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