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