1 2 #include <../src/mat/impls/aij/seq/aij.h> 3 #include <../src/mat/impls/sbaij/seq/sbaij.h> 4 #include <petscbt.h> 5 #include <../src/mat/utils/freespace.h> 6 7 /* 8 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 9 10 This code does not work and is not called anywhere. It would be registered with MatOrderingRegisterAll() 11 */ 12 PetscErrorCode MatGetOrdering_Flow_SeqAIJ(Mat mat,MatOrderingType type,IS *irow,IS *icol) 13 { 14 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 15 PetscErrorCode ierr; 16 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 17 const PetscInt *ai = a->i, *aj = a->j; 18 const PetscScalar *aa = a->a; 19 PetscBool *done; 20 PetscReal best,past = 0,future; 21 22 PetscFunctionBegin; 23 /* pick initial row */ 24 best = -1; 25 for (i=0; i<n; i++) { 26 future = 0.0; 27 for (j=ai[i]; j<ai[i+1]; j++) { 28 if (aj[j] != i) future += PetscAbsScalar(aa[j]); 29 else past = PetscAbsScalar(aa[j]); 30 } 31 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 32 if (past/future > best) { 33 best = past/future; 34 current = i; 35 } 36 } 37 38 ierr = PetscMalloc1(n,&done);CHKERRQ(ierr); 39 ierr = PetscMemzero(done,n*sizeof(PetscBool));CHKERRQ(ierr); 40 ierr = PetscMalloc1(n,&order);CHKERRQ(ierr); 41 order[0] = current; 42 for (i=0; i<n-1; i++) { 43 done[current] = PETSC_TRUE; 44 best = -1; 45 /* loop over all neighbors of current pivot */ 46 for (j=ai[current]; j<ai[current+1]; j++) { 47 jj = aj[j]; 48 if (done[jj]) continue; 49 /* loop over columns of potential next row computing weights for below and above diagonal */ 50 past = future = 0.0; 51 for (k=ai[jj]; k<ai[jj+1]; k++) { 52 kk = aj[k]; 53 if (done[kk]) past += PetscAbsScalar(aa[k]); 54 else if (kk != jj) future += PetscAbsScalar(aa[k]); 55 } 56 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 57 if (past/future > best) { 58 best = past/future; 59 newcurrent = jj; 60 } 61 } 62 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 63 best = -1; 64 for (k=0; k<n; k++) { 65 if (done[k]) continue; 66 future = 0.0; 67 past = 0.0; 68 for (j=ai[k]; j<ai[k+1]; j++) { 69 kk = aj[j]; 70 if (done[kk]) past += PetscAbsScalar(aa[j]); 71 else if (kk != k) future += PetscAbsScalar(aa[j]); 72 } 73 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 74 if (past/future > best) { 75 best = past/future; 76 newcurrent = k; 77 } 78 } 79 } 80 if (current == newcurrent) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"newcurrent cannot be current"); 81 current = newcurrent; 82 order[i+1] = current; 83 } 84 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,PETSC_COPY_VALUES,irow);CHKERRQ(ierr); 85 *icol = *irow; 86 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 87 ierr = PetscFree(done);CHKERRQ(ierr); 88 ierr = PetscFree(order);CHKERRQ(ierr); 89 PetscFunctionReturn(0); 90 } 91 92 PETSC_INTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 93 { 94 PetscInt n = A->rmap->n; 95 PetscErrorCode ierr; 96 97 PetscFunctionBegin; 98 #if defined(PETSC_USE_COMPLEX) 99 if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported"); 100 #endif 101 ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr); 102 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 103 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) { 104 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 105 106 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 107 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 108 109 ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr); 110 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 111 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 112 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 113 114 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 115 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 116 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported"); 117 (*B)->factortype = ftype; 118 119 ierr = PetscFree((*B)->solvertype);CHKERRQ(ierr); 120 ierr = PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);CHKERRQ(ierr); 121 PetscFunctionReturn(0); 122 } 123 124 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 125 { 126 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 127 IS isicol; 128 PetscErrorCode ierr; 129 const PetscInt *r,*ic; 130 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 131 PetscInt *bi,*bj,*ajtmp; 132 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 133 PetscReal f; 134 PetscInt nlnk,*lnk,k,**bi_ptr; 135 PetscFreeSpaceList free_space=NULL,current_space=NULL; 136 PetscBT lnkbt; 137 PetscBool missing; 138 139 PetscFunctionBegin; 140 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 141 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 142 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 143 144 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 145 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 146 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 147 148 /* get new row pointers */ 149 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 150 bi[0] = 0; 151 152 /* bdiag is location of diagonal in factor */ 153 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 154 bdiag[0] = 0; 155 156 /* linked list for storing column indices of the active row */ 157 nlnk = n + 1; 158 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 159 160 ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr); 161 162 /* initial FreeSpace size is f*(ai[n]+1) */ 163 f = info->fill; 164 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 165 current_space = free_space; 166 167 for (i=0; i<n; i++) { 168 /* copy previous fill into linked list */ 169 nzi = 0; 170 nnz = ai[r[i]+1] - ai[r[i]]; 171 ajtmp = aj + ai[r[i]]; 172 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 173 nzi += nlnk; 174 175 /* add pivot rows into linked list */ 176 row = lnk[n]; 177 while (row < i) { 178 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 179 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 180 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 181 nzi += nlnk; 182 row = lnk[row]; 183 } 184 bi[i+1] = bi[i] + nzi; 185 im[i] = nzi; 186 187 /* mark bdiag */ 188 nzbd = 0; 189 nnz = nzi; 190 k = lnk[n]; 191 while (nnz-- && k < i) { 192 nzbd++; 193 k = lnk[k]; 194 } 195 bdiag[i] = bi[i] + nzbd; 196 197 /* if free space is not available, make more free space */ 198 if (current_space->local_remaining<nzi) { 199 nnz = PetscIntMultTruncate(n - i,nzi); /* estimated and max additional space needed */ 200 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 201 reallocs++; 202 } 203 204 /* copy data into free space, then initialize lnk */ 205 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 206 207 bi_ptr[i] = current_space->array; 208 current_space->array += nzi; 209 current_space->local_used += nzi; 210 current_space->local_remaining -= nzi; 211 } 212 #if defined(PETSC_USE_INFO) 213 if (ai[n] != 0) { 214 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 215 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 216 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 217 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr); 218 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 219 } else { 220 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 221 } 222 #endif 223 224 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 225 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 226 227 /* destroy list of free space and other temporary array(s) */ 228 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 229 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 230 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 231 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 232 233 /* put together the new matrix */ 234 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 235 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 236 b = (Mat_SeqAIJ*)(B)->data; 237 238 b->free_a = PETSC_TRUE; 239 b->free_ij = PETSC_TRUE; 240 b->singlemalloc = PETSC_FALSE; 241 242 ierr = PetscMalloc1(bi[n]+1,&b->a);CHKERRQ(ierr); 243 b->j = bj; 244 b->i = bi; 245 b->diag = bdiag; 246 b->ilen = 0; 247 b->imax = 0; 248 b->row = isrow; 249 b->col = iscol; 250 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 251 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 252 b->icol = isicol; 253 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 254 255 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 256 ierr = PetscLogObjectMemory((PetscObject)B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 257 b->maxnz = b->nz = bi[n]; 258 259 (B)->factortype = MAT_FACTOR_LU; 260 (B)->info.factor_mallocs = reallocs; 261 (B)->info.fill_ratio_given = f; 262 263 if (ai[n]) { 264 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 265 } else { 266 (B)->info.fill_ratio_needed = 0.0; 267 } 268 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 269 if (a->inode.size) { 270 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 271 } 272 PetscFunctionReturn(0); 273 } 274 275 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 276 { 277 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 278 IS isicol; 279 PetscErrorCode ierr; 280 const PetscInt *r,*ic,*ai=a->i,*aj=a->j,*ajtmp; 281 PetscInt i,n=A->rmap->n; 282 PetscInt *bi,*bj; 283 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 284 PetscReal f; 285 PetscInt nlnk,*lnk,k,**bi_ptr; 286 PetscFreeSpaceList free_space=NULL,current_space=NULL; 287 PetscBT lnkbt; 288 PetscBool missing; 289 290 PetscFunctionBegin; 291 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 292 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 293 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 294 295 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 296 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 297 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 298 299 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 300 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 301 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 302 bi[0] = bdiag[0] = 0; 303 304 /* linked list for storing column indices of the active row */ 305 nlnk = n + 1; 306 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 307 308 ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr); 309 310 /* initial FreeSpace size is f*(ai[n]+1) */ 311 f = info->fill; 312 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 313 current_space = free_space; 314 315 for (i=0; i<n; i++) { 316 /* copy previous fill into linked list */ 317 nzi = 0; 318 nnz = ai[r[i]+1] - ai[r[i]]; 319 ajtmp = aj + ai[r[i]]; 320 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 321 nzi += nlnk; 322 323 /* add pivot rows into linked list */ 324 row = lnk[n]; 325 while (row < i) { 326 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 327 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 328 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 329 nzi += nlnk; 330 row = lnk[row]; 331 } 332 bi[i+1] = bi[i] + nzi; 333 im[i] = nzi; 334 335 /* mark bdiag */ 336 nzbd = 0; 337 nnz = nzi; 338 k = lnk[n]; 339 while (nnz-- && k < i) { 340 nzbd++; 341 k = lnk[k]; 342 } 343 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 344 345 /* if free space is not available, make more free space */ 346 if (current_space->local_remaining<nzi) { 347 /* estimated additional space needed */ 348 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(n-1,nzi)); 349 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 350 reallocs++; 351 } 352 353 /* copy data into free space, then initialize lnk */ 354 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 355 356 bi_ptr[i] = current_space->array; 357 current_space->array += nzi; 358 current_space->local_used += nzi; 359 current_space->local_remaining -= nzi; 360 } 361 362 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 363 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 364 365 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 366 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 367 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 368 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 369 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 370 371 /* put together the new matrix */ 372 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 373 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 374 b = (Mat_SeqAIJ*)(B)->data; 375 376 b->free_a = PETSC_TRUE; 377 b->free_ij = PETSC_TRUE; 378 b->singlemalloc = PETSC_FALSE; 379 380 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 381 382 b->j = bj; 383 b->i = bi; 384 b->diag = bdiag; 385 b->ilen = 0; 386 b->imax = 0; 387 b->row = isrow; 388 b->col = iscol; 389 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 390 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 391 b->icol = isicol; 392 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 393 394 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 395 ierr = PetscLogObjectMemory((PetscObject)B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 396 b->maxnz = b->nz = bdiag[0]+1; 397 398 B->factortype = MAT_FACTOR_LU; 399 B->info.factor_mallocs = reallocs; 400 B->info.fill_ratio_given = f; 401 402 if (ai[n]) { 403 B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 404 } else { 405 B->info.fill_ratio_needed = 0.0; 406 } 407 #if defined(PETSC_USE_INFO) 408 if (ai[n] != 0) { 409 PetscReal af = B->info.fill_ratio_needed; 410 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 411 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 412 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr); 413 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 414 } else { 415 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 416 } 417 #endif 418 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 419 if (a->inode.size) { 420 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 421 } 422 ierr = MatSeqAIJCheckInode_FactorLU(B);CHKERRQ(ierr); 423 PetscFunctionReturn(0); 424 } 425 426 /* 427 Trouble in factorization, should we dump the original matrix? 428 */ 429 PetscErrorCode MatFactorDumpMatrix(Mat A) 430 { 431 PetscErrorCode ierr; 432 PetscBool flg = PETSC_FALSE; 433 434 PetscFunctionBegin; 435 ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-mat_factor_dump_on_error",&flg,NULL);CHKERRQ(ierr); 436 if (flg) { 437 PetscViewer viewer; 438 char filename[PETSC_MAX_PATH_LEN]; 439 440 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 441 ierr = PetscViewerBinaryOpen(PetscObjectComm((PetscObject)A),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 442 ierr = MatView(A,viewer);CHKERRQ(ierr); 443 ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr); 444 } 445 PetscFunctionReturn(0); 446 } 447 448 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 449 { 450 Mat C =B; 451 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 452 IS isrow = b->row,isicol = b->icol; 453 PetscErrorCode ierr; 454 const PetscInt *r,*ic,*ics; 455 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 456 PetscInt i,j,k,nz,nzL,row,*pj; 457 const PetscInt *ajtmp,*bjtmp; 458 MatScalar *rtmp,*pc,multiplier,*pv; 459 const MatScalar *aa=a->a,*v; 460 PetscBool row_identity,col_identity; 461 FactorShiftCtx sctx; 462 const PetscInt *ddiag; 463 PetscReal rs; 464 MatScalar d; 465 466 PetscFunctionBegin; 467 /* MatPivotSetUp(): initialize shift context sctx */ 468 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 469 470 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 471 ddiag = a->diag; 472 sctx.shift_top = info->zeropivot; 473 for (i=0; i<n; i++) { 474 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 475 d = (aa)[ddiag[i]]; 476 rs = -PetscAbsScalar(d) - PetscRealPart(d); 477 v = aa+ai[i]; 478 nz = ai[i+1] - ai[i]; 479 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 480 if (rs>sctx.shift_top) sctx.shift_top = rs; 481 } 482 sctx.shift_top *= 1.1; 483 sctx.nshift_max = 5; 484 sctx.shift_lo = 0.; 485 sctx.shift_hi = 1.; 486 } 487 488 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 489 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 490 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 491 ics = ic; 492 493 do { 494 sctx.newshift = PETSC_FALSE; 495 for (i=0; i<n; i++) { 496 /* zero rtmp */ 497 /* L part */ 498 nz = bi[i+1] - bi[i]; 499 bjtmp = bj + bi[i]; 500 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 501 502 /* U part */ 503 nz = bdiag[i]-bdiag[i+1]; 504 bjtmp = bj + bdiag[i+1]+1; 505 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 506 507 /* load in initial (unfactored row) */ 508 nz = ai[r[i]+1] - ai[r[i]]; 509 ajtmp = aj + ai[r[i]]; 510 v = aa + ai[r[i]]; 511 for (j=0; j<nz; j++) { 512 rtmp[ics[ajtmp[j]]] = v[j]; 513 } 514 /* ZeropivotApply() */ 515 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 516 517 /* elimination */ 518 bjtmp = bj + bi[i]; 519 row = *bjtmp++; 520 nzL = bi[i+1] - bi[i]; 521 for (k=0; k < nzL; k++) { 522 pc = rtmp + row; 523 if (*pc != 0.0) { 524 pv = b->a + bdiag[row]; 525 multiplier = *pc * (*pv); 526 *pc = multiplier; 527 528 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 529 pv = b->a + bdiag[row+1]+1; 530 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 531 532 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 533 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 534 } 535 row = *bjtmp++; 536 } 537 538 /* finished row so stick it into b->a */ 539 rs = 0.0; 540 /* L part */ 541 pv = b->a + bi[i]; 542 pj = b->j + bi[i]; 543 nz = bi[i+1] - bi[i]; 544 for (j=0; j<nz; j++) { 545 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 546 } 547 548 /* U part */ 549 pv = b->a + bdiag[i+1]+1; 550 pj = b->j + bdiag[i+1]+1; 551 nz = bdiag[i] - bdiag[i+1]-1; 552 for (j=0; j<nz; j++) { 553 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 554 } 555 556 sctx.rs = rs; 557 sctx.pv = rtmp[i]; 558 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 559 if (sctx.newshift) break; /* break for-loop */ 560 rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */ 561 562 /* Mark diagonal and invert diagonal for simplier triangular solves */ 563 pv = b->a + bdiag[i]; 564 *pv = 1.0/rtmp[i]; 565 566 } /* endof for (i=0; i<n; i++) { */ 567 568 /* MatPivotRefine() */ 569 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 570 /* 571 * if no shift in this attempt & shifting & started shifting & can refine, 572 * then try lower shift 573 */ 574 sctx.shift_hi = sctx.shift_fraction; 575 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 576 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 577 sctx.newshift = PETSC_TRUE; 578 sctx.nshift++; 579 } 580 } while (sctx.newshift); 581 582 ierr = PetscFree(rtmp);CHKERRQ(ierr); 583 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 584 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 585 586 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 587 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 588 if (b->inode.size) { 589 C->ops->solve = MatSolve_SeqAIJ_Inode; 590 } else if (row_identity && col_identity) { 591 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 592 } else { 593 C->ops->solve = MatSolve_SeqAIJ; 594 } 595 C->ops->solveadd = MatSolveAdd_SeqAIJ; 596 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 597 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 598 C->ops->matsolve = MatMatSolve_SeqAIJ; 599 C->assembled = PETSC_TRUE; 600 C->preallocated = PETSC_TRUE; 601 602 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 603 604 /* MatShiftView(A,info,&sctx) */ 605 if (sctx.nshift) { 606 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 607 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 608 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 609 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 610 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 611 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 612 } 613 } 614 PetscFunctionReturn(0); 615 } 616 617 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 618 { 619 Mat C =B; 620 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 621 IS isrow = b->row,isicol = b->icol; 622 PetscErrorCode ierr; 623 const PetscInt *r,*ic,*ics; 624 PetscInt nz,row,i,j,n=A->rmap->n,diag; 625 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 626 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 627 MatScalar *pv,*rtmp,*pc,multiplier,d; 628 const MatScalar *v,*aa=a->a; 629 PetscReal rs=0.0; 630 FactorShiftCtx sctx; 631 const PetscInt *ddiag; 632 PetscBool row_identity, col_identity; 633 634 PetscFunctionBegin; 635 /* MatPivotSetUp(): initialize shift context sctx */ 636 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 637 638 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 639 ddiag = a->diag; 640 sctx.shift_top = info->zeropivot; 641 for (i=0; i<n; i++) { 642 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 643 d = (aa)[ddiag[i]]; 644 rs = -PetscAbsScalar(d) - PetscRealPart(d); 645 v = aa+ai[i]; 646 nz = ai[i+1] - ai[i]; 647 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 648 if (rs>sctx.shift_top) sctx.shift_top = rs; 649 } 650 sctx.shift_top *= 1.1; 651 sctx.nshift_max = 5; 652 sctx.shift_lo = 0.; 653 sctx.shift_hi = 1.; 654 } 655 656 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 657 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 658 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 659 ics = ic; 660 661 do { 662 sctx.newshift = PETSC_FALSE; 663 for (i=0; i<n; i++) { 664 nz = bi[i+1] - bi[i]; 665 bjtmp = bj + bi[i]; 666 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 667 668 /* load in initial (unfactored row) */ 669 nz = ai[r[i]+1] - ai[r[i]]; 670 ajtmp = aj + ai[r[i]]; 671 v = aa + ai[r[i]]; 672 for (j=0; j<nz; j++) { 673 rtmp[ics[ajtmp[j]]] = v[j]; 674 } 675 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 676 677 row = *bjtmp++; 678 while (row < i) { 679 pc = rtmp + row; 680 if (*pc != 0.0) { 681 pv = b->a + diag_offset[row]; 682 pj = b->j + diag_offset[row] + 1; 683 multiplier = *pc / *pv++; 684 *pc = multiplier; 685 nz = bi[row+1] - diag_offset[row] - 1; 686 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 687 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 688 } 689 row = *bjtmp++; 690 } 691 /* finished row so stick it into b->a */ 692 pv = b->a + bi[i]; 693 pj = b->j + bi[i]; 694 nz = bi[i+1] - bi[i]; 695 diag = diag_offset[i] - bi[i]; 696 rs = 0.0; 697 for (j=0; j<nz; j++) { 698 pv[j] = rtmp[pj[j]]; 699 rs += PetscAbsScalar(pv[j]); 700 } 701 rs -= PetscAbsScalar(pv[diag]); 702 703 sctx.rs = rs; 704 sctx.pv = pv[diag]; 705 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 706 if (sctx.newshift) break; 707 pv[diag] = sctx.pv; 708 } 709 710 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 711 /* 712 * if no shift in this attempt & shifting & started shifting & can refine, 713 * then try lower shift 714 */ 715 sctx.shift_hi = sctx.shift_fraction; 716 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 717 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 718 sctx.newshift = PETSC_TRUE; 719 sctx.nshift++; 720 } 721 } while (sctx.newshift); 722 723 /* invert diagonal entries for simplier triangular solves */ 724 for (i=0; i<n; i++) { 725 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 726 } 727 ierr = PetscFree(rtmp);CHKERRQ(ierr); 728 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 729 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 730 731 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 732 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 733 if (row_identity && col_identity) { 734 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 735 } else { 736 C->ops->solve = MatSolve_SeqAIJ_inplace; 737 } 738 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 739 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 740 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 741 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 742 743 C->assembled = PETSC_TRUE; 744 C->preallocated = PETSC_TRUE; 745 746 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 747 if (sctx.nshift) { 748 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 749 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 750 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 751 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 752 } 753 } 754 (C)->ops->solve = MatSolve_SeqAIJ_inplace; 755 (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 756 757 ierr = MatSeqAIJCheckInode(C);CHKERRQ(ierr); 758 PetscFunctionReturn(0); 759 } 760 761 /* 762 This routine implements inplace ILU(0) with row or/and column permutations. 763 Input: 764 A - original matrix 765 Output; 766 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 767 a->j (col index) is permuted by the inverse of colperm, then sorted 768 a->a reordered accordingly with a->j 769 a->diag (ptr to diagonal elements) is updated. 770 */ 771 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 772 { 773 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data; 774 IS isrow = a->row,isicol = a->icol; 775 PetscErrorCode ierr; 776 const PetscInt *r,*ic,*ics; 777 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 778 PetscInt *ajtmp,nz,row; 779 PetscInt *diag = a->diag,nbdiag,*pj; 780 PetscScalar *rtmp,*pc,multiplier,d; 781 MatScalar *pv,*v; 782 PetscReal rs; 783 FactorShiftCtx sctx; 784 const MatScalar *aa=a->a,*vtmp; 785 786 PetscFunctionBegin; 787 if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 788 789 /* MatPivotSetUp(): initialize shift context sctx */ 790 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 791 792 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 793 const PetscInt *ddiag = a->diag; 794 sctx.shift_top = info->zeropivot; 795 for (i=0; i<n; i++) { 796 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 797 d = (aa)[ddiag[i]]; 798 rs = -PetscAbsScalar(d) - PetscRealPart(d); 799 vtmp = aa+ai[i]; 800 nz = ai[i+1] - ai[i]; 801 for (j=0; j<nz; j++) rs += PetscAbsScalar(vtmp[j]); 802 if (rs>sctx.shift_top) sctx.shift_top = rs; 803 } 804 sctx.shift_top *= 1.1; 805 sctx.nshift_max = 5; 806 sctx.shift_lo = 0.; 807 sctx.shift_hi = 1.; 808 } 809 810 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 811 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 812 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 813 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 814 ics = ic; 815 816 #if defined(MV) 817 sctx.shift_top = 0.; 818 sctx.nshift_max = 0; 819 sctx.shift_lo = 0.; 820 sctx.shift_hi = 0.; 821 sctx.shift_fraction = 0.; 822 823 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 824 sctx.shift_top = 0.; 825 for (i=0; i<n; i++) { 826 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 827 d = (a->a)[diag[i]]; 828 rs = -PetscAbsScalar(d) - PetscRealPart(d); 829 v = a->a+ai[i]; 830 nz = ai[i+1] - ai[i]; 831 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 832 if (rs>sctx.shift_top) sctx.shift_top = rs; 833 } 834 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 835 sctx.shift_top *= 1.1; 836 sctx.nshift_max = 5; 837 sctx.shift_lo = 0.; 838 sctx.shift_hi = 1.; 839 } 840 841 sctx.shift_amount = 0.; 842 sctx.nshift = 0; 843 #endif 844 845 do { 846 sctx.newshift = PETSC_FALSE; 847 for (i=0; i<n; i++) { 848 /* load in initial unfactored row */ 849 nz = ai[r[i]+1] - ai[r[i]]; 850 ajtmp = aj + ai[r[i]]; 851 v = a->a + ai[r[i]]; 852 /* sort permuted ajtmp and values v accordingly */ 853 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 854 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 855 856 diag[r[i]] = ai[r[i]]; 857 for (j=0; j<nz; j++) { 858 rtmp[ajtmp[j]] = v[j]; 859 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 860 } 861 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 862 863 row = *ajtmp++; 864 while (row < i) { 865 pc = rtmp + row; 866 if (*pc != 0.0) { 867 pv = a->a + diag[r[row]]; 868 pj = aj + diag[r[row]] + 1; 869 870 multiplier = *pc / *pv++; 871 *pc = multiplier; 872 nz = ai[r[row]+1] - diag[r[row]] - 1; 873 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 874 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 875 } 876 row = *ajtmp++; 877 } 878 /* finished row so overwrite it onto a->a */ 879 pv = a->a + ai[r[i]]; 880 pj = aj + ai[r[i]]; 881 nz = ai[r[i]+1] - ai[r[i]]; 882 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 883 884 rs = 0.0; 885 for (j=0; j<nz; j++) { 886 pv[j] = rtmp[pj[j]]; 887 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 888 } 889 890 sctx.rs = rs; 891 sctx.pv = pv[nbdiag]; 892 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 893 if (sctx.newshift) break; 894 pv[nbdiag] = sctx.pv; 895 } 896 897 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 898 /* 899 * if no shift in this attempt & shifting & started shifting & can refine, 900 * then try lower shift 901 */ 902 sctx.shift_hi = sctx.shift_fraction; 903 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 904 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 905 sctx.newshift = PETSC_TRUE; 906 sctx.nshift++; 907 } 908 } while (sctx.newshift); 909 910 /* invert diagonal entries for simplier triangular solves */ 911 for (i=0; i<n; i++) { 912 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 913 } 914 915 ierr = PetscFree(rtmp);CHKERRQ(ierr); 916 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 917 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 918 919 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 920 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 921 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 922 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 923 924 A->assembled = PETSC_TRUE; 925 A->preallocated = PETSC_TRUE; 926 927 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 928 if (sctx.nshift) { 929 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 930 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 931 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 932 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 933 } 934 } 935 PetscFunctionReturn(0); 936 } 937 938 /* ----------------------------------------------------------- */ 939 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 940 { 941 PetscErrorCode ierr; 942 Mat C; 943 944 PetscFunctionBegin; 945 ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 946 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 947 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 948 949 A->ops->solve = C->ops->solve; 950 A->ops->solvetranspose = C->ops->solvetranspose; 951 952 ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr); 953 ierr = PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 954 PetscFunctionReturn(0); 955 } 956 /* ----------------------------------------------------------- */ 957 958 959 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 960 { 961 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 962 IS iscol = a->col,isrow = a->row; 963 PetscErrorCode ierr; 964 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 965 PetscInt nz; 966 const PetscInt *rout,*cout,*r,*c; 967 PetscScalar *x,*tmp,*tmps,sum; 968 const PetscScalar *b; 969 const MatScalar *aa = a->a,*v; 970 971 PetscFunctionBegin; 972 if (!n) PetscFunctionReturn(0); 973 974 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 975 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 976 tmp = a->solve_work; 977 978 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 979 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 980 981 /* forward solve the lower triangular */ 982 tmp[0] = b[*r++]; 983 tmps = tmp; 984 for (i=1; i<n; i++) { 985 v = aa + ai[i]; 986 vi = aj + ai[i]; 987 nz = a->diag[i] - ai[i]; 988 sum = b[*r++]; 989 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 990 tmp[i] = sum; 991 } 992 993 /* backward solve the upper triangular */ 994 for (i=n-1; i>=0; i--) { 995 v = aa + a->diag[i] + 1; 996 vi = aj + a->diag[i] + 1; 997 nz = ai[i+1] - a->diag[i] - 1; 998 sum = tmp[i]; 999 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1000 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1001 } 1002 1003 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1004 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1005 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1006 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1007 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1008 PetscFunctionReturn(0); 1009 } 1010 1011 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1012 { 1013 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1014 IS iscol = a->col,isrow = a->row; 1015 PetscErrorCode ierr; 1016 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1017 PetscInt nz,neq; 1018 const PetscInt *rout,*cout,*r,*c; 1019 PetscScalar *x,*b,*tmp,*tmps,sum; 1020 const MatScalar *aa = a->a,*v; 1021 PetscBool bisdense,xisdense; 1022 1023 PetscFunctionBegin; 1024 if (!n) PetscFunctionReturn(0); 1025 1026 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1027 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1028 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1029 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1030 1031 ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr); 1032 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1033 1034 tmp = a->solve_work; 1035 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1036 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1037 1038 for (neq=0; neq<B->cmap->n; neq++) { 1039 /* forward solve the lower triangular */ 1040 tmp[0] = b[r[0]]; 1041 tmps = tmp; 1042 for (i=1; i<n; i++) { 1043 v = aa + ai[i]; 1044 vi = aj + ai[i]; 1045 nz = a->diag[i] - ai[i]; 1046 sum = b[r[i]]; 1047 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1048 tmp[i] = sum; 1049 } 1050 /* backward solve the upper triangular */ 1051 for (i=n-1; i>=0; i--) { 1052 v = aa + a->diag[i] + 1; 1053 vi = aj + a->diag[i] + 1; 1054 nz = ai[i+1] - a->diag[i] - 1; 1055 sum = tmp[i]; 1056 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1057 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1058 } 1059 1060 b += n; 1061 x += n; 1062 } 1063 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1064 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1065 ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr); 1066 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1067 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1068 PetscFunctionReturn(0); 1069 } 1070 1071 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1072 { 1073 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1074 IS iscol = a->col,isrow = a->row; 1075 PetscErrorCode ierr; 1076 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1077 PetscInt nz,neq; 1078 const PetscInt *rout,*cout,*r,*c; 1079 PetscScalar *x,*b,*tmp,sum; 1080 const MatScalar *aa = a->a,*v; 1081 PetscBool bisdense,xisdense; 1082 1083 PetscFunctionBegin; 1084 if (!n) PetscFunctionReturn(0); 1085 1086 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1087 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1088 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1089 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1090 1091 ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr); 1092 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1093 1094 tmp = a->solve_work; 1095 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1096 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1097 1098 for (neq=0; neq<B->cmap->n; neq++) { 1099 /* forward solve the lower triangular */ 1100 tmp[0] = b[r[0]]; 1101 v = aa; 1102 vi = aj; 1103 for (i=1; i<n; i++) { 1104 nz = ai[i+1] - ai[i]; 1105 sum = b[r[i]]; 1106 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1107 tmp[i] = sum; 1108 v += nz; vi += nz; 1109 } 1110 1111 /* backward solve the upper triangular */ 1112 for (i=n-1; i>=0; i--) { 1113 v = aa + adiag[i+1]+1; 1114 vi = aj + adiag[i+1]+1; 1115 nz = adiag[i]-adiag[i+1]-1; 1116 sum = tmp[i]; 1117 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1118 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1119 } 1120 1121 b += n; 1122 x += n; 1123 } 1124 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1125 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1126 ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr); 1127 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1128 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1129 PetscFunctionReturn(0); 1130 } 1131 1132 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1133 { 1134 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1135 IS iscol = a->col,isrow = a->row; 1136 PetscErrorCode ierr; 1137 const PetscInt *r,*c,*rout,*cout; 1138 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1139 PetscInt nz,row; 1140 PetscScalar *x,*b,*tmp,*tmps,sum; 1141 const MatScalar *aa = a->a,*v; 1142 1143 PetscFunctionBegin; 1144 if (!n) PetscFunctionReturn(0); 1145 1146 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1147 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1148 tmp = a->solve_work; 1149 1150 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1151 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1152 1153 /* forward solve the lower triangular */ 1154 tmp[0] = b[*r++]; 1155 tmps = tmp; 1156 for (row=1; row<n; row++) { 1157 i = rout[row]; /* permuted row */ 1158 v = aa + ai[i]; 1159 vi = aj + ai[i]; 1160 nz = a->diag[i] - ai[i]; 1161 sum = b[*r++]; 1162 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1163 tmp[row] = sum; 1164 } 1165 1166 /* backward solve the upper triangular */ 1167 for (row=n-1; row>=0; row--) { 1168 i = rout[row]; /* permuted row */ 1169 v = aa + a->diag[i] + 1; 1170 vi = aj + a->diag[i] + 1; 1171 nz = ai[i+1] - a->diag[i] - 1; 1172 sum = tmp[row]; 1173 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1174 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1175 } 1176 1177 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1178 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1179 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1180 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1181 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1182 PetscFunctionReturn(0); 1183 } 1184 1185 /* ----------------------------------------------------------- */ 1186 #include <../src/mat/impls/aij/seq/ftn-kernels/fsolve.h> 1187 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1188 { 1189 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1190 PetscErrorCode ierr; 1191 PetscInt n = A->rmap->n; 1192 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1193 PetscScalar *x; 1194 const PetscScalar *b; 1195 const MatScalar *aa = a->a; 1196 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1197 PetscInt adiag_i,i,nz,ai_i; 1198 const PetscInt *vi; 1199 const MatScalar *v; 1200 PetscScalar sum; 1201 #endif 1202 1203 PetscFunctionBegin; 1204 if (!n) PetscFunctionReturn(0); 1205 1206 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1207 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1208 1209 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1210 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1211 #else 1212 /* forward solve the lower triangular */ 1213 x[0] = b[0]; 1214 for (i=1; i<n; i++) { 1215 ai_i = ai[i]; 1216 v = aa + ai_i; 1217 vi = aj + ai_i; 1218 nz = adiag[i] - ai_i; 1219 sum = b[i]; 1220 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1221 x[i] = sum; 1222 } 1223 1224 /* backward solve the upper triangular */ 1225 for (i=n-1; i>=0; i--) { 1226 adiag_i = adiag[i]; 1227 v = aa + adiag_i + 1; 1228 vi = aj + adiag_i + 1; 1229 nz = ai[i+1] - adiag_i - 1; 1230 sum = x[i]; 1231 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1232 x[i] = sum*aa[adiag_i]; 1233 } 1234 #endif 1235 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1236 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1237 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1238 PetscFunctionReturn(0); 1239 } 1240 1241 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1242 { 1243 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1244 IS iscol = a->col,isrow = a->row; 1245 PetscErrorCode ierr; 1246 PetscInt i, n = A->rmap->n,j; 1247 PetscInt nz; 1248 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1249 PetscScalar *x,*tmp,sum; 1250 const PetscScalar *b; 1251 const MatScalar *aa = a->a,*v; 1252 1253 PetscFunctionBegin; 1254 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1255 1256 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1257 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1258 tmp = a->solve_work; 1259 1260 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1261 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1262 1263 /* forward solve the lower triangular */ 1264 tmp[0] = b[*r++]; 1265 for (i=1; i<n; i++) { 1266 v = aa + ai[i]; 1267 vi = aj + ai[i]; 1268 nz = a->diag[i] - ai[i]; 1269 sum = b[*r++]; 1270 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1271 tmp[i] = sum; 1272 } 1273 1274 /* backward solve the upper triangular */ 1275 for (i=n-1; i>=0; i--) { 1276 v = aa + a->diag[i] + 1; 1277 vi = aj + a->diag[i] + 1; 1278 nz = ai[i+1] - a->diag[i] - 1; 1279 sum = tmp[i]; 1280 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1281 tmp[i] = sum*aa[a->diag[i]]; 1282 x[*c--] += tmp[i]; 1283 } 1284 1285 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1286 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1287 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1288 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1289 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1290 PetscFunctionReturn(0); 1291 } 1292 1293 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1294 { 1295 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1296 IS iscol = a->col,isrow = a->row; 1297 PetscErrorCode ierr; 1298 PetscInt i, n = A->rmap->n,j; 1299 PetscInt nz; 1300 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1301 PetscScalar *x,*tmp,sum; 1302 const PetscScalar *b; 1303 const MatScalar *aa = a->a,*v; 1304 1305 PetscFunctionBegin; 1306 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1307 1308 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1309 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1310 tmp = a->solve_work; 1311 1312 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1313 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1314 1315 /* forward solve the lower triangular */ 1316 tmp[0] = b[r[0]]; 1317 v = aa; 1318 vi = aj; 1319 for (i=1; i<n; i++) { 1320 nz = ai[i+1] - ai[i]; 1321 sum = b[r[i]]; 1322 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1323 tmp[i] = sum; 1324 v += nz; 1325 vi += nz; 1326 } 1327 1328 /* backward solve the upper triangular */ 1329 v = aa + adiag[n-1]; 1330 vi = aj + adiag[n-1]; 1331 for (i=n-1; i>=0; i--) { 1332 nz = adiag[i] - adiag[i+1] - 1; 1333 sum = tmp[i]; 1334 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1335 tmp[i] = sum*v[nz]; 1336 x[c[i]] += tmp[i]; 1337 v += nz+1; vi += nz+1; 1338 } 1339 1340 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1341 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1342 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1343 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1344 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1345 PetscFunctionReturn(0); 1346 } 1347 1348 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1349 { 1350 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1351 IS iscol = a->col,isrow = a->row; 1352 PetscErrorCode ierr; 1353 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1354 PetscInt i,n = A->rmap->n,j; 1355 PetscInt nz; 1356 PetscScalar *x,*tmp,s1; 1357 const MatScalar *aa = a->a,*v; 1358 const PetscScalar *b; 1359 1360 PetscFunctionBegin; 1361 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1362 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1363 tmp = a->solve_work; 1364 1365 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1366 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1367 1368 /* copy the b into temp work space according to permutation */ 1369 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1370 1371 /* forward solve the U^T */ 1372 for (i=0; i<n; i++) { 1373 v = aa + diag[i]; 1374 vi = aj + diag[i] + 1; 1375 nz = ai[i+1] - diag[i] - 1; 1376 s1 = tmp[i]; 1377 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1378 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1379 tmp[i] = s1; 1380 } 1381 1382 /* backward solve the L^T */ 1383 for (i=n-1; i>=0; i--) { 1384 v = aa + diag[i] - 1; 1385 vi = aj + diag[i] - 1; 1386 nz = diag[i] - ai[i]; 1387 s1 = tmp[i]; 1388 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1389 } 1390 1391 /* copy tmp into x according to permutation */ 1392 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1393 1394 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1395 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1396 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1397 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1398 1399 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1400 PetscFunctionReturn(0); 1401 } 1402 1403 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1404 { 1405 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1406 IS iscol = a->col,isrow = a->row; 1407 PetscErrorCode ierr; 1408 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1409 PetscInt i,n = A->rmap->n,j; 1410 PetscInt nz; 1411 PetscScalar *x,*tmp,s1; 1412 const MatScalar *aa = a->a,*v; 1413 const PetscScalar *b; 1414 1415 PetscFunctionBegin; 1416 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1417 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1418 tmp = a->solve_work; 1419 1420 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1421 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1422 1423 /* copy the b into temp work space according to permutation */ 1424 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1425 1426 /* forward solve the U^T */ 1427 for (i=0; i<n; i++) { 1428 v = aa + adiag[i+1] + 1; 1429 vi = aj + adiag[i+1] + 1; 1430 nz = adiag[i] - adiag[i+1] - 1; 1431 s1 = tmp[i]; 1432 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1433 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1434 tmp[i] = s1; 1435 } 1436 1437 /* backward solve the L^T */ 1438 for (i=n-1; i>=0; i--) { 1439 v = aa + ai[i]; 1440 vi = aj + ai[i]; 1441 nz = ai[i+1] - ai[i]; 1442 s1 = tmp[i]; 1443 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1444 } 1445 1446 /* copy tmp into x according to permutation */ 1447 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1448 1449 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1450 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1451 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1452 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1453 1454 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1455 PetscFunctionReturn(0); 1456 } 1457 1458 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1459 { 1460 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1461 IS iscol = a->col,isrow = a->row; 1462 PetscErrorCode ierr; 1463 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1464 PetscInt i,n = A->rmap->n,j; 1465 PetscInt nz; 1466 PetscScalar *x,*tmp,s1; 1467 const MatScalar *aa = a->a,*v; 1468 const PetscScalar *b; 1469 1470 PetscFunctionBegin; 1471 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1472 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1473 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1474 tmp = a->solve_work; 1475 1476 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1477 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1478 1479 /* copy the b into temp work space according to permutation */ 1480 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1481 1482 /* forward solve the U^T */ 1483 for (i=0; i<n; i++) { 1484 v = aa + diag[i]; 1485 vi = aj + diag[i] + 1; 1486 nz = ai[i+1] - diag[i] - 1; 1487 s1 = tmp[i]; 1488 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1489 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1490 tmp[i] = s1; 1491 } 1492 1493 /* backward solve the L^T */ 1494 for (i=n-1; i>=0; i--) { 1495 v = aa + diag[i] - 1; 1496 vi = aj + diag[i] - 1; 1497 nz = diag[i] - ai[i]; 1498 s1 = tmp[i]; 1499 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1500 } 1501 1502 /* copy tmp into x according to permutation */ 1503 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1504 1505 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1506 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1507 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1508 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1509 1510 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1511 PetscFunctionReturn(0); 1512 } 1513 1514 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1515 { 1516 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1517 IS iscol = a->col,isrow = a->row; 1518 PetscErrorCode ierr; 1519 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1520 PetscInt i,n = A->rmap->n,j; 1521 PetscInt nz; 1522 PetscScalar *x,*tmp,s1; 1523 const MatScalar *aa = a->a,*v; 1524 const PetscScalar *b; 1525 1526 PetscFunctionBegin; 1527 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1528 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1529 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1530 tmp = a->solve_work; 1531 1532 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1533 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1534 1535 /* copy the b into temp work space according to permutation */ 1536 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1537 1538 /* forward solve the U^T */ 1539 for (i=0; i<n; i++) { 1540 v = aa + adiag[i+1] + 1; 1541 vi = aj + adiag[i+1] + 1; 1542 nz = adiag[i] - adiag[i+1] - 1; 1543 s1 = tmp[i]; 1544 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1545 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1546 tmp[i] = s1; 1547 } 1548 1549 1550 /* backward solve the L^T */ 1551 for (i=n-1; i>=0; i--) { 1552 v = aa + ai[i]; 1553 vi = aj + ai[i]; 1554 nz = ai[i+1] - ai[i]; 1555 s1 = tmp[i]; 1556 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1557 } 1558 1559 /* copy tmp into x according to permutation */ 1560 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1561 1562 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1563 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1564 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1565 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1566 1567 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1568 PetscFunctionReturn(0); 1569 } 1570 1571 /* ----------------------------------------------------------------*/ 1572 1573 extern PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscBool); 1574 1575 /* 1576 ilu() under revised new data structure. 1577 Factored arrays bj and ba are stored as 1578 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1579 1580 bi=fact->i is an array of size n+1, in which 1581 bi+ 1582 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1583 bi[n]: points to L(n-1,n-1)+1 1584 1585 bdiag=fact->diag is an array of size n+1,in which 1586 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1587 bdiag[n]: points to entry of U(n-1,0)-1 1588 1589 U(i,:) contains bdiag[i] as its last entry, i.e., 1590 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1591 */ 1592 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1593 { 1594 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1595 PetscErrorCode ierr; 1596 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1597 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1598 IS isicol; 1599 1600 PetscFunctionBegin; 1601 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1602 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1603 b = (Mat_SeqAIJ*)(fact)->data; 1604 1605 /* allocate matrix arrays for new data structure */ 1606 ierr = PetscMalloc3(ai[n]+1,&b->a,ai[n]+1,&b->j,n+1,&b->i);CHKERRQ(ierr); 1607 ierr = PetscLogObjectMemory((PetscObject)fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1608 1609 b->singlemalloc = PETSC_TRUE; 1610 if (!b->diag) { 1611 ierr = PetscMalloc1(n+1,&b->diag);CHKERRQ(ierr); 1612 ierr = PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1613 } 1614 bdiag = b->diag; 1615 1616 if (n > 0) { 1617 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1618 } 1619 1620 /* set bi and bj with new data structure */ 1621 bi = b->i; 1622 bj = b->j; 1623 1624 /* L part */ 1625 bi[0] = 0; 1626 for (i=0; i<n; i++) { 1627 nz = adiag[i] - ai[i]; 1628 bi[i+1] = bi[i] + nz; 1629 aj = a->j + ai[i]; 1630 for (j=0; j<nz; j++) { 1631 /* *bj = aj[j]; bj++; */ 1632 bj[k++] = aj[j]; 1633 } 1634 } 1635 1636 /* U part */ 1637 bdiag[n] = bi[n]-1; 1638 for (i=n-1; i>=0; i--) { 1639 nz = ai[i+1] - adiag[i] - 1; 1640 aj = a->j + adiag[i] + 1; 1641 for (j=0; j<nz; j++) { 1642 /* *bj = aj[j]; bj++; */ 1643 bj[k++] = aj[j]; 1644 } 1645 /* diag[i] */ 1646 /* *bj = i; bj++; */ 1647 bj[k++] = i; 1648 bdiag[i] = bdiag[i+1] + nz + 1; 1649 } 1650 1651 fact->factortype = MAT_FACTOR_ILU; 1652 fact->info.factor_mallocs = 0; 1653 fact->info.fill_ratio_given = info->fill; 1654 fact->info.fill_ratio_needed = 1.0; 1655 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1656 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1657 1658 b = (Mat_SeqAIJ*)(fact)->data; 1659 b->row = isrow; 1660 b->col = iscol; 1661 b->icol = isicol; 1662 ierr = PetscMalloc1(fact->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1663 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1664 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1665 PetscFunctionReturn(0); 1666 } 1667 1668 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1669 { 1670 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1671 IS isicol; 1672 PetscErrorCode ierr; 1673 const PetscInt *r,*ic; 1674 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1675 PetscInt *bi,*cols,nnz,*cols_lvl; 1676 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1677 PetscInt i,levels,diagonal_fill; 1678 PetscBool col_identity,row_identity,missing; 1679 PetscReal f; 1680 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1681 PetscBT lnkbt; 1682 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1683 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1684 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1685 1686 PetscFunctionBegin; 1687 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1688 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1689 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1690 1691 levels = (PetscInt)info->levels; 1692 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1693 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1694 if (!levels && row_identity && col_identity) { 1695 /* special case: ilu(0) with natural ordering */ 1696 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1697 if (a->inode.size) { 1698 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1699 } 1700 PetscFunctionReturn(0); 1701 } 1702 1703 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1704 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1705 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1706 1707 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1708 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1709 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1710 bi[0] = bdiag[0] = 0; 1711 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1712 1713 /* create a linked list for storing column indices of the active row */ 1714 nlnk = n + 1; 1715 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1716 1717 /* initial FreeSpace size is f*(ai[n]+1) */ 1718 f = info->fill; 1719 diagonal_fill = (PetscInt)info->diagonal_fill; 1720 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1721 current_space = free_space; 1722 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1723 current_space_lvl = free_space_lvl; 1724 for (i=0; i<n; i++) { 1725 nzi = 0; 1726 /* copy current row into linked list */ 1727 nnz = ai[r[i]+1] - ai[r[i]]; 1728 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1729 cols = aj + ai[r[i]]; 1730 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1731 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1732 nzi += nlnk; 1733 1734 /* make sure diagonal entry is included */ 1735 if (diagonal_fill && lnk[i] == -1) { 1736 fm = n; 1737 while (lnk[fm] < i) fm = lnk[fm]; 1738 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1739 lnk[fm] = i; 1740 lnk_lvl[i] = 0; 1741 nzi++; dcount++; 1742 } 1743 1744 /* add pivot rows into the active row */ 1745 nzbd = 0; 1746 prow = lnk[n]; 1747 while (prow < i) { 1748 nnz = bdiag[prow]; 1749 cols = bj_ptr[prow] + nnz + 1; 1750 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1751 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1752 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1753 nzi += nlnk; 1754 prow = lnk[prow]; 1755 nzbd++; 1756 } 1757 bdiag[i] = nzbd; 1758 bi[i+1] = bi[i] + nzi; 1759 /* if free space is not available, make more free space */ 1760 if (current_space->local_remaining<nzi) { 1761 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(nzi,n - i)); /* estimated and max additional space needed */ 1762 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1763 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1764 reallocs++; 1765 } 1766 1767 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1768 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1769 bj_ptr[i] = current_space->array; 1770 bjlvl_ptr[i] = current_space_lvl->array; 1771 1772 /* make sure the active row i has diagonal entry */ 1773 if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1774 1775 current_space->array += nzi; 1776 current_space->local_used += nzi; 1777 current_space->local_remaining -= nzi; 1778 current_space_lvl->array += nzi; 1779 current_space_lvl->local_used += nzi; 1780 current_space_lvl->local_remaining -= nzi; 1781 } 1782 1783 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1784 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1785 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1786 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1787 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1788 1789 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1790 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1791 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1792 1793 #if defined(PETSC_USE_INFO) 1794 { 1795 PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1796 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 1797 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1798 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 1799 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1800 if (diagonal_fill) { 1801 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 1802 } 1803 } 1804 #endif 1805 /* put together the new matrix */ 1806 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 1807 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 1808 b = (Mat_SeqAIJ*)(fact)->data; 1809 1810 b->free_a = PETSC_TRUE; 1811 b->free_ij = PETSC_TRUE; 1812 b->singlemalloc = PETSC_FALSE; 1813 1814 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 1815 1816 b->j = bj; 1817 b->i = bi; 1818 b->diag = bdiag; 1819 b->ilen = 0; 1820 b->imax = 0; 1821 b->row = isrow; 1822 b->col = iscol; 1823 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1824 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1825 b->icol = isicol; 1826 1827 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 1828 /* In b structure: Free imax, ilen, old a, old j. 1829 Allocate bdiag, solve_work, new a, new j */ 1830 ierr = PetscLogObjectMemory((PetscObject)fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1831 b->maxnz = b->nz = bdiag[0]+1; 1832 1833 (fact)->info.factor_mallocs = reallocs; 1834 (fact)->info.fill_ratio_given = f; 1835 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1836 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1837 if (a->inode.size) { 1838 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1839 } 1840 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1841 PetscFunctionReturn(0); 1842 } 1843 1844 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1845 { 1846 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1847 IS isicol; 1848 PetscErrorCode ierr; 1849 const PetscInt *r,*ic; 1850 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1851 PetscInt *bi,*cols,nnz,*cols_lvl; 1852 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1853 PetscInt i,levels,diagonal_fill; 1854 PetscBool col_identity,row_identity; 1855 PetscReal f; 1856 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1857 PetscBT lnkbt; 1858 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1859 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1860 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1861 PetscBool missing; 1862 1863 PetscFunctionBegin; 1864 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1865 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1866 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1867 1868 f = info->fill; 1869 levels = (PetscInt)info->levels; 1870 diagonal_fill = (PetscInt)info->diagonal_fill; 1871 1872 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1873 1874 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1875 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1876 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1877 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1878 1879 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1880 if (a->inode.size) { 1881 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1882 } 1883 fact->factortype = MAT_FACTOR_ILU; 1884 (fact)->info.factor_mallocs = 0; 1885 (fact)->info.fill_ratio_given = info->fill; 1886 (fact)->info.fill_ratio_needed = 1.0; 1887 1888 b = (Mat_SeqAIJ*)(fact)->data; 1889 b->row = isrow; 1890 b->col = iscol; 1891 b->icol = isicol; 1892 ierr = PetscMalloc1((fact)->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1893 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1894 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1895 PetscFunctionReturn(0); 1896 } 1897 1898 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1899 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1900 1901 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1902 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1903 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1904 bi[0] = bdiag[0] = 0; 1905 1906 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1907 1908 /* create a linked list for storing column indices of the active row */ 1909 nlnk = n + 1; 1910 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1911 1912 /* initial FreeSpace size is f*(ai[n]+1) */ 1913 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1914 current_space = free_space; 1915 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1916 current_space_lvl = free_space_lvl; 1917 1918 for (i=0; i<n; i++) { 1919 nzi = 0; 1920 /* copy current row into linked list */ 1921 nnz = ai[r[i]+1] - ai[r[i]]; 1922 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1923 cols = aj + ai[r[i]]; 1924 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1925 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1926 nzi += nlnk; 1927 1928 /* make sure diagonal entry is included */ 1929 if (diagonal_fill && lnk[i] == -1) { 1930 fm = n; 1931 while (lnk[fm] < i) fm = lnk[fm]; 1932 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1933 lnk[fm] = i; 1934 lnk_lvl[i] = 0; 1935 nzi++; dcount++; 1936 } 1937 1938 /* add pivot rows into the active row */ 1939 nzbd = 0; 1940 prow = lnk[n]; 1941 while (prow < i) { 1942 nnz = bdiag[prow]; 1943 cols = bj_ptr[prow] + nnz + 1; 1944 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1945 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1946 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1947 nzi += nlnk; 1948 prow = lnk[prow]; 1949 nzbd++; 1950 } 1951 bdiag[i] = nzbd; 1952 bi[i+1] = bi[i] + nzi; 1953 1954 /* if free space is not available, make more free space */ 1955 if (current_space->local_remaining<nzi) { 1956 nnz = PetscIntMultTruncate(nzi,n - i); /* estimated and max additional space needed */ 1957 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1958 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1959 reallocs++; 1960 } 1961 1962 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1963 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1964 bj_ptr[i] = current_space->array; 1965 bjlvl_ptr[i] = current_space_lvl->array; 1966 1967 /* make sure the active row i has diagonal entry */ 1968 if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1969 1970 current_space->array += nzi; 1971 current_space->local_used += nzi; 1972 current_space->local_remaining -= nzi; 1973 current_space_lvl->array += nzi; 1974 current_space_lvl->local_used += nzi; 1975 current_space_lvl->local_remaining -= nzi; 1976 } 1977 1978 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1979 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1980 1981 /* destroy list of free space and other temporary arrays */ 1982 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1983 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1984 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1985 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1986 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1987 1988 #if defined(PETSC_USE_INFO) 1989 { 1990 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1991 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 1992 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1993 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 1994 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1995 if (diagonal_fill) { 1996 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 1997 } 1998 } 1999 #endif 2000 2001 /* put together the new matrix */ 2002 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 2003 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 2004 b = (Mat_SeqAIJ*)(fact)->data; 2005 2006 b->free_a = PETSC_TRUE; 2007 b->free_ij = PETSC_TRUE; 2008 b->singlemalloc = PETSC_FALSE; 2009 2010 ierr = PetscMalloc1(bi[n],&b->a);CHKERRQ(ierr); 2011 b->j = bj; 2012 b->i = bi; 2013 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2014 b->diag = bdiag; 2015 b->ilen = 0; 2016 b->imax = 0; 2017 b->row = isrow; 2018 b->col = iscol; 2019 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2020 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2021 b->icol = isicol; 2022 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 2023 /* In b structure: Free imax, ilen, old a, old j. 2024 Allocate bdiag, solve_work, new a, new j */ 2025 ierr = PetscLogObjectMemory((PetscObject)fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2026 b->maxnz = b->nz = bi[n]; 2027 2028 (fact)->info.factor_mallocs = reallocs; 2029 (fact)->info.fill_ratio_given = f; 2030 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2031 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2032 if (a->inode.size) { 2033 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2034 } 2035 PetscFunctionReturn(0); 2036 } 2037 2038 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2039 { 2040 Mat C = B; 2041 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2042 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2043 IS ip=b->row,iip = b->icol; 2044 PetscErrorCode ierr; 2045 const PetscInt *rip,*riip; 2046 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2047 PetscInt *ai=a->i,*aj=a->j; 2048 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2049 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2050 PetscBool perm_identity; 2051 FactorShiftCtx sctx; 2052 PetscReal rs; 2053 MatScalar d,*v; 2054 2055 PetscFunctionBegin; 2056 /* MatPivotSetUp(): initialize shift context sctx */ 2057 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2058 2059 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2060 sctx.shift_top = info->zeropivot; 2061 for (i=0; i<mbs; i++) { 2062 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2063 d = (aa)[a->diag[i]]; 2064 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2065 v = aa+ai[i]; 2066 nz = ai[i+1] - ai[i]; 2067 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2068 if (rs>sctx.shift_top) sctx.shift_top = rs; 2069 } 2070 sctx.shift_top *= 1.1; 2071 sctx.nshift_max = 5; 2072 sctx.shift_lo = 0.; 2073 sctx.shift_hi = 1.; 2074 } 2075 2076 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2077 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2078 2079 /* allocate working arrays 2080 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2081 il: for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays 2082 */ 2083 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);CHKERRQ(ierr); 2084 2085 do { 2086 sctx.newshift = PETSC_FALSE; 2087 2088 for (i=0; i<mbs; i++) c2r[i] = mbs; 2089 if (mbs) il[0] = 0; 2090 2091 for (k = 0; k<mbs; k++) { 2092 /* zero rtmp */ 2093 nz = bi[k+1] - bi[k]; 2094 bjtmp = bj + bi[k]; 2095 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2096 2097 /* load in initial unfactored row */ 2098 bval = ba + bi[k]; 2099 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2100 for (j = jmin; j < jmax; j++) { 2101 col = riip[aj[j]]; 2102 if (col >= k) { /* only take upper triangular entry */ 2103 rtmp[col] = aa[j]; 2104 *bval++ = 0.0; /* for in-place factorization */ 2105 } 2106 } 2107 /* shift the diagonal of the matrix: ZeropivotApply() */ 2108 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2109 2110 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2111 dk = rtmp[k]; 2112 i = c2r[k]; /* first row to be added to k_th row */ 2113 2114 while (i < k) { 2115 nexti = c2r[i]; /* next row to be added to k_th row */ 2116 2117 /* compute multiplier, update diag(k) and U(i,k) */ 2118 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2119 uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2120 dk += uikdi*ba[ili]; /* update diag[k] */ 2121 ba[ili] = uikdi; /* -U(i,k) */ 2122 2123 /* add multiple of row i to k-th row */ 2124 jmin = ili + 1; jmax = bi[i+1]; 2125 if (jmin < jmax) { 2126 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2127 /* update il and c2r for row i */ 2128 il[i] = jmin; 2129 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2130 } 2131 i = nexti; 2132 } 2133 2134 /* copy data into U(k,:) */ 2135 rs = 0.0; 2136 jmin = bi[k]; jmax = bi[k+1]-1; 2137 if (jmin < jmax) { 2138 for (j=jmin; j<jmax; j++) { 2139 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2140 } 2141 /* add the k-th row into il and c2r */ 2142 il[k] = jmin; 2143 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2144 } 2145 2146 /* MatPivotCheck() */ 2147 sctx.rs = rs; 2148 sctx.pv = dk; 2149 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 2150 if (sctx.newshift) break; 2151 dk = sctx.pv; 2152 2153 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2154 } 2155 } while (sctx.newshift); 2156 2157 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2158 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2159 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2160 2161 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2162 if (perm_identity) { 2163 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2164 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2165 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2166 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2167 } else { 2168 B->ops->solve = MatSolve_SeqSBAIJ_1; 2169 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2170 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2171 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2172 } 2173 2174 C->assembled = PETSC_TRUE; 2175 C->preallocated = PETSC_TRUE; 2176 2177 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2178 2179 /* MatPivotView() */ 2180 if (sctx.nshift) { 2181 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2182 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);CHKERRQ(ierr); 2183 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2184 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2185 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 2186 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 2187 } 2188 } 2189 PetscFunctionReturn(0); 2190 } 2191 2192 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2193 { 2194 Mat C = B; 2195 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2196 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2197 IS ip=b->row,iip = b->icol; 2198 PetscErrorCode ierr; 2199 const PetscInt *rip,*riip; 2200 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2201 PetscInt *ai=a->i,*aj=a->j; 2202 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2203 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2204 PetscBool perm_identity; 2205 FactorShiftCtx sctx; 2206 PetscReal rs; 2207 MatScalar d,*v; 2208 2209 PetscFunctionBegin; 2210 /* MatPivotSetUp(): initialize shift context sctx */ 2211 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2212 2213 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2214 sctx.shift_top = info->zeropivot; 2215 for (i=0; i<mbs; i++) { 2216 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2217 d = (aa)[a->diag[i]]; 2218 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2219 v = aa+ai[i]; 2220 nz = ai[i+1] - ai[i]; 2221 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2222 if (rs>sctx.shift_top) sctx.shift_top = rs; 2223 } 2224 sctx.shift_top *= 1.1; 2225 sctx.nshift_max = 5; 2226 sctx.shift_lo = 0.; 2227 sctx.shift_hi = 1.; 2228 } 2229 2230 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2231 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2232 2233 /* initialization */ 2234 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);CHKERRQ(ierr); 2235 2236 do { 2237 sctx.newshift = PETSC_FALSE; 2238 2239 for (i=0; i<mbs; i++) jl[i] = mbs; 2240 il[0] = 0; 2241 2242 for (k = 0; k<mbs; k++) { 2243 /* zero rtmp */ 2244 nz = bi[k+1] - bi[k]; 2245 bjtmp = bj + bi[k]; 2246 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2247 2248 bval = ba + bi[k]; 2249 /* initialize k-th row by the perm[k]-th row of A */ 2250 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2251 for (j = jmin; j < jmax; j++) { 2252 col = riip[aj[j]]; 2253 if (col >= k) { /* only take upper triangular entry */ 2254 rtmp[col] = aa[j]; 2255 *bval++ = 0.0; /* for in-place factorization */ 2256 } 2257 } 2258 /* shift the diagonal of the matrix */ 2259 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2260 2261 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2262 dk = rtmp[k]; 2263 i = jl[k]; /* first row to be added to k_th row */ 2264 2265 while (i < k) { 2266 nexti = jl[i]; /* next row to be added to k_th row */ 2267 2268 /* compute multiplier, update diag(k) and U(i,k) */ 2269 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2270 uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2271 dk += uikdi*ba[ili]; 2272 ba[ili] = uikdi; /* -U(i,k) */ 2273 2274 /* add multiple of row i to k-th row */ 2275 jmin = ili + 1; jmax = bi[i+1]; 2276 if (jmin < jmax) { 2277 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2278 /* update il and jl for row i */ 2279 il[i] = jmin; 2280 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2281 } 2282 i = nexti; 2283 } 2284 2285 /* shift the diagonals when zero pivot is detected */ 2286 /* compute rs=sum of abs(off-diagonal) */ 2287 rs = 0.0; 2288 jmin = bi[k]+1; 2289 nz = bi[k+1] - jmin; 2290 bcol = bj + jmin; 2291 for (j=0; j<nz; j++) { 2292 rs += PetscAbsScalar(rtmp[bcol[j]]); 2293 } 2294 2295 sctx.rs = rs; 2296 sctx.pv = dk; 2297 ierr = MatPivotCheck(B,A,info,&sctx,k);CHKERRQ(ierr); 2298 if (sctx.newshift) break; 2299 dk = sctx.pv; 2300 2301 /* copy data into U(k,:) */ 2302 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2303 jmin = bi[k]+1; jmax = bi[k+1]; 2304 if (jmin < jmax) { 2305 for (j=jmin; j<jmax; j++) { 2306 col = bj[j]; ba[j] = rtmp[col]; 2307 } 2308 /* add the k-th row into il and jl */ 2309 il[k] = jmin; 2310 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2311 } 2312 } 2313 } while (sctx.newshift); 2314 2315 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2316 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2317 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2318 2319 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2320 if (perm_identity) { 2321 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2322 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2323 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2324 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2325 } else { 2326 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2327 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2328 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2329 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2330 } 2331 2332 C->assembled = PETSC_TRUE; 2333 C->preallocated = PETSC_TRUE; 2334 2335 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2336 if (sctx.nshift) { 2337 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2338 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2339 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2340 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2341 } 2342 } 2343 PetscFunctionReturn(0); 2344 } 2345 2346 /* 2347 icc() under revised new data structure. 2348 Factored arrays bj and ba are stored as 2349 U(0,:),...,U(i,:),U(n-1,:) 2350 2351 ui=fact->i is an array of size n+1, in which 2352 ui+ 2353 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2354 ui[n]: points to U(n-1,n-1)+1 2355 2356 udiag=fact->diag is an array of size n,in which 2357 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2358 2359 U(i,:) contains udiag[i] as its last entry, i.e., 2360 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2361 */ 2362 2363 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2364 { 2365 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2366 Mat_SeqSBAIJ *b; 2367 PetscErrorCode ierr; 2368 PetscBool perm_identity,missing; 2369 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2370 const PetscInt *rip,*riip; 2371 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2372 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2373 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2374 PetscReal fill =info->fill,levels=info->levels; 2375 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2376 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2377 PetscBT lnkbt; 2378 IS iperm; 2379 2380 PetscFunctionBegin; 2381 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2382 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2383 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2384 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2385 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2386 2387 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2388 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2389 ui[0] = 0; 2390 2391 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2392 if (!levels && perm_identity) { 2393 for (i=0; i<am; i++) { 2394 ncols = ai[i+1] - a->diag[i]; 2395 ui[i+1] = ui[i] + ncols; 2396 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2397 } 2398 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2399 cols = uj; 2400 for (i=0; i<am; i++) { 2401 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2402 ncols = ai[i+1] - a->diag[i] -1; 2403 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2404 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2405 } 2406 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2407 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2408 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2409 2410 /* initialization */ 2411 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2412 2413 /* jl: linked list for storing indices of the pivot rows 2414 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2415 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2416 for (i=0; i<am; i++) { 2417 jl[i] = am; il[i] = 0; 2418 } 2419 2420 /* create and initialize a linked list for storing column indices of the active row k */ 2421 nlnk = am + 1; 2422 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2423 2424 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2425 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2426 current_space = free_space; 2427 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space_lvl);CHKERRQ(ierr); 2428 current_space_lvl = free_space_lvl; 2429 2430 for (k=0; k<am; k++) { /* for each active row k */ 2431 /* initialize lnk by the column indices of row rip[k] of A */ 2432 nzk = 0; 2433 ncols = ai[rip[k]+1] - ai[rip[k]]; 2434 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2435 ncols_upper = 0; 2436 for (j=0; j<ncols; j++) { 2437 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2438 if (riip[i] >= k) { /* only take upper triangular entry */ 2439 ajtmp[ncols_upper] = i; 2440 ncols_upper++; 2441 } 2442 } 2443 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2444 nzk += nlnk; 2445 2446 /* update lnk by computing fill-in for each pivot row to be merged in */ 2447 prow = jl[k]; /* 1st pivot row */ 2448 2449 while (prow < k) { 2450 nextprow = jl[prow]; 2451 2452 /* merge prow into k-th row */ 2453 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2454 jmax = ui[prow+1]; 2455 ncols = jmax-jmin; 2456 i = jmin - ui[prow]; 2457 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2458 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2459 j = *(uj - 1); 2460 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2461 nzk += nlnk; 2462 2463 /* update il and jl for prow */ 2464 if (jmin < jmax) { 2465 il[prow] = jmin; 2466 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2467 } 2468 prow = nextprow; 2469 } 2470 2471 /* if free space is not available, make more free space */ 2472 if (current_space->local_remaining<nzk) { 2473 i = am - k + 1; /* num of unfactored rows */ 2474 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2475 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2476 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2477 reallocs++; 2478 } 2479 2480 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2481 if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2482 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2483 2484 /* add the k-th row into il and jl */ 2485 if (nzk > 1) { 2486 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2487 jl[k] = jl[i]; jl[i] = k; 2488 il[k] = ui[k] + 1; 2489 } 2490 uj_ptr[k] = current_space->array; 2491 uj_lvl_ptr[k] = current_space_lvl->array; 2492 2493 current_space->array += nzk; 2494 current_space->local_used += nzk; 2495 current_space->local_remaining -= nzk; 2496 2497 current_space_lvl->array += nzk; 2498 current_space_lvl->local_used += nzk; 2499 current_space_lvl->local_remaining -= nzk; 2500 2501 ui[k+1] = ui[k] + nzk; 2502 } 2503 2504 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2505 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2506 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2507 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2508 2509 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2510 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2511 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2512 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2513 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2514 2515 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2516 2517 /* put together the new matrix in MATSEQSBAIJ format */ 2518 b = (Mat_SeqSBAIJ*)(fact)->data; 2519 b->singlemalloc = PETSC_FALSE; 2520 2521 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2522 2523 b->j = uj; 2524 b->i = ui; 2525 b->diag = udiag; 2526 b->free_diag = PETSC_TRUE; 2527 b->ilen = 0; 2528 b->imax = 0; 2529 b->row = perm; 2530 b->col = perm; 2531 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2532 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2533 b->icol = iperm; 2534 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2535 2536 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2537 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2538 2539 b->maxnz = b->nz = ui[am]; 2540 b->free_a = PETSC_TRUE; 2541 b->free_ij = PETSC_TRUE; 2542 2543 fact->info.factor_mallocs = reallocs; 2544 fact->info.fill_ratio_given = fill; 2545 if (ai[am] != 0) { 2546 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2547 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2548 } else { 2549 fact->info.fill_ratio_needed = 0.0; 2550 } 2551 #if defined(PETSC_USE_INFO) 2552 if (ai[am] != 0) { 2553 PetscReal af = fact->info.fill_ratio_needed; 2554 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2555 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2556 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2557 } else { 2558 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2559 } 2560 #endif 2561 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2562 PetscFunctionReturn(0); 2563 } 2564 2565 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2566 { 2567 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2568 Mat_SeqSBAIJ *b; 2569 PetscErrorCode ierr; 2570 PetscBool perm_identity,missing; 2571 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2572 const PetscInt *rip,*riip; 2573 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2574 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2575 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2576 PetscReal fill =info->fill,levels=info->levels; 2577 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2578 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2579 PetscBT lnkbt; 2580 IS iperm; 2581 2582 PetscFunctionBegin; 2583 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2584 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2585 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2586 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2587 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2588 2589 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2590 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2591 ui[0] = 0; 2592 2593 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2594 if (!levels && perm_identity) { 2595 2596 for (i=0; i<am; i++) { 2597 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2598 udiag[i] = ui[i]; 2599 } 2600 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2601 cols = uj; 2602 for (i=0; i<am; i++) { 2603 aj = a->j + a->diag[i]; 2604 ncols = ui[i+1] - ui[i]; 2605 for (j=0; j<ncols; j++) *cols++ = *aj++; 2606 } 2607 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2608 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2609 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2610 2611 /* initialization */ 2612 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2613 2614 /* jl: linked list for storing indices of the pivot rows 2615 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2616 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2617 for (i=0; i<am; i++) { 2618 jl[i] = am; il[i] = 0; 2619 } 2620 2621 /* create and initialize a linked list for storing column indices of the active row k */ 2622 nlnk = am + 1; 2623 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2624 2625 /* initial FreeSpace size is fill*(ai[am]+1) */ 2626 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2627 current_space = free_space; 2628 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space_lvl);CHKERRQ(ierr); 2629 current_space_lvl = free_space_lvl; 2630 2631 for (k=0; k<am; k++) { /* for each active row k */ 2632 /* initialize lnk by the column indices of row rip[k] of A */ 2633 nzk = 0; 2634 ncols = ai[rip[k]+1] - ai[rip[k]]; 2635 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2636 ncols_upper = 0; 2637 for (j=0; j<ncols; j++) { 2638 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2639 if (riip[i] >= k) { /* only take upper triangular entry */ 2640 ajtmp[ncols_upper] = i; 2641 ncols_upper++; 2642 } 2643 } 2644 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2645 nzk += nlnk; 2646 2647 /* update lnk by computing fill-in for each pivot row to be merged in */ 2648 prow = jl[k]; /* 1st pivot row */ 2649 2650 while (prow < k) { 2651 nextprow = jl[prow]; 2652 2653 /* merge prow into k-th row */ 2654 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2655 jmax = ui[prow+1]; 2656 ncols = jmax-jmin; 2657 i = jmin - ui[prow]; 2658 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2659 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2660 j = *(uj - 1); 2661 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2662 nzk += nlnk; 2663 2664 /* update il and jl for prow */ 2665 if (jmin < jmax) { 2666 il[prow] = jmin; 2667 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2668 } 2669 prow = nextprow; 2670 } 2671 2672 /* if free space is not available, make more free space */ 2673 if (current_space->local_remaining<nzk) { 2674 i = am - k + 1; /* num of unfactored rows */ 2675 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2676 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2677 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2678 reallocs++; 2679 } 2680 2681 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2682 if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2683 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2684 2685 /* add the k-th row into il and jl */ 2686 if (nzk > 1) { 2687 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2688 jl[k] = jl[i]; jl[i] = k; 2689 il[k] = ui[k] + 1; 2690 } 2691 uj_ptr[k] = current_space->array; 2692 uj_lvl_ptr[k] = current_space_lvl->array; 2693 2694 current_space->array += nzk; 2695 current_space->local_used += nzk; 2696 current_space->local_remaining -= nzk; 2697 2698 current_space_lvl->array += nzk; 2699 current_space_lvl->local_used += nzk; 2700 current_space_lvl->local_remaining -= nzk; 2701 2702 ui[k+1] = ui[k] + nzk; 2703 } 2704 2705 #if defined(PETSC_USE_INFO) 2706 if (ai[am] != 0) { 2707 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2708 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2709 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2710 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2711 } else { 2712 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2713 } 2714 #endif 2715 2716 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2717 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2718 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2719 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2720 2721 /* destroy list of free space and other temporary array(s) */ 2722 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2723 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2724 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2725 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2726 2727 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2728 2729 /* put together the new matrix in MATSEQSBAIJ format */ 2730 2731 b = (Mat_SeqSBAIJ*)fact->data; 2732 b->singlemalloc = PETSC_FALSE; 2733 2734 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2735 2736 b->j = uj; 2737 b->i = ui; 2738 b->diag = udiag; 2739 b->free_diag = PETSC_TRUE; 2740 b->ilen = 0; 2741 b->imax = 0; 2742 b->row = perm; 2743 b->col = perm; 2744 2745 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2746 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2747 2748 b->icol = iperm; 2749 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2750 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2751 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2752 b->maxnz = b->nz = ui[am]; 2753 b->free_a = PETSC_TRUE; 2754 b->free_ij = PETSC_TRUE; 2755 2756 fact->info.factor_mallocs = reallocs; 2757 fact->info.fill_ratio_given = fill; 2758 if (ai[am] != 0) { 2759 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2760 } else { 2761 fact->info.fill_ratio_needed = 0.0; 2762 } 2763 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2764 PetscFunctionReturn(0); 2765 } 2766 2767 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2768 { 2769 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2770 Mat_SeqSBAIJ *b; 2771 PetscErrorCode ierr; 2772 PetscBool perm_identity,missing; 2773 PetscReal fill = info->fill; 2774 const PetscInt *rip,*riip; 2775 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2776 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2777 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2778 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2779 PetscBT lnkbt; 2780 IS iperm; 2781 2782 PetscFunctionBegin; 2783 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2784 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2785 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2786 2787 /* check whether perm is the identity mapping */ 2788 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2789 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2790 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2791 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2792 2793 /* initialization */ 2794 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2795 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2796 ui[0] = 0; 2797 2798 /* jl: linked list for storing indices of the pivot rows 2799 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2800 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2801 for (i=0; i<am; i++) { 2802 jl[i] = am; il[i] = 0; 2803 } 2804 2805 /* create and initialize a linked list for storing column indices of the active row k */ 2806 nlnk = am + 1; 2807 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2808 2809 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2810 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2811 current_space = free_space; 2812 2813 for (k=0; k<am; k++) { /* for each active row k */ 2814 /* initialize lnk by the column indices of row rip[k] of A */ 2815 nzk = 0; 2816 ncols = ai[rip[k]+1] - ai[rip[k]]; 2817 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2818 ncols_upper = 0; 2819 for (j=0; j<ncols; j++) { 2820 i = riip[*(aj + ai[rip[k]] + j)]; 2821 if (i >= k) { /* only take upper triangular entry */ 2822 cols[ncols_upper] = i; 2823 ncols_upper++; 2824 } 2825 } 2826 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2827 nzk += nlnk; 2828 2829 /* update lnk by computing fill-in for each pivot row to be merged in */ 2830 prow = jl[k]; /* 1st pivot row */ 2831 2832 while (prow < k) { 2833 nextprow = jl[prow]; 2834 /* merge prow into k-th row */ 2835 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2836 jmax = ui[prow+1]; 2837 ncols = jmax-jmin; 2838 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2839 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2840 nzk += nlnk; 2841 2842 /* update il and jl for prow */ 2843 if (jmin < jmax) { 2844 il[prow] = jmin; 2845 j = *uj_ptr; 2846 jl[prow] = jl[j]; 2847 jl[j] = prow; 2848 } 2849 prow = nextprow; 2850 } 2851 2852 /* if free space is not available, make more free space */ 2853 if (current_space->local_remaining<nzk) { 2854 i = am - k + 1; /* num of unfactored rows */ 2855 i = PetscIntMultTruncate(i,PetscMin(nzk,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2856 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2857 reallocs++; 2858 } 2859 2860 /* copy data into free space, then initialize lnk */ 2861 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2862 2863 /* add the k-th row into il and jl */ 2864 if (nzk > 1) { 2865 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2866 jl[k] = jl[i]; jl[i] = k; 2867 il[k] = ui[k] + 1; 2868 } 2869 ui_ptr[k] = current_space->array; 2870 2871 current_space->array += nzk; 2872 current_space->local_used += nzk; 2873 current_space->local_remaining -= nzk; 2874 2875 ui[k+1] = ui[k] + nzk; 2876 } 2877 2878 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2879 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2880 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2881 2882 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2883 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2884 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2885 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2886 2887 /* put together the new matrix in MATSEQSBAIJ format */ 2888 2889 b = (Mat_SeqSBAIJ*)fact->data; 2890 b->singlemalloc = PETSC_FALSE; 2891 b->free_a = PETSC_TRUE; 2892 b->free_ij = PETSC_TRUE; 2893 2894 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2895 2896 b->j = uj; 2897 b->i = ui; 2898 b->diag = udiag; 2899 b->free_diag = PETSC_TRUE; 2900 b->ilen = 0; 2901 b->imax = 0; 2902 b->row = perm; 2903 b->col = perm; 2904 2905 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2906 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2907 2908 b->icol = iperm; 2909 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2910 2911 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2912 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2913 2914 b->maxnz = b->nz = ui[am]; 2915 2916 fact->info.factor_mallocs = reallocs; 2917 fact->info.fill_ratio_given = fill; 2918 if (ai[am] != 0) { 2919 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2920 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2921 } else { 2922 fact->info.fill_ratio_needed = 0.0; 2923 } 2924 #if defined(PETSC_USE_INFO) 2925 if (ai[am] != 0) { 2926 PetscReal af = fact->info.fill_ratio_needed; 2927 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2928 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2929 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2930 } else { 2931 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2932 } 2933 #endif 2934 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2935 PetscFunctionReturn(0); 2936 } 2937 2938 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2939 { 2940 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2941 Mat_SeqSBAIJ *b; 2942 PetscErrorCode ierr; 2943 PetscBool perm_identity,missing; 2944 PetscReal fill = info->fill; 2945 const PetscInt *rip,*riip; 2946 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2947 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2948 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2949 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2950 PetscBT lnkbt; 2951 IS iperm; 2952 2953 PetscFunctionBegin; 2954 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2955 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2956 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2957 2958 /* check whether perm is the identity mapping */ 2959 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2960 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2961 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2962 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2963 2964 /* initialization */ 2965 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2966 ui[0] = 0; 2967 2968 /* jl: linked list for storing indices of the pivot rows 2969 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2970 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2971 for (i=0; i<am; i++) { 2972 jl[i] = am; il[i] = 0; 2973 } 2974 2975 /* create and initialize a linked list for storing column indices of the active row k */ 2976 nlnk = am + 1; 2977 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2978 2979 /* initial FreeSpace size is fill*(ai[am]+1) */ 2980 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2981 current_space = free_space; 2982 2983 for (k=0; k<am; k++) { /* for each active row k */ 2984 /* initialize lnk by the column indices of row rip[k] of A */ 2985 nzk = 0; 2986 ncols = ai[rip[k]+1] - ai[rip[k]]; 2987 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2988 ncols_upper = 0; 2989 for (j=0; j<ncols; j++) { 2990 i = riip[*(aj + ai[rip[k]] + j)]; 2991 if (i >= k) { /* only take upper triangular entry */ 2992 cols[ncols_upper] = i; 2993 ncols_upper++; 2994 } 2995 } 2996 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2997 nzk += nlnk; 2998 2999 /* update lnk by computing fill-in for each pivot row to be merged in */ 3000 prow = jl[k]; /* 1st pivot row */ 3001 3002 while (prow < k) { 3003 nextprow = jl[prow]; 3004 /* merge prow into k-th row */ 3005 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3006 jmax = ui[prow+1]; 3007 ncols = jmax-jmin; 3008 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3009 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3010 nzk += nlnk; 3011 3012 /* update il and jl for prow */ 3013 if (jmin < jmax) { 3014 il[prow] = jmin; 3015 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3016 } 3017 prow = nextprow; 3018 } 3019 3020 /* if free space is not available, make more free space */ 3021 if (current_space->local_remaining<nzk) { 3022 i = am - k + 1; /* num of unfactored rows */ 3023 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3024 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3025 reallocs++; 3026 } 3027 3028 /* copy data into free space, then initialize lnk */ 3029 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3030 3031 /* add the k-th row into il and jl */ 3032 if (nzk-1 > 0) { 3033 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3034 jl[k] = jl[i]; jl[i] = k; 3035 il[k] = ui[k] + 1; 3036 } 3037 ui_ptr[k] = current_space->array; 3038 3039 current_space->array += nzk; 3040 current_space->local_used += nzk; 3041 current_space->local_remaining -= nzk; 3042 3043 ui[k+1] = ui[k] + nzk; 3044 } 3045 3046 #if defined(PETSC_USE_INFO) 3047 if (ai[am] != 0) { 3048 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3049 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 3050 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 3051 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 3052 } else { 3053 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3054 } 3055 #endif 3056 3057 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3058 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3059 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3060 3061 /* destroy list of free space and other temporary array(s) */ 3062 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 3063 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3064 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3065 3066 /* put together the new matrix in MATSEQSBAIJ format */ 3067 3068 b = (Mat_SeqSBAIJ*)fact->data; 3069 b->singlemalloc = PETSC_FALSE; 3070 b->free_a = PETSC_TRUE; 3071 b->free_ij = PETSC_TRUE; 3072 3073 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 3074 3075 b->j = uj; 3076 b->i = ui; 3077 b->diag = 0; 3078 b->ilen = 0; 3079 b->imax = 0; 3080 b->row = perm; 3081 b->col = perm; 3082 3083 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3084 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3085 3086 b->icol = iperm; 3087 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3088 3089 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 3090 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3091 b->maxnz = b->nz = ui[am]; 3092 3093 fact->info.factor_mallocs = reallocs; 3094 fact->info.fill_ratio_given = fill; 3095 if (ai[am] != 0) { 3096 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3097 } else { 3098 fact->info.fill_ratio_needed = 0.0; 3099 } 3100 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3101 PetscFunctionReturn(0); 3102 } 3103 3104 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3105 { 3106 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3107 PetscErrorCode ierr; 3108 PetscInt n = A->rmap->n; 3109 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3110 PetscScalar *x,sum; 3111 const PetscScalar *b; 3112 const MatScalar *aa = a->a,*v; 3113 PetscInt i,nz; 3114 3115 PetscFunctionBegin; 3116 if (!n) PetscFunctionReturn(0); 3117 3118 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3119 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3120 3121 /* forward solve the lower triangular */ 3122 x[0] = b[0]; 3123 v = aa; 3124 vi = aj; 3125 for (i=1; i<n; i++) { 3126 nz = ai[i+1] - ai[i]; 3127 sum = b[i]; 3128 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3129 v += nz; 3130 vi += nz; 3131 x[i] = sum; 3132 } 3133 3134 /* backward solve the upper triangular */ 3135 for (i=n-1; i>=0; i--) { 3136 v = aa + adiag[i+1] + 1; 3137 vi = aj + adiag[i+1] + 1; 3138 nz = adiag[i] - adiag[i+1]-1; 3139 sum = x[i]; 3140 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3141 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3142 } 3143 3144 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3145 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3146 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3147 PetscFunctionReturn(0); 3148 } 3149 3150 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3151 { 3152 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3153 IS iscol = a->col,isrow = a->row; 3154 PetscErrorCode ierr; 3155 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3156 const PetscInt *rout,*cout,*r,*c; 3157 PetscScalar *x,*tmp,sum; 3158 const PetscScalar *b; 3159 const MatScalar *aa = a->a,*v; 3160 3161 PetscFunctionBegin; 3162 if (!n) PetscFunctionReturn(0); 3163 3164 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3165 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3166 tmp = a->solve_work; 3167 3168 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3169 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3170 3171 /* forward solve the lower triangular */ 3172 tmp[0] = b[r[0]]; 3173 v = aa; 3174 vi = aj; 3175 for (i=1; i<n; i++) { 3176 nz = ai[i+1] - ai[i]; 3177 sum = b[r[i]]; 3178 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3179 tmp[i] = sum; 3180 v += nz; vi += nz; 3181 } 3182 3183 /* backward solve the upper triangular */ 3184 for (i=n-1; i>=0; i--) { 3185 v = aa + adiag[i+1]+1; 3186 vi = aj + adiag[i+1]+1; 3187 nz = adiag[i]-adiag[i+1]-1; 3188 sum = tmp[i]; 3189 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3190 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3191 } 3192 3193 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3194 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3195 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3196 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3197 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3198 PetscFunctionReturn(0); 3199 } 3200 3201 /* 3202 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors 3203 */ 3204 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3205 { 3206 Mat B = *fact; 3207 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3208 IS isicol; 3209 PetscErrorCode ierr; 3210 const PetscInt *r,*ic; 3211 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3212 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3213 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3214 PetscInt nlnk,*lnk; 3215 PetscBT lnkbt; 3216 PetscBool row_identity,icol_identity; 3217 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3218 const PetscInt *ics; 3219 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3220 PetscReal dt =info->dt,shift=info->shiftamount; 3221 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3222 PetscBool missing; 3223 3224 PetscFunctionBegin; 3225 if (dt == PETSC_DEFAULT) dt = 0.005; 3226 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3227 3228 /* ------- symbolic factorization, can be reused ---------*/ 3229 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3230 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3231 adiag=a->diag; 3232 3233 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3234 3235 /* bdiag is location of diagonal in factor */ 3236 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3237 ierr = PetscMalloc1(n+1,&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3238 3239 /* allocate row pointers bi */ 3240 ierr = PetscMalloc1(2*n+2,&bi);CHKERRQ(ierr); 3241 3242 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3243 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3244 nnz_max = ai[n]+2*n*dtcount+2; 3245 3246 ierr = PetscMalloc1(nnz_max+1,&bj);CHKERRQ(ierr); 3247 ierr = PetscMalloc1(nnz_max+1,&ba);CHKERRQ(ierr); 3248 3249 /* put together the new matrix */ 3250 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 3251 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 3252 b = (Mat_SeqAIJ*)B->data; 3253 3254 b->free_a = PETSC_TRUE; 3255 b->free_ij = PETSC_TRUE; 3256 b->singlemalloc = PETSC_FALSE; 3257 3258 b->a = ba; 3259 b->j = bj; 3260 b->i = bi; 3261 b->diag = bdiag; 3262 b->ilen = 0; 3263 b->imax = 0; 3264 b->row = isrow; 3265 b->col = iscol; 3266 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3267 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3268 b->icol = isicol; 3269 3270 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 3271 ierr = PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3272 b->maxnz = nnz_max; 3273 3274 B->factortype = MAT_FACTOR_ILUDT; 3275 B->info.factor_mallocs = 0; 3276 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3277 /* ------- end of symbolic factorization ---------*/ 3278 3279 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3280 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3281 ics = ic; 3282 3283 /* linked list for storing column indices of the active row */ 3284 nlnk = n + 1; 3285 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3286 3287 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3288 ierr = PetscMalloc2(n,&im,n,&jtmp);CHKERRQ(ierr); 3289 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3290 ierr = PetscMalloc2(n,&rtmp,n,&vtmp);CHKERRQ(ierr); 3291 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3292 3293 bi[0] = 0; 3294 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3295 bdiag_rev[n] = bdiag[0]; 3296 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3297 for (i=0; i<n; i++) { 3298 /* copy initial fill into linked list */ 3299 nzi = ai[r[i]+1] - ai[r[i]]; 3300 if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3301 nzi_al = adiag[r[i]] - ai[r[i]]; 3302 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3303 ajtmp = aj + ai[r[i]]; 3304 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3305 3306 /* load in initial (unfactored row) */ 3307 aatmp = a->a + ai[r[i]]; 3308 for (j=0; j<nzi; j++) { 3309 rtmp[ics[*ajtmp++]] = *aatmp++; 3310 } 3311 3312 /* add pivot rows into linked list */ 3313 row = lnk[n]; 3314 while (row < i) { 3315 nzi_bl = bi[row+1] - bi[row] + 1; 3316 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3317 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3318 nzi += nlnk; 3319 row = lnk[row]; 3320 } 3321 3322 /* copy data from lnk into jtmp, then initialize lnk */ 3323 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3324 3325 /* numerical factorization */ 3326 bjtmp = jtmp; 3327 row = *bjtmp++; /* 1st pivot row */ 3328 while (row < i) { 3329 pc = rtmp + row; 3330 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3331 multiplier = (*pc) * (*pv); 3332 *pc = multiplier; 3333 if (PetscAbsScalar(*pc) > dt) { /* apply tolerance dropping rule */ 3334 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3335 pv = ba + bdiag[row+1] + 1; 3336 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3337 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3338 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3339 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 3340 } 3341 row = *bjtmp++; 3342 } 3343 3344 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3345 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3346 nzi_bl = 0; j = 0; 3347 while (jtmp[j] < i) { /* Note: jtmp is sorted */ 3348 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3349 nzi_bl++; j++; 3350 } 3351 nzi_bu = nzi - nzi_bl -1; 3352 while (j < nzi) { 3353 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3354 j++; 3355 } 3356 3357 bjtmp = bj + bi[i]; 3358 batmp = ba + bi[i]; 3359 /* apply level dropping rule to L part */ 3360 ncut = nzi_al + dtcount; 3361 if (ncut < nzi_bl) { 3362 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3363 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3364 } else { 3365 ncut = nzi_bl; 3366 } 3367 for (j=0; j<ncut; j++) { 3368 bjtmp[j] = jtmp[j]; 3369 batmp[j] = vtmp[j]; 3370 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3371 } 3372 bi[i+1] = bi[i] + ncut; 3373 nzi = ncut + 1; 3374 3375 /* apply level dropping rule to U part */ 3376 ncut = nzi_au + dtcount; 3377 if (ncut < nzi_bu) { 3378 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3379 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3380 } else { 3381 ncut = nzi_bu; 3382 } 3383 nzi += ncut; 3384 3385 /* mark bdiagonal */ 3386 bdiag[i+1] = bdiag[i] - (ncut + 1); 3387 bdiag_rev[n-i-1] = bdiag[i+1]; 3388 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3389 bjtmp = bj + bdiag[i]; 3390 batmp = ba + bdiag[i]; 3391 *bjtmp = i; 3392 *batmp = diag_tmp; /* rtmp[i]; */ 3393 if (*batmp == 0.0) { 3394 *batmp = dt+shift; 3395 /* printf(" row %d add shift %g\n",i,shift); */ 3396 } 3397 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3398 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3399 3400 bjtmp = bj + bdiag[i+1]+1; 3401 batmp = ba + bdiag[i+1]+1; 3402 for (k=0; k<ncut; k++) { 3403 bjtmp[k] = jtmp[nzi_bl+1+k]; 3404 batmp[k] = vtmp[nzi_bl+1+k]; 3405 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3406 } 3407 /* printf("\n"); */ 3408 3409 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3410 /* 3411 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3412 printf(" ----------------------------\n"); 3413 */ 3414 } /* for (i=0; i<n; i++) */ 3415 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3416 if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]); 3417 3418 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3419 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3420 3421 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3422 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3423 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3424 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3425 3426 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3427 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3428 3429 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3430 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3431 if (row_identity && icol_identity) { 3432 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3433 } else { 3434 B->ops->solve = MatSolve_SeqAIJ; 3435 } 3436 3437 B->ops->solveadd = 0; 3438 B->ops->solvetranspose = 0; 3439 B->ops->solvetransposeadd = 0; 3440 B->ops->matsolve = 0; 3441 B->assembled = PETSC_TRUE; 3442 B->preallocated = PETSC_TRUE; 3443 PetscFunctionReturn(0); 3444 } 3445 3446 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3447 /* 3448 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors 3449 */ 3450 3451 PetscErrorCode MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3452 { 3453 PetscErrorCode ierr; 3454 3455 PetscFunctionBegin; 3456 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3457 PetscFunctionReturn(0); 3458 } 3459 3460 /* 3461 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3462 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3463 */ 3464 /* 3465 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors 3466 */ 3467 3468 PetscErrorCode MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3469 { 3470 Mat C =fact; 3471 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 3472 IS isrow = b->row,isicol = b->icol; 3473 PetscErrorCode ierr; 3474 const PetscInt *r,*ic,*ics; 3475 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3476 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3477 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3478 PetscReal dt=info->dt,shift=info->shiftamount; 3479 PetscBool row_identity, col_identity; 3480 3481 PetscFunctionBegin; 3482 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3483 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3484 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 3485 ics = ic; 3486 3487 for (i=0; i<n; i++) { 3488 /* initialize rtmp array */ 3489 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3490 bjtmp = bj + bi[i]; 3491 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3492 rtmp[i] = 0.0; 3493 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3494 bjtmp = bj + bdiag[i+1] + 1; 3495 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3496 3497 /* load in initial unfactored row of A */ 3498 /* printf("row %d\n",i); */ 3499 nz = ai[r[i]+1] - ai[r[i]]; 3500 ajtmp = aj + ai[r[i]]; 3501 v = aa + ai[r[i]]; 3502 for (j=0; j<nz; j++) { 3503 rtmp[ics[*ajtmp++]] = v[j]; 3504 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3505 } 3506 /* printf("\n"); */ 3507 3508 /* numerical factorization */ 3509 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3510 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3511 k = 0; 3512 while (k < nzl) { 3513 row = *bjtmp++; 3514 /* printf(" prow %d\n",row); */ 3515 pc = rtmp + row; 3516 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3517 multiplier = (*pc) * (*pv); 3518 *pc = multiplier; 3519 if (PetscAbsScalar(multiplier) > dt) { 3520 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3521 pv = b->a + bdiag[row+1] + 1; 3522 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3523 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3524 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 3525 } 3526 k++; 3527 } 3528 3529 /* finished row so stick it into b->a */ 3530 /* L-part */ 3531 pv = b->a + bi[i]; 3532 pj = bj + bi[i]; 3533 nzl = bi[i+1] - bi[i]; 3534 for (j=0; j<nzl; j++) { 3535 pv[j] = rtmp[pj[j]]; 3536 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3537 } 3538 3539 /* diagonal: invert diagonal entries for simplier triangular solves */ 3540 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3541 b->a[bdiag[i]] = 1.0/rtmp[i]; 3542 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3543 3544 /* U-part */ 3545 pv = b->a + bdiag[i+1] + 1; 3546 pj = bj + bdiag[i+1] + 1; 3547 nzu = bdiag[i] - bdiag[i+1] - 1; 3548 for (j=0; j<nzu; j++) { 3549 pv[j] = rtmp[pj[j]]; 3550 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3551 } 3552 /* printf("\n"); */ 3553 } 3554 3555 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3556 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3557 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3558 3559 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3560 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3561 if (row_identity && col_identity) { 3562 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3563 } else { 3564 C->ops->solve = MatSolve_SeqAIJ; 3565 } 3566 C->ops->solveadd = 0; 3567 C->ops->solvetranspose = 0; 3568 C->ops->solvetransposeadd = 0; 3569 C->ops->matsolve = 0; 3570 C->assembled = PETSC_TRUE; 3571 C->preallocated = PETSC_TRUE; 3572 3573 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3574 PetscFunctionReturn(0); 3575 } 3576