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