local_remaining<cnzi) { 466 ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr); 467 ndouble++; 468 } 469 470 /* Copy data into free space, then initialize lnk */ 471 ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr); 472 473 current_space->array += cnzi; 474 current_space->local_used += cnzi; 475 current_space->local_remaining -= cnzi; 476 477 ci[i+1] = ci[i] + cnzi; 478 } 479 480 /* Column indices are in the list of free space */ 481 /* Allocate space for cj, initialize cj, and */ 482 /* destroy list of free space and other temporary array(s) */ 483 ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr); 484 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 485 ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); 486 487 /* Allocate space for ca */ 488 /*-----------------------*/ 489 ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr); 490 ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr); 491 492 /* put together the new symbolic matrix */ 493 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr); 494 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 495 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 496 497 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 498 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 499 c = (Mat_SeqAIJ*)((*C)->data); 500 c->free_a = PETSC_TRUE; 501 c->free_ij = PETSC_TRUE; 502 c->nonew = 0; 503 504 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */ 505 506 /* set MatInfo */ 507 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 508 if (afill < 1.0) afill = 1.0; 509 c->maxnz = ci[am]; 510 c->nz = ci[am]; 511 (*C)->info.mallocs = ndouble; 512 (*C)->info.fill_ratio_given = fill; 513 (*C)->info.fill_ratio_needed = afill; 514 515 #if defined(PETSC_USE_INFO) 516 if (ci[am]) { 517 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 518 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 519 } else { 520 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 521 } 522 #endif 523 PetscFunctionReturn(0); 524 } 525 526 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C) 527 { 528 PetscErrorCode ierr; 529 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 530 const PetscInt *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j; 531 PetscInt *ci,*cj,*bb; 532 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 533 PetscReal afill; 534 PetscInt i,j,col,ndouble = 0; 535 PetscFreeSpaceList free_space=NULL,current_space=NULL; 536 PetscHeap h; 537 538 PetscFunctionBegin; 539 /* Get ci and cj - by merging sorted rows using a heap */ 540 /*---------------------------------------------------------------------------------------------*/ 541 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 542 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 543 ci[0] = 0; 544 545 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 546 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 547 current_space = free_space; 548 549 ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr); 550 ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr); 551 552 /* Determine ci and cj */ 553 for (i=0; i<am; i++) { 554 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 */ 555 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 556 ci[i+1] = ci[i]; 557 /* Populate the min heap */ 558 for (j=0; j<anzi; j++) { 559 bb[j] = bi[acol[j]]; /* bb points at the start of the row */ 560 if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */ 561 ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr); 562 } 563 } 564 /* Pick off the min element, adding it to free space */ 565 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 566 while (j >= 0) { 567 if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */ 568 ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),¤t_space);CHKERRQ(ierr); 569 ndouble++; 570 } 571 *(current_space->array++) = col; 572 current_space->local_used++; 573 current_space->local_remaining--; 574 ci[i+1]++; 575 576 /* stash if anything else remains in this row of B */ 577 if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);} 578 while (1) { /* pop and stash any other rows of B that also had an entry in this column */ 579 PetscInt j2,col2; 580 ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr); 581 if (col2 != col) break; 582 ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr); 583 if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);} 584 } 585 /* Put any stashed elements back into the min heap */ 586 ierr = PetscHeapUnstash(h);CHKERRQ(ierr); 587 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 588 } 589 } 590 ierr = PetscFree(bb);CHKERRQ(ierr); 591 ierr = PetscHeapDestroy(&h);CHKERRQ(ierr); 592 593 /* Column indices are in the list of free space */ 594 /* Allocate space for cj, initialize cj, and */ 595 /* destroy list of free space and other temporary array(s) */ 596 ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr); 597 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 598 599 /* put together the new symbolic matrix */ 600 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 601 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 602 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 603 604 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 605 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 606 c = (Mat_SeqAIJ*)((*C)->data); 607 c->free_a = PETSC_TRUE; 608 c->free_ij = PETSC_TRUE; 609 c->nonew = 0; 610 611 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted; 612 613 /* set MatInfo */ 614 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 615 if (afill < 1.0) afill = 1.0; 616 c->maxnz = ci[am]; 617 c->nz = ci[am]; 618 (*C)->info.mallocs = ndouble; 619 (*C)->info.fill_ratio_given = fill; 620 (*C)->info.fill_ratio_needed = afill; 621 622 #if defined(PETSC_USE_INFO) 623 if (ci[am]) { 624 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 625 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 626 } else { 627 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 628 } 629 #endif 630 PetscFunctionReturn(0); 631 } 632 633 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C) 634 { 635 PetscErrorCode ierr; 636 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 637 const PetscInt *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j; 638 PetscInt *ci,*cj,*bb; 639 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 640 PetscReal afill; 641 PetscInt i,j,col,ndouble = 0; 642 PetscFreeSpaceList free_space=NULL,current_space=NULL; 643 PetscHeap h; 644 PetscBT bt; 645 646 PetscFunctionBegin; 647 /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */ 648 /*---------------------------------------------------------------------------------------------*/ 649 /* Allocate arrays for fill computation and free space for accumulating nonzero column */ 650 ierr = PetscMalloc1(am+2,&ci);CHKERRQ(ierr); 651 ci[0] = 0; 652 653 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 654 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr); 655 656 current_space = free_space; 657 658 ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr); 659 ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr); 660 ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr); 661 662 /* Determine ci and cj */ 663 for (i=0; i<am; i++) { 664 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 */ 665 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 666 const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */ 667 ci[i+1] = ci[i]; 668 /* Populate the min heap */ 669 for (j=0; j<anzi; j++) { 670 PetscInt brow = acol[j]; 671 for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) { 672 PetscInt bcol = bj[bb[j]]; 673 if (!PetscBTLookupSet(bt,bcol)) { /* new entry */ 674 ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr); 675 bb[j]++; 676 break; 677 } 678 } 679 } 680 /* Pick off the min element, adding it to free space */ 681 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 682 while (j >= 0) { 683 if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */ 684 fptr = NULL; /* need PetscBTMemzero */ 685 ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),¤t_space);CHKERRQ(ierr); 686 ndouble++; 687 } 688 *(current_space->array++) = col; 689 current_space->local_used++; 690 current_space->local_remaining--; 691 ci[i+1]++; 692 693 /* stash if anything else remains in this row of B */ 694 for (; bb[j] < bi[acol[j]+1]; bb[j]++) { 695 PetscInt bcol = bj[bb[j]]; 696 if (!PetscBTLookupSet(bt,bcol)) { /* new entry */ 697 ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr); 698 bb[j]++; 699 break; 700 } 701 } 702 ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr); 703 } 704 if (fptr) { /* Clear the bits for this row */ 705 for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);} 706 } else { /* We reallocated so we don't remember (easily) how to clear only the bits we changed */ 707 ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr); 708 } 709 } 710 ierr = PetscFree(bb);CHKERRQ(ierr); 711 ierr = PetscHeapDestroy(&h);CHKERRQ(ierr); 712 ierr = PetscBTDestroy(&bt);CHKERRQ(ierr); 713 714 /* Column indices are in the list of free space */ 715 /* Allocate space for cj, initialize cj, and */ 716 /* destroy list of free space and other temporary array(s) */ 717 ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr); 718 ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr); 719 720 /* put together the new symbolic matrix */ 721 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 722 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 723 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 724 725 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 726 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 727 c = (Mat_SeqAIJ*)((*C)->data); 728 c->free_a = PETSC_TRUE; 729 c->free_ij = PETSC_TRUE; 730 c->nonew = 0; 731 732 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted; 733 734 /* set MatInfo */ 735 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 736 if (afill < 1.0) afill = 1.0; 737 c->maxnz = ci[am]; 738 c->nz = ci[am]; 739 (*C)->info.mallocs = ndouble; 740 (*C)->info.fill_ratio_given = fill; 741 (*C)->info.fill_ratio_needed = afill; 742 743 #if defined(PETSC_USE_INFO) 744 if (ci[am]) { 745 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 746 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 747 } else { 748 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 749 } 750 #endif 751 PetscFunctionReturn(0); 752 } 753 754 755 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A,Mat B,PetscReal fill,Mat *C) 756 { 757 PetscErrorCode ierr; 758 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 759 const PetscInt *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j,*inputi,*inputj,*inputcol,*inputcol_L1; 760 PetscInt *ci,*cj,*outputj,worki_L1[9],worki_L2[9]; 761 PetscInt c_maxmem,a_maxrownnz=0,a_rownnz; 762 const PetscInt workcol[8]={0,1,2,3,4,5,6,7}; 763 const PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 764 const PetscInt *brow_ptr[8],*brow_end[8]; 765 PetscInt window[8]; 766 PetscInt window_min,old_window_min,ci_nnz,outputi_nnz=0,L1_nrows,L2_nrows; 767 PetscInt i,k,ndouble=0,L1_rowsleft,rowsleft; 768 PetscReal afill; 769 PetscInt *workj_L1,*workj_L2,*workj_L3; 770 PetscInt L1_nnz,L2_nnz; 771 772 /* Step 1: Get upper bound on memory required for allocation. 773 Because of the way virtual memory works, 774 only the memory pages that are actually needed will be physically allocated. */ 775 PetscFunctionBegin; 776 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 777 for (i=0; i<am; i++) { 778 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 */ 779 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 780 a_rownnz = 0; 781 for (k=0; k<anzi; ++k) { 782 a_rownnz += bi[acol[k]+1] - bi[acol[k]]; 783 if (a_rownnz > bn) { 784 a_rownnz = bn; 785 break; 786 } 787 } 788 a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz); 789 } 790 /* temporary work areas for merging rows */ 791 ierr = PetscMalloc1(a_maxrownnz*8,&workj_L1);CHKERRQ(ierr); 792 ierr = PetscMalloc1(a_maxrownnz*8,&workj_L2);CHKERRQ(ierr); 793 ierr = PetscMalloc1(a_maxrownnz,&workj_L3);CHKERRQ(ierr); 794 795 /* This should be enough for almost all matrices. If not, memory is reallocated later. */ 796 c_maxmem = 8*(ai[am]+bi[bm]); 797 /* Step 2: Populate pattern for C */ 798 ierr = PetscMalloc1(c_maxmem,&cj);CHKERRQ(ierr); 799 800 ci_nnz = 0; 801 ci[0] = 0; 802 worki_L1[0] = 0; 803 worki_L2[0] = 0; 804 for (i=0; i<am; i++) { 805 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 */ 806 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 807 rowsleft = anzi; 808 inputcol_L1 = acol; 809 L2_nnz = 0; 810 L2_nrows = 1; /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1 */ 811 worki_L2[1] = 0; 812 outputi_nnz = 0; 813 814 /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem -> allocate more memory */ 815 while (ci_nnz+a_maxrownnz > c_maxmem) { 816 c_maxmem *= 2; 817 ndouble++; 818 ierr = PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);CHKERRQ(ierr); 819 } 820 821 while (rowsleft) { 822 L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */ 823 L1_nrows = 0; 824 L1_nnz = 0; 825 inputcol = inputcol_L1; 826 inputi = bi; 827 inputj = bj; 828 829 /* The following macro is used to specialize for small rows in A. 830 This helps with compiler unrolling, improving performance substantially. 831 Input: inputj inputi inputcol bn 832 Output: outputj outputi_nnz */ 833 #define MatMatMultSymbolic_RowMergeMacro(ANNZ) \ 834 window_min = bn; \ 835 outputi_nnz = 0; \ 836 for (k=0; k<ANNZ; ++k) { \ 837 brow_ptr[k] = inputj + inputi[inputcol[k]]; \ 838 brow_end[k] = inputj + inputi[inputcol[k]+1]; \ 839 window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \ 840 window_min = PetscMin(window[k], window_min); \ 841 } \ 842 while (window_min < bn) { \ 843 outputj[outputi_nnz++] = window_min; \ 844 /* advance front and compute new minimum */ \ 845 old_window_min = window_min; \ 846 window_min = bn; \ 847 for (k=0; k<ANNZ; ++k) { \ 848 if (window[k] == old_window_min) { \ 849 brow_ptr[k]++; \ 850 window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \ 851 } \ 852 window_min = PetscMin(window[k], window_min); \ 853 } \ 854 } 855 856 /************** L E V E L 1 ***************/ 857 /* Merge up to 8 rows of B to L1 work array*/ 858 while (L1_rowsleft) { 859 outputi_nnz = 0; 860 if (anzi > 8) outputj = workj_L1 + L1_nnz; /* Level 1 rowmerge*/ 861 else outputj = cj + ci_nnz; /* Merge directly to C */ 862 863 switch (L1_rowsleft) { 864 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 865 brow_end[0] = inputj + inputi[inputcol[0]+1]; 866 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 867 inputcol += L1_rowsleft; 868 rowsleft -= L1_rowsleft; 869 L1_rowsleft = 0; 870 break; 871 case 2: MatMatMultSymbolic_RowMergeMacro(2); 872 inputcol += L1_rowsleft; 873 rowsleft -= L1_rowsleft; 874 L1_rowsleft = 0; 875 break; 876 case 3: MatMatMultSymbolic_RowMergeMacro(3); 877 inputcol += L1_rowsleft; 878 rowsleft -= L1_rowsleft; 879 L1_rowsleft = 0; 880 break; 881 case 4: MatMatMultSymbolic_RowMergeMacro(4); 882 inputcol += L1_rowsleft; 883 rowsleft -= L1_rowsleft; 884 L1_rowsleft = 0; 885 break; 886 case 5: MatMatMultSymbolic_RowMergeMacro(5); 887 inputcol += L1_rowsleft; 888 rowsleft -= L1_rowsleft; 889 L1_rowsleft = 0; 890 break; 891 case 6: MatMatMultSymbolic_RowMergeMacro(6); 892 inputcol += L1_rowsleft; 893 rowsleft -= L1_rowsleft; 894 L1_rowsleft = 0; 895 break; 896 case 7: MatMatMultSymbolic_RowMergeMacro(7); 897 inputcol += L1_rowsleft; 898 rowsleft -= L1_rowsleft; 899 L1_rowsleft = 0; 900 break; 901 default: MatMatMultSymbolic_RowMergeMacro(8); 902 inputcol += 8; 903 rowsleft -= 8; 904 L1_rowsleft -= 8; 905 break; 906 } 907 inputcol_L1 = inputcol; 908 L1_nnz += outputi_nnz; 909 worki_L1[++L1_nrows] = L1_nnz; 910 } 911 912 /********************** L E V E L 2 ************************/ 913 /* Merge from L1 work array to either C or to L2 work array */ 914 if (anzi > 8) { 915 inputi = worki_L1; 916 inputj = workj_L1; 917 inputcol = workcol; 918 outputi_nnz = 0; 919 920 if (anzi <= 64) outputj = cj + ci_nnz; /* Merge from L1 work array to C */ 921 else outputj = workj_L2 + L2_nnz; /* Merge from L1 work array to L2 work array */ 922 923 switch (L1_nrows) { 924 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 925 brow_end[0] = inputj + inputi[inputcol[0]+1]; 926 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 927 break; 928 case 2: MatMatMultSymbolic_RowMergeMacro(2); break; 929 case 3: MatMatMultSymbolic_RowMergeMacro(3); break; 930 case 4: MatMatMultSymbolic_RowMergeMacro(4); break; 931 case 5: MatMatMultSymbolic_RowMergeMacro(5); break; 932 case 6: MatMatMultSymbolic_RowMergeMacro(6); break; 933 case 7: MatMatMultSymbolic_RowMergeMacro(7); break; 934 case 8: MatMatMultSymbolic_RowMergeMacro(8); break; 935 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L1 work array!"); 936 } 937 L2_nnz += outputi_nnz; 938 worki_L2[++L2_nrows] = L2_nnz; 939 940 /************************ L E V E L 3 **********************/ 941 /* Merge from L2 work array to either C or to L2 work array */ 942 if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) { 943 inputi = worki_L2; 944 inputj = workj_L2; 945 inputcol = workcol; 946 outputi_nnz = 0; 947 if (rowsleft) outputj = workj_L3; 948 else outputj = cj + ci_nnz; 949 switch (L2_nrows) { 950 case 1: brow_ptr[0] = inputj + inputi[inputcol[0]]; 951 brow_end[0] = inputj + inputi[inputcol[0]+1]; 952 for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */ 953 break; 954 case 2: MatMatMultSymbolic_RowMergeMacro(2); break; 955 case 3: MatMatMultSymbolic_RowMergeMacro(3); break; 956 case 4: MatMatMultSymbolic_RowMergeMacro(4); break; 957 case 5: MatMatMultSymbolic_RowMergeMacro(5); break; 958 case 6: MatMatMultSymbolic_RowMergeMacro(6); break; 959 case 7: MatMatMultSymbolic_RowMergeMacro(7); break; 960 case 8: MatMatMultSymbolic_RowMergeMacro(8); break; 961 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L2 work array!"); 962 } 963 L2_nrows = 1; 964 L2_nnz = outputi_nnz; 965 worki_L2[1] = outputi_nnz; 966 /* Copy to workj_L2 */ 967 if (rowsleft) { 968 for (k=0; k<outputi_nnz; ++k) workj_L2[k] = outputj[k]; 969 } 970 } 971 } 972 } /* while (rowsleft) */ 973 #undef MatMatMultSymbolic_RowMergeMacro 974 975 /* terminate current row */ 976 ci_nnz += outputi_nnz; 977 ci[i+1] = ci_nnz; 978 } 979 980 /* Step 3: Create the new symbolic matrix */ 981 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 982 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 983 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 984 985 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 986 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 987 c = (Mat_SeqAIJ*)((*C)->data); 988 c->free_a = PETSC_TRUE; 989 c->free_ij = PETSC_TRUE; 990 c->nonew = 0; 991 992 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted; 993 994 /* set MatInfo */ 995 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 996 if (afill < 1.0) afill = 1.0; 997 c->maxnz = ci[am]; 998 c->nz = ci[am]; 999 (*C)->info.mallocs = ndouble; 1000 (*C)->info.fill_ratio_given = fill; 1001 (*C)->info.fill_ratio_needed = afill; 1002 1003 #if defined(PETSC_USE_INFO) 1004 if (ci[am]) { 1005 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 1006 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 1007 } else { 1008 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 1009 } 1010 #endif 1011 1012 /* Step 4: Free temporary work areas */ 1013 ierr = PetscFree(workj_L1);CHKERRQ(ierr); 1014 ierr = PetscFree(workj_L2);CHKERRQ(ierr); 1015 ierr = PetscFree(workj_L3);CHKERRQ(ierr); 1016 PetscFunctionReturn(0); 1017 } 1018 1019 /* concatenate unique entries and then sort */ 1020 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat A,Mat B,PetscReal fill,Mat *C) 1021 { 1022 PetscErrorCode ierr; 1023 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 1024 const PetscInt *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j; 1025 PetscInt *ci,*cj; 1026 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 1027 PetscReal afill; 1028 PetscInt i,j,ndouble = 0; 1029 PetscSegBuffer seg,segrow; 1030 char *seen; 1031 1032 PetscFunctionBegin; 1033 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 1034 ci[0] = 0; 1035 1036 /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */ 1037 ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr); 1038 ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr); 1039 ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr); 1040 ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr); 1041 1042 /* Determine ci and cj */ 1043 for (i=0; i<am; i++) { 1044 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 */ 1045 const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */ 1046 PetscInt packlen = 0,*PETSC_RESTRICT crow; 1047 /* Pack segrow */ 1048 for (j=0; j<anzi; j++) { 1049 PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k; 1050 for (k=bjstart; k<bjend; k++) { 1051 PetscInt bcol = bj[k]; 1052 if (!seen[bcol]) { /* new entry */ 1053 PetscInt *PETSC_RESTRICT slot; 1054 ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr); 1055 *slot = bcol; 1056 seen[bcol] = 1; 1057 packlen++; 1058 } 1059 } 1060 } 1061 ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr); 1062 ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr); 1063 ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr); 1064 ci[i+1] = ci[i] + packlen; 1065 for (j=0; j<packlen; j++) seen[crow[j]] = 0; 1066 } 1067 ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr); 1068 ierr = PetscFree(seen);CHKERRQ(ierr); 1069 1070 /* Column indices are in the segmented buffer */ 1071 ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr); 1072 ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr); 1073 1074 /* put together the new symbolic matrix */ 1075 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 1076 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 1077 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 1078 1079 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 1080 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 1081 c = (Mat_SeqAIJ*)((*C)->data); 1082 c->free_a = PETSC_TRUE; 1083 c->free_ij = PETSC_TRUE; 1084 c->nonew = 0; 1085 1086 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted; 1087 1088 /* set MatInfo */ 1089 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 1090 if (afill < 1.0) afill = 1.0; 1091 c->maxnz = ci[am]; 1092 c->nz = ci[am]; 1093 (*C)->info.mallocs = ndouble; 1094 (*C)->info.fill_ratio_given = fill; 1095 (*C)->info.fill_ratio_needed = afill; 1096 1097 #if defined(PETSC_USE_INFO) 1098 if (ci[am]) { 1099 ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr); 1100 ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr); 1101 } else { 1102 ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr); 1103 } 1104 #endif 1105 PetscFunctionReturn(0); 1106 } 1107 1108 /* This routine is not used. Should be removed! */ 1109 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1110 { 1111 PetscErrorCode ierr; 1112 1113 PetscFunctionBegin; 1114 if (scall == MAT_INITIAL_MATRIX) { 1115 ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1116 ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 1117 ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1118 } 1119 ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr); 1120 ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr); 1121 ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr); 1122 PetscFunctionReturn(0); 1123 } 1124 1125 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A) 1126 { 1127 PetscErrorCode ierr; 1128 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1129 Mat_MatMatTransMult *abt=a->abt; 1130 1131 PetscFunctionBegin; 1132 ierr = (abt->destroy)(A);CHKERRQ(ierr); 1133 ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr); 1134 ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr); 1135 ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr); 1136 ierr = PetscFree(abt);CHKERRQ(ierr); 1137 PetscFunctionReturn(0); 1138 } 1139 1140 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1141 { 1142 PetscErrorCode ierr; 1143 Mat Bt; 1144 PetscInt *bti,*btj; 1145 Mat_MatMatTransMult *abt; 1146 Mat_SeqAIJ *c; 1147 1148 PetscFunctionBegin; 1149 /* create symbolic Bt */ 1150 ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr); 1151 ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr); 1152 ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr); 1153 ierr = MatSetType(Bt,((PetscObject)A)->type_name);CHKERRQ(ierr); 1154 1155 /* get symbolic C=A*Bt */ 1156 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr); 1157 1158 /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */ 1159 ierr = PetscNew(&abt);CHKERRQ(ierr); 1160 c = (Mat_SeqAIJ*)(*C)->data; 1161 c->abt = abt; 1162 1163 abt->usecoloring = PETSC_FALSE; 1164 abt->destroy = (*C)->ops->destroy; 1165 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans; 1166 1167 ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr); 1168 if (abt->usecoloring) { 1169 /* Create MatTransposeColoring from symbolic C=A*B^T */ 1170 MatTransposeColoring matcoloring; 1171 MatColoring coloring; 1172 ISColoring iscoloring; 1173 Mat Bt_dense,C_dense; 1174 Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data; 1175 /* inode causes memory problem, don't know why */ 1176 if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'"); 1177 1178 ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr); 1179 ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr); 1180 ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr); 1181 ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr); 1182 ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr); 1183 ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr); 1184 ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr); 1185 1186 abt->matcoloring = matcoloring; 1187 1188 ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr); 1189 1190 /* Create Bt_dense and C_dense = A*Bt_dense */ 1191 ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr); 1192 ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr); 1193 ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr); 1194 ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr); 1195 1196 Bt_dense->assembled = PETSC_TRUE; 1197 abt->Bt_den = Bt_dense; 1198 1199 ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr); 1200 ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr); 1201 ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr); 1202 ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr); 1203 1204 Bt_dense->assembled = PETSC_TRUE; 1205 abt->ABt_den = C_dense; 1206 1207 #if defined(PETSC_USE_INFO) 1208 { 1209 Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data; 1210 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); 1211 } 1212 #endif 1213 } 1214 /* clean up */ 1215 ierr = MatDestroy(&Bt);CHKERRQ(ierr); 1216 ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr); 1217 PetscFunctionReturn(0); 1218 } 1219 1220 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 1221 { 1222 PetscErrorCode ierr; 1223 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data; 1224 PetscInt *ai =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow; 1225 PetscInt cm =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol; 1226 PetscLogDouble flops=0.0; 1227 MatScalar *aa =a->a,*aval,*ba=b->a,*bval,*ca,*cval; 1228 Mat_MatMatTransMult *abt = c->abt; 1229 1230 PetscFunctionBegin; 1231 /* clear old values in C */ 1232 if (!c->a) { 1233 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 1234 c->a = ca; 1235 c->free_a = PETSC_TRUE; 1236 } else { 1237 ca = c->a; 1238 } 1239 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 1240 1241 if (abt->usecoloring) { 1242 MatTransposeColoring matcoloring = abt->matcoloring; 1243 Mat Bt_dense,C_dense = abt->ABt_den; 1244 1245 /* Get Bt_dense by Apply MatTransposeColoring to B */ 1246 Bt_dense = abt->Bt_den; 1247 ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr); 1248 1249 /* C_dense = A*Bt_dense */ 1250 ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr); 1251 1252 /* Recover C from C_dense */ 1253 ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr); 1254 PetscFunctionReturn(0); 1255 } 1256 1257 for (i=0; i<cm; i++) { 1258 anzi = ai[i+1] - ai[i]; 1259 acol = aj + ai[i]; 1260 aval = aa + ai[i]; 1261 cnzi = ci[i+1] - ci[i]; 1262 ccol = cj + ci[i]; 1263 cval = ca + ci[i]; 1264 for (j=0; j<cnzi; j++) { 1265 brow = ccol[j]; 1266 bnzj = bi[brow+1] - bi[brow]; 1267 bcol = bj + bi[brow]; 1268 bval = ba + bi[brow]; 1269 1270 /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */ 1271 nexta = 0; nextb = 0; 1272 while (nexta<anzi && nextb<bnzj) { 1273 while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++; 1274 if (nexta == anzi) break; 1275 while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++; 1276 if (nextb == bnzj) break; 1277 if (acol[nexta] == bcol[nextb]) { 1278 cval[j] += aval[nexta]*bval[nextb]; 1279 nexta++; nextb++; 1280 flops += 2; 1281 } 1282 } 1283 } 1284 } 1285 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1286 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1287 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1288 PetscFunctionReturn(0); 1289 } 1290 1291 PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(Mat A) 1292 { 1293 PetscErrorCode ierr; 1294 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1295 Mat_MatTransMatMult *atb = a->atb; 1296 1297 PetscFunctionBegin; 1298 if (atb) { 1299 ierr = MatDestroy(&atb->At);CHKERRQ(ierr); 1300 ierr = (*atb->destroy)(A);CHKERRQ(ierr); 1301 } 1302 ierr = PetscFree(atb);CHKERRQ(ierr); 1303 PetscFunctionReturn(0); 1304 } 1305 1306 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1307 { 1308 PetscErrorCode ierr; 1309 const char *algTypes[2] = {"matmatmult","outerproduct"}; 1310 PetscInt alg=0; /* set default algorithm */ 1311 Mat At; 1312 Mat_MatTransMatMult *atb; 1313 Mat_SeqAIJ *c; 1314 1315 PetscFunctionBegin; 1316 if (scall == MAT_INITIAL_MATRIX) { 1317 ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr); 1318 ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,2,algTypes[0],&alg,NULL);CHKERRQ(ierr); 1319 ierr = PetscOptionsEnd();CHKERRQ(ierr); 1320 1321 switch (alg) { 1322 case 1: 1323 ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr); 1324 break; 1325 default: 1326 ierr = PetscNew(&atb);CHKERRQ(ierr); 1327 ierr = MatTranspose_SeqAIJ(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr); 1328 ierr = MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_INITIAL_MATRIX,fill,C);CHKERRQ(ierr); 1329 1330 c = (Mat_SeqAIJ*)(*C)->data; 1331 c->atb = atb; 1332 atb->At = At; 1333 atb->destroy = (*C)->ops->destroy; 1334 (*C)->ops->destroy = MatDestroy_SeqAIJ_MatTransMatMult; 1335 1336 break; 1337 } 1338 } 1339 if (alg) { 1340 ierr = (*(*C)->ops->mattransposemultnumeric)(A,B,*C);CHKERRQ(ierr); 1341 } else if (!alg && scall == MAT_REUSE_MATRIX) { 1342 c = (Mat_SeqAIJ*)(*C)->data; 1343 atb = c->atb; 1344 At = atb->At; 1345 ierr = MatTranspose_SeqAIJ(A,MAT_REUSE_MATRIX,&At);CHKERRQ(ierr); 1346 ierr = MatMatMult_SeqAIJ_SeqAIJ(At,B,MAT_REUSE_MATRIX,fill,C);CHKERRQ(ierr); 1347 } 1348 PetscFunctionReturn(0); 1349 } 1350 1351 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C) 1352 { 1353 PetscErrorCode ierr; 1354 Mat At; 1355 PetscInt *ati,*atj; 1356 1357 PetscFunctionBegin; 1358 /* create symbolic At */ 1359 ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr); 1360 ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr); 1361 ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr); 1362 ierr = MatSetType(At,((PetscObject)A)->type_name);CHKERRQ(ierr); 1363 1364 /* get symbolic C=At*B */ 1365 ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr); 1366 1367 /* clean up */ 1368 ierr = MatDestroy(&At);CHKERRQ(ierr); 1369 ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr); 1370 1371 (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; 1372 PetscFunctionReturn(0); 1373 } 1374 1375 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C) 1376 { 1377 PetscErrorCode ierr; 1378 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data; 1379 PetscInt am =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb; 1380 PetscInt cm =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k; 1381 PetscLogDouble flops=0.0; 1382 MatScalar *aa =a->a,*ba,*ca,*caj; 1383 1384 PetscFunctionBegin; 1385 if (!c->a) { 1386 ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr); 1387 1388 c->a = ca; 1389 c->free_a = PETSC_TRUE; 1390 } else { 1391 ca = c->a; 1392 } 1393 /* clear old values in C */ 1394 ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr); 1395 1396 /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */ 1397 for (i=0; i<am; i++) { 1398 bj = b->j + bi[i]; 1399 ba = b->a + bi[i]; 1400 bnzi = bi[i+1] - bi[i]; 1401 anzi = ai[i+1] - ai[i]; 1402 for (j=0; j<anzi; j++) { 1403 nextb = 0; 1404 crow = *aj++; 1405 cjj = cj + ci[crow]; 1406 caj = ca + ci[crow]; 1407 /* perform sparse axpy operation. Note cjj includes bj. */ 1408 for (k=0; nextb<bnzi; k++) { 1409 if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */ 1410 caj[k] += (*aa)*(*(ba+nextb)); 1411 nextb++; 1412 } 1413 } 1414 flops += 2*bnzi; 1415 aa++; 1416 } 1417 } 1418 1419 /* Assemble the final matrix and clean up */ 1420 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1421 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1422 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1423 PetscFunctionReturn(0); 1424 } 1425 1426 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) 1427 { 1428 PetscErrorCode ierr; 1429 1430 PetscFunctionBegin; 1431 if (scall == MAT_INITIAL_MATRIX) { 1432 ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1433 ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr); 1434 ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr); 1435 } 1436 ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 1437 ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr); 1438 ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr); 1439 PetscFunctionReturn(0); 1440 } 1441 1442 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C) 1443 { 1444 PetscErrorCode ierr; 1445 1446 PetscFunctionBegin; 1447 ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr); 1448 1449 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense; 1450 PetscFunctionReturn(0); 1451 } 1452 1453 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C) 1454 { 1455 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1456 Mat_SeqDense *bd = (Mat_SeqDense*)B->data; 1457 PetscErrorCode ierr; 1458 PetscScalar *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp; 1459 const PetscScalar *aa,*b1,*b2,*b3,*b4; 1460 const PetscInt *aj; 1461 PetscInt cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n; 1462 PetscInt am4=4*am,bm4=4*bm,col,i,j,n,ajtmp; 1463 1464 PetscFunctionBegin; 1465 if (!cm || !cn) PetscFunctionReturn(0); 1466 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); 1467 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); 1468 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); 1469 b = bd->v; 1470 ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr); 1471 b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm; 1472 c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am; 1473 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1474 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1475 r1 = r2 = r3 = r4 = 0.0; 1476 n = a->i[i+1] - a->i[i]; 1477 aj = a->j + a->i[i]; 1478 aa = a->a + a->i[i]; 1479 for (j=0; j<n; j++) { 1480 aatmp = aa[j]; ajtmp = aj[j]; 1481 r1 += aatmp*b1[ajtmp]; 1482 r2 += aatmp*b2[ajtmp]; 1483 r3 += aatmp*b3[ajtmp]; 1484 r4 += aatmp*b4[ajtmp]; 1485 } 1486 c1[i] = r1; 1487 c2[i] = r2; 1488 c3[i] = r3; 1489 c4[i] = r4; 1490 } 1491 b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4; 1492 c1 += am4; c2 += am4; c3 += am4; c4 += am4; 1493 } 1494 for (; col<cn; col++) { /* over extra columns of C */ 1495 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1496 r1 = 0.0; 1497 n = a->i[i+1] - a->i[i]; 1498 aj = a->j + a->i[i]; 1499 aa = a->a + a->i[i]; 1500 for (j=0; j<n; j++) { 1501 r1 += aa[j]*b1[aj[j]]; 1502 } 1503 c1[i] = r1; 1504 } 1505 b1 += bm; 1506 c1 += am; 1507 } 1508 ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr); 1509 ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr); 1510 ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1511 ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1512 PetscFunctionReturn(0); 1513 } 1514 1515 /* 1516 Note very similar to MatMult_SeqAIJ(), should generate both codes from same base 1517 */ 1518 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C) 1519 { 1520 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1521 Mat_SeqDense *bd = (Mat_SeqDense*)B->data; 1522 PetscErrorCode ierr; 1523 PetscScalar *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4; 1524 MatScalar *aa; 1525 PetscInt cm = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm; 1526 PetscInt am2 = 2*am, am3 = 3*am, bm4 = 4*bm,colam,*ridx; 1527 1528 PetscFunctionBegin; 1529 if (!cm || !cn) PetscFunctionReturn(0); 1530 b = bd->v; 1531 ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr); 1532 b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm; 1533 1534 if (a->compressedrow.use) { /* use compressed row format */ 1535 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1536 colam = col*am; 1537 arm = a->compressedrow.nrows; 1538 ii = a->compressedrow.i; 1539 ridx = a->compressedrow.rindex; 1540 for (i=0; i<arm; i++) { /* over rows of C in those columns */ 1541 r1 = r2 = r3 = r4 = 0.0; 1542 n = ii[i+1] - ii[i]; 1543 aj = a->j + ii[i]; 1544 aa = a->a + ii[i]; 1545 for (j=0; j<n; j++) { 1546 r1 += (*aa)*b1[*aj]; 1547 r2 += (*aa)*b2[*aj]; 1548 r3 += (*aa)*b3[*aj]; 1549 r4 += (*aa++)*b4[*aj++]; 1550 } 1551 c[colam + ridx[i]] += r1; 1552 c[colam + am + ridx[i]] += r2; 1553 c[colam + am2 + ridx[i]] += r3; 1554 c[colam + am3 + ridx[i]] += r4; 1555 } 1556 b1 += bm4; 1557 b2 += bm4; 1558 b3 += bm4; 1559 b4 += bm4; 1560 } 1561 for (; col<cn; col++) { /* over extra columns of C */ 1562 colam = col*am; 1563 arm = a->compressedrow.nrows; 1564 ii = a->compressedrow.i; 1565 ridx = a->compressedrow.rindex; 1566 for (i=0; i<arm; i++) { /* over rows of C in those columns */ 1567 r1 = 0.0; 1568 n = ii[i+1] - ii[i]; 1569 aj = a->j + ii[i]; 1570 aa = a->a + ii[i]; 1571 1572 for (j=0; j<n; j++) { 1573 r1 += (*aa++)*b1[*aj++]; 1574 } 1575 c[colam + ridx[i]] += r1; 1576 } 1577 b1 += bm; 1578 } 1579 } else { 1580 for (col=0; col<cn-4; col += 4) { /* over columns of C */ 1581 colam = col*am; 1582 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1583 r1 = r2 = r3 = r4 = 0.0; 1584 n = a->i[i+1] - a->i[i]; 1585 aj = a->j + a->i[i]; 1586 aa = a->a + a->i[i]; 1587 for (j=0; j<n; j++) { 1588 r1 += (*aa)*b1[*aj]; 1589 r2 += (*aa)*b2[*aj]; 1590 r3 += (*aa)*b3[*aj]; 1591 r4 += (*aa++)*b4[*aj++]; 1592 } 1593 c[colam + i] += r1; 1594 c[colam + am + i] += r2; 1595 c[colam + am2 + i] += r3; 1596 c[colam + am3 + i] += r4; 1597 } 1598 b1 += bm4; 1599 b2 += bm4; 1600 b3 += bm4; 1601 b4 += bm4; 1602 } 1603 for (; col<cn; col++) { /* over extra columns of C */ 1604 colam = col*am; 1605 for (i=0; i<am; i++) { /* over rows of C in those columns */ 1606 r1 = 0.0; 1607 n = a->i[i+1] - a->i[i]; 1608 aj = a->j + a->i[i]; 1609 aa = a->a + a->i[i]; 1610 1611 for (j=0; j<n; j++) { 1612 r1 += (*aa++)*b1[*aj++]; 1613 } 1614 c[colam + i] += r1; 1615 } 1616 b1 += bm; 1617 } 1618 } 1619 ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr); 1620 ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr); 1621 PetscFunctionReturn(0); 1622 } 1623 1624 PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense) 1625 { 1626 PetscErrorCode ierr; 1627 Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data; 1628 Mat_SeqDense *btdense = (Mat_SeqDense*)Btdense->data; 1629 PetscInt *bi = b->i,*bj=b->j; 1630 PetscInt m = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns; 1631 MatScalar *btval,*btval_den,*ba=b->a; 1632 PetscInt *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors; 1633 1634 PetscFunctionBegin; 1635 btval_den=btdense->v; 1636 ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr); 1637 for (k=0; k<ncolors; k++) { 1638 ncolumns = coloring->ncolumns[k]; 1639 for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */ 1640 col = *(columns + colorforcol[k] + l); 1641 btcol = bj + bi[col]; 1642 btval = ba + bi[col]; 1643 anz = bi[col+1] - bi[col]; 1644 for (j=0; j<anz; j++) { 1645 brow = btcol[j]; 1646 btval_den[brow] = btval[j]; 1647 } 1648 } 1649 btval_den += m; 1650 } 1651 PetscFunctionReturn(0); 1652 } 1653 1654 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp) 1655 { 1656 PetscErrorCode ierr; 1657 Mat_SeqAIJ *csp = (Mat_SeqAIJ*)Csp->data; 1658 const PetscScalar *ca_den,*ca_den_ptr; 1659 PetscScalar *ca=csp->a; 1660 PetscInt k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors; 1661 PetscInt brows=matcoloring->brows,*den2sp=matcoloring->den2sp; 1662 PetscInt nrows,*row,*idx; 1663 PetscInt *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow; 1664 1665 PetscFunctionBegin; 1666 ierr = MatDenseGetArrayRead(Cden,&ca_den);CHKERRQ(ierr); 1667 1668 if (brows > 0) { 1669 PetscInt *lstart,row_end,row_start; 1670 lstart = matcoloring->lstart; 1671 ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr); 1672 1673 row_end = brows; 1674 if (row_end > m) row_end = m; 1675 for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */ 1676 ca_den_ptr = ca_den; 1677 for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */ 1678 nrows = matcoloring->nrows[k]; 1679 row = rows + colorforrow[k]; 1680 idx = den2sp + colorforrow[k]; 1681 for (l=lstart[k]; l<nrows; l++) { 1682 if (row[l] >= row_end) { 1683 lstart[k] = l; 1684 break; 1685 } else { 1686 ca[idx[l]] = ca_den_ptr[row[l]]; 1687 } 1688 } 1689 ca_den_ptr += m; 1690 } 1691 row_end += brows; 1692 if (row_end > m) row_end = m; 1693 } 1694 } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */ 1695 ca_den_ptr = ca_den; 1696 for (k=0; k<ncolors; k++) { 1697 nrows = matcoloring->nrows[k]; 1698 row = rows + colorforrow[k]; 1699 idx = den2sp + colorforrow[k]; 1700 for (l=0; l<nrows; l++) { 1701 ca[idx[l]] = ca_den_ptr[row[l]]; 1702 } 1703 ca_den_ptr += m; 1704 } 1705 } 1706 1707 ierr = MatDenseRestoreArrayRead(Cden,&ca_den);CHKERRQ(ierr); 1708 #if defined(PETSC_USE_INFO) 1709 if (matcoloring->brows > 0) { 1710 ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr); 1711 } else { 1712 ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr); 1713 } 1714 #endif 1715 PetscFunctionReturn(0); 1716 } 1717 1718 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c) 1719 { 1720 PetscErrorCode ierr; 1721 PetscInt i,n,nrows,Nbs,j,k,m,ncols,col,cm; 1722 const PetscInt *is,*ci,*cj,*row_idx; 1723 PetscInt nis = iscoloring->n,*rowhit,bs = 1; 1724 IS *isa; 1725 Mat_SeqAIJ *csp = (Mat_SeqAIJ*)mat->data; 1726 PetscInt *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i; 1727 PetscInt *colorforcol,*columns,*columns_i,brows; 1728 PetscBool flg; 1729 1730 PetscFunctionBegin; 1731 ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr); 1732 1733 /* bs >1 is not being tested yet! */ 1734 Nbs = mat->cmap->N/bs; 1735 c->M = mat->rmap->N/bs; /* set total rows, columns and local rows */ 1736 c->N = Nbs; 1737 c->m = c->M; 1738 c->rstart = 0; 1739 c->brows = 100; 1740 1741 c->ncolors = nis; 1742 ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr); 1743 ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr); 1744 ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr); 1745 1746 brows = c->brows; 1747 ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr); 1748 if (flg) c->brows = brows; 1749 if (brows > 0) { 1750 ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr); 1751 } 1752 1753 colorforrow[0] = 0; 1754 rows_i = rows; 1755 den2sp_i = den2sp; 1756 1757 ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr); 1758 ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr); 1759 1760 colorforcol[0] = 0; 1761 columns_i = columns; 1762 1763 /* get column-wise storage of mat */ 1764 ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); 1765 1766 cm = c->m; 1767 ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr); 1768 ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr); 1769 for (i=0; i<nis; i++) { /* loop over color */ 1770 ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr); 1771 ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr); 1772 1773 c->ncolumns[i] = n; 1774 if (n) { 1775 ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr); 1776 } 1777 colorforcol[i+1] = colorforcol[i] + n; 1778 columns_i += n; 1779 1780 /* fast, crude version requires O(N*N) work */ 1781 ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr); 1782 1783 for (j=0; j<n; j++) { /* loop over columns*/ 1784 col = is[j]; 1785 row_idx = cj + ci[col]; 1786 m = ci[col+1] - ci[col]; 1787 for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */ 1788 idxhit[*row_idx] = spidx[ci[col] + k]; 1789 rowhit[*row_idx++] = col + 1; 1790 } 1791 } 1792 /* count the number of hits */ 1793 nrows = 0; 1794 for (j=0; j<cm; j++) { 1795 if (rowhit[j]) nrows++; 1796 } 1797 c->nrows[i] = nrows; 1798 colorforrow[i+1] = colorforrow[i] + nrows; 1799 1800 nrows = 0; 1801 for (j=0; j<cm; j++) { /* loop over rows */ 1802 if (rowhit[j]) { 1803 rows_i[nrows] = j; 1804 den2sp_i[nrows] = idxhit[j]; 1805 nrows++; 1806 } 1807 } 1808 den2sp_i += nrows; 1809 1810 ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr); 1811 rows_i += nrows; 1812 } 1813 ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); 1814 ierr = PetscFree(rowhit);CHKERRQ(ierr); 1815 ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr); 1816 if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]); 1817 1818 c->colorforrow = colorforrow; 1819 c->rows = rows; 1820 c->den2sp = den2sp; 1821 c->colorforcol = colorforcol; 1822 c->columns = columns; 1823 1824 ierr = PetscFree(idxhit);CHKERRQ(ierr); 1825 PetscFunctionReturn(0); 1826 } 1827 1828 /* The combine method has done the symbolic and numeric in the first phase, and so we just return here */ 1829 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Combined(Mat A,Mat B,Mat C) 1830 { 1831 PetscFunctionBegin; 1832 /* Empty function */ 1833 PetscFunctionReturn(0); 1834 } 1835 1836 /* This algorithm combines the symbolic and numeric phase of matrix-matrix multiplication. */ 1837 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ_Combined(Mat A,Mat B,PetscReal fill,Mat *C) 1838 { 1839 PetscErrorCode ierr; 1840 PetscLogDouble flops=0.0; 1841 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c; 1842 const PetscInt *ai=a->i,*bi=b->i; 1843 PetscInt *ci,*cj,*cj_i; 1844 PetscScalar *ca,*ca_i; 1845 PetscInt b_maxmemrow,c_maxmem,a_col; 1846 PetscInt am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N; 1847 PetscInt i,k,ndouble=0; 1848 PetscReal afill; 1849 PetscScalar *c_row_val_dense; 1850 PetscBool *c_row_idx_flags; 1851 PetscInt *aj_i=a->j; 1852 PetscScalar *aa_i=a->a; 1853 1854 PetscFunctionBegin; 1855 1856 /* Step 1: Determine upper bounds on memory for C and allocate memory */ 1857 /* This should be enough for almost all matrices. If still more memory is needed, it is reallocated later. */ 1858 c_maxmem = 8*(ai[am]+bi[bm]); 1859 b_maxmemrow = PetscMin(bi[bm],bn); 1860 ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr); 1861 ierr = PetscMalloc1(bn,&c_row_val_dense);CHKERRQ(ierr); 1862 ierr = PetscMalloc1(bn,&c_row_idx_flags);CHKERRQ(ierr); 1863 ierr = PetscMalloc1(c_maxmem,&cj);CHKERRQ(ierr); 1864 ierr = PetscMalloc1(c_maxmem,&ca);CHKERRQ(ierr); 1865 ca_i = ca; 1866 cj_i = cj; 1867 ci[0] = 0; 1868 ierr = PetscMemzero(c_row_val_dense,bn*sizeof(PetscScalar));CHKERRQ(ierr); 1869 ierr = PetscMemzero(c_row_idx_flags,bn*sizeof(PetscBool));CHKERRQ(ierr); 1870 for (i=0; i<am; i++) { 1871 /* Step 2: Initialize the dense row vector for C */ 1872 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 */ 1873 PetscInt cnzi = 0; 1874 PetscInt *bj_i; 1875 PetscScalar *ba_i; 1876 /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem -> allocate more memory 1877 Usually, there is enough memory in the first place, so this is not executed. */ 1878 while (ci[i] + b_maxmemrow > c_maxmem) { 1879 c_maxmem *= 2; 1880 ndouble++; 1881 ierr = PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);CHKERRQ(ierr); 1882 ierr = PetscRealloc(sizeof(PetscScalar)*c_maxmem,&ca);CHKERRQ(ierr); 1883 } 1884 1885 /* Step 3: Do the numerical calculations */ 1886 for (a_col=0; a_col<anzi; a_col++) { /* iterate over all non zero values in a row of A */ 1887 PetscInt a_col_index = aj_i[a_col]; 1888 const PetscInt bnzi = bi[a_col_index+1] - bi[a_col_index]; 1889 flops += 2*bnzi; 1890 bj_i = b->j + bi[a_col_index]; /* points to the current row in bj */ 1891 ba_i = b->a + bi[a_col_index]; /* points to the current row in ba */ 1892 for (k=0; k<bnzi; ++k) { /* iterate over all non zeros of this row in B */ 1893 if (c_row_idx_flags[bj_i[k]] == PETSC_FALSE) { 1894 cj_i[cnzi++] = bj_i[k]; 1895 c_row_idx_flags[bj_i[k]] = PETSC_TRUE; 1896 } 1897 c_row_val_dense[bj_i[k]] += aa_i[a_col] * ba_i[k]; 1898 } 1899 } 1900 1901 /* Sort array */ 1902 ierr = PetscSortInt(cnzi,cj_i);CHKERRQ(ierr); 1903 /* Step 4 */ 1904 for (k=0; k<cnzi; k++) { 1905 ca_i[k] = c_row_val_dense[cj_i[k]]; 1906 c_row_val_dense[cj_i[k]] = 0.; 1907 c_row_idx_flags[cj_i[k]] = PETSC_FALSE; 1908 } 1909 /* terminate current row */ 1910 aa_i += anzi; 1911 aj_i += anzi; 1912 ca_i += cnzi; 1913 cj_i += cnzi; 1914 ci[i+1] = ci[i] + cnzi; 1915 flops += cnzi; 1916 } 1917 1918 /* Step 5 */ 1919 /* Create the new matrix */ 1920 ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr); 1921 ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr); 1922 ierr = MatSetType(*C,((PetscObject)A)->type_name);CHKERRQ(ierr); 1923 1924 /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */ 1925 /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */ 1926 c = (Mat_SeqAIJ*)((*C)->data); 1927 c->a = ca; 1928 c->free_a = PETSC_TRUE; 1929 c->free_ij = PETSC_TRUE; 1930 c->nonew = 0; 1931 1932 /* set MatInfo */ 1933 afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5; 1934 if (afill < 1.0) afill = 1.0; 1935 c->maxnz = ci[am]; 1936 c->nz = ci[am]; 1937 (*C)->info.mallocs = ndouble; 1938 (*C)->info.fill_ratio_given = fill; 1939 (*C)->info.fill_ratio_needed = afill; 1940 (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Combined; 1941 1942 ierr = PetscFree(c_row_val_dense);CHKERRQ(ierr); 1943 ierr = PetscFree(c_row_idx_flags);CHKERRQ(ierr); 1944 1945 ierr = MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1946 ierr = MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 1947 ierr = PetscLogFlops(flops);CHKERRQ(ierr); 1948 PetscFunctionReturn(0); 1949 } 1950