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 = PetscArrayzero(done,n);CHKERRQ(ierr); 40 ierr = PetscMalloc1(n,&order);CHKERRQ(ierr); 41 order[0] = current; 42 for (i=0; i<n-1; i++) { 43 done[current] = PETSC_TRUE; 44 best = -1; 45 /* loop over all neighbors of current pivot */ 46 for (j=ai[current]; j<ai[current+1]; j++) { 47 jj = aj[j]; 48 if (done[jj]) continue; 49 /* loop over columns of potential next row computing weights for below and above diagonal */ 50 past = future = 0.0; 51 for (k=ai[jj]; k<ai[jj+1]; k++) { 52 kk = aj[k]; 53 if (done[kk]) past += PetscAbsScalar(aa[k]); 54 else if (kk != jj) future += PetscAbsScalar(aa[k]); 55 } 56 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 57 if (past/future > best) { 58 best = past/future; 59 newcurrent = jj; 60 } 61 } 62 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 63 best = -1; 64 for (k=0; k<n; k++) { 65 if (done[k]) continue; 66 future = 0.0; 67 past = 0.0; 68 for (j=ai[k]; j<ai[k+1]; j++) { 69 kk = aj[j]; 70 if (done[kk]) past += PetscAbsScalar(aa[j]); 71 else if (kk != k) future += PetscAbsScalar(aa[j]); 72 } 73 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 74 if (past/future > best) { 75 best = past/future; 76 newcurrent = k; 77 } 78 } 79 } 80 if (current == newcurrent) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"newcurrent cannot be current"); 81 current = newcurrent; 82 order[i+1] = current; 83 } 84 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,PETSC_COPY_VALUES,irow);CHKERRQ(ierr); 85 *icol = *irow; 86 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 87 ierr = PetscFree(done);CHKERRQ(ierr); 88 ierr = PetscFree(order);CHKERRQ(ierr); 89 PetscFunctionReturn(0); 90 } 91 92 PETSC_INTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 93 { 94 PetscInt n = A->rmap->n; 95 PetscErrorCode ierr; 96 97 PetscFunctionBegin; 98 #if defined(PETSC_USE_COMPLEX) 99 if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported"); 100 #endif 101 ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr); 102 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 103 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) { 104 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 105 106 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 107 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 108 109 ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr); 110 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 111 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 112 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 113 114 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 115 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 116 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported"); 117 (*B)->factortype = ftype; 118 119 ierr = PetscFree((*B)->solvertype);CHKERRQ(ierr); 120 ierr = PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);CHKERRQ(ierr); 121 PetscFunctionReturn(0); 122 } 123 124 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 125 { 126 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 127 IS isicol; 128 PetscErrorCode ierr; 129 const PetscInt *r,*ic; 130 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 131 PetscInt *bi,*bj,*ajtmp; 132 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 133 PetscReal f; 134 PetscInt nlnk,*lnk,k,**bi_ptr; 135 PetscFreeSpaceList free_space=NULL,current_space=NULL; 136 PetscBT lnkbt; 137 PetscBool missing; 138 139 PetscFunctionBegin; 140 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 141 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 142 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 143 144 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 145 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 146 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 147 148 /* get new row pointers */ 149 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 150 bi[0] = 0; 151 152 /* bdiag is location of diagonal in factor */ 153 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 154 bdiag[0] = 0; 155 156 /* linked list for storing column indices of the active row */ 157 nlnk = n + 1; 158 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 159 160 ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr); 161 162 /* initial FreeSpace size is f*(ai[n]+1) */ 163 f = info->fill; 164 if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */ 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 if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */ 314 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 315 current_space = free_space; 316 317 for (i=0; i<n; i++) { 318 /* copy previous fill into linked list */ 319 nzi = 0; 320 nnz = ai[r[i]+1] - ai[r[i]]; 321 ajtmp = aj + ai[r[i]]; 322 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 323 nzi += nlnk; 324 325 /* add pivot rows into linked list */ 326 row = lnk[n]; 327 while (row < i) { 328 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 329 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 330 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 331 nzi += nlnk; 332 row = lnk[row]; 333 } 334 bi[i+1] = bi[i] + nzi; 335 im[i] = nzi; 336 337 /* mark bdiag */ 338 nzbd = 0; 339 nnz = nzi; 340 k = lnk[n]; 341 while (nnz-- && k < i) { 342 nzbd++; 343 k = lnk[k]; 344 } 345 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 346 347 /* if free space is not available, make more free space */ 348 if (current_space->local_remaining<nzi) { 349 /* estimated additional space needed */ 350 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(n-1,nzi)); 351 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 352 reallocs++; 353 } 354 355 /* copy data into free space, then initialize lnk */ 356 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 357 358 bi_ptr[i] = current_space->array; 359 current_space->array += nzi; 360 current_space->local_used += nzi; 361 current_space->local_remaining -= nzi; 362 } 363 364 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 365 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 366 367 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 368 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 369 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 370 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 371 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 372 373 /* put together the new matrix */ 374 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 375 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 376 b = (Mat_SeqAIJ*)(B)->data; 377 378 b->free_a = PETSC_TRUE; 379 b->free_ij = PETSC_TRUE; 380 b->singlemalloc = PETSC_FALSE; 381 382 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 383 384 b->j = bj; 385 b->i = bi; 386 b->diag = bdiag; 387 b->ilen = 0; 388 b->imax = 0; 389 b->row = isrow; 390 b->col = iscol; 391 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 392 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 393 b->icol = isicol; 394 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 395 396 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 397 ierr = PetscLogObjectMemory((PetscObject)B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 398 b->maxnz = b->nz = bdiag[0]+1; 399 400 B->factortype = MAT_FACTOR_LU; 401 B->info.factor_mallocs = reallocs; 402 B->info.fill_ratio_given = f; 403 404 if (ai[n]) { 405 B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 406 } else { 407 B->info.fill_ratio_needed = 0.0; 408 } 409 #if defined(PETSC_USE_INFO) 410 if (ai[n] != 0) { 411 PetscReal af = B->info.fill_ratio_needed; 412 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 413 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 414 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr); 415 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 416 } else { 417 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 418 } 419 #endif 420 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 421 if (a->inode.size) { 422 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 423 } 424 ierr = MatSeqAIJCheckInode_FactorLU(B);CHKERRQ(ierr); 425 PetscFunctionReturn(0); 426 } 427 428 /* 429 Trouble in factorization, should we dump the original matrix? 430 */ 431 PetscErrorCode MatFactorDumpMatrix(Mat A) 432 { 433 PetscErrorCode ierr; 434 PetscBool flg = PETSC_FALSE; 435 436 PetscFunctionBegin; 437 ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-mat_factor_dump_on_error",&flg,NULL);CHKERRQ(ierr); 438 if (flg) { 439 PetscViewer viewer; 440 char filename[PETSC_MAX_PATH_LEN]; 441 442 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 443 ierr = PetscViewerBinaryOpen(PetscObjectComm((PetscObject)A),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 444 ierr = MatView(A,viewer);CHKERRQ(ierr); 445 ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr); 446 } 447 PetscFunctionReturn(0); 448 } 449 450 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 451 { 452 Mat C =B; 453 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 454 IS isrow = b->row,isicol = b->icol; 455 PetscErrorCode ierr; 456 const PetscInt *r,*ic,*ics; 457 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 458 PetscInt i,j,k,nz,nzL,row,*pj; 459 const PetscInt *ajtmp,*bjtmp; 460 MatScalar *rtmp,*pc,multiplier,*pv; 461 const MatScalar *aa=a->a,*v; 462 PetscBool row_identity,col_identity; 463 FactorShiftCtx sctx; 464 const PetscInt *ddiag; 465 PetscReal rs; 466 MatScalar d; 467 468 PetscFunctionBegin; 469 /* MatPivotSetUp(): initialize shift context sctx */ 470 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 471 472 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 473 ddiag = a->diag; 474 sctx.shift_top = info->zeropivot; 475 for (i=0; i<n; i++) { 476 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 477 d = (aa)[ddiag[i]]; 478 rs = -PetscAbsScalar(d) - PetscRealPart(d); 479 v = aa+ai[i]; 480 nz = ai[i+1] - ai[i]; 481 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 482 if (rs>sctx.shift_top) sctx.shift_top = rs; 483 } 484 sctx.shift_top *= 1.1; 485 sctx.nshift_max = 5; 486 sctx.shift_lo = 0.; 487 sctx.shift_hi = 1.; 488 } 489 490 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 491 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 492 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 493 ics = ic; 494 495 do { 496 sctx.newshift = PETSC_FALSE; 497 for (i=0; i<n; i++) { 498 /* zero rtmp */ 499 /* L part */ 500 nz = bi[i+1] - bi[i]; 501 bjtmp = bj + bi[i]; 502 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 503 504 /* U part */ 505 nz = bdiag[i]-bdiag[i+1]; 506 bjtmp = bj + bdiag[i+1]+1; 507 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 508 509 /* load in initial (unfactored row) */ 510 nz = ai[r[i]+1] - ai[r[i]]; 511 ajtmp = aj + ai[r[i]]; 512 v = aa + ai[r[i]]; 513 for (j=0; j<nz; j++) { 514 rtmp[ics[ajtmp[j]]] = v[j]; 515 } 516 /* ZeropivotApply() */ 517 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 518 519 /* elimination */ 520 bjtmp = bj + bi[i]; 521 row = *bjtmp++; 522 nzL = bi[i+1] - bi[i]; 523 for (k=0; k < nzL; k++) { 524 pc = rtmp + row; 525 if (*pc != 0.0) { 526 pv = b->a + bdiag[row]; 527 multiplier = *pc * (*pv); 528 *pc = multiplier; 529 530 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 531 pv = b->a + bdiag[row+1]+1; 532 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 533 534 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 535 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 536 } 537 row = *bjtmp++; 538 } 539 540 /* finished row so stick it into b->a */ 541 rs = 0.0; 542 /* L part */ 543 pv = b->a + bi[i]; 544 pj = b->j + bi[i]; 545 nz = bi[i+1] - bi[i]; 546 for (j=0; j<nz; j++) { 547 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 548 } 549 550 /* U part */ 551 pv = b->a + bdiag[i+1]+1; 552 pj = b->j + bdiag[i+1]+1; 553 nz = bdiag[i] - bdiag[i+1]-1; 554 for (j=0; j<nz; j++) { 555 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 556 } 557 558 sctx.rs = rs; 559 sctx.pv = rtmp[i]; 560 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 561 if (sctx.newshift) break; /* break for-loop */ 562 rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */ 563 564 /* Mark diagonal and invert diagonal for simplier triangular solves */ 565 pv = b->a + bdiag[i]; 566 *pv = 1.0/rtmp[i]; 567 568 } /* endof for (i=0; i<n; i++) { */ 569 570 /* MatPivotRefine() */ 571 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 572 /* 573 * if no shift in this attempt & shifting & started shifting & can refine, 574 * then try lower shift 575 */ 576 sctx.shift_hi = sctx.shift_fraction; 577 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 578 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 579 sctx.newshift = PETSC_TRUE; 580 sctx.nshift++; 581 } 582 } while (sctx.newshift); 583 584 ierr = PetscFree(rtmp);CHKERRQ(ierr); 585 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 586 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 587 588 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 589 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 590 if (b->inode.size) { 591 C->ops->solve = MatSolve_SeqAIJ_Inode; 592 } else if (row_identity && col_identity) { 593 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 594 } else { 595 C->ops->solve = MatSolve_SeqAIJ; 596 } 597 C->ops->solveadd = MatSolveAdd_SeqAIJ; 598 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 599 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 600 C->ops->matsolve = MatMatSolve_SeqAIJ; 601 C->assembled = PETSC_TRUE; 602 C->preallocated = PETSC_TRUE; 603 604 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 605 606 /* MatShiftView(A,info,&sctx) */ 607 if (sctx.nshift) { 608 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 609 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); 610 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 611 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 612 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 613 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 614 } 615 } 616 PetscFunctionReturn(0); 617 } 618 619 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 620 { 621 Mat C =B; 622 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 623 IS isrow = b->row,isicol = b->icol; 624 PetscErrorCode ierr; 625 const PetscInt *r,*ic,*ics; 626 PetscInt nz,row,i,j,n=A->rmap->n,diag; 627 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 628 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 629 MatScalar *pv,*rtmp,*pc,multiplier,d; 630 const MatScalar *v,*aa=a->a; 631 PetscReal rs=0.0; 632 FactorShiftCtx sctx; 633 const PetscInt *ddiag; 634 PetscBool row_identity, col_identity; 635 636 PetscFunctionBegin; 637 /* MatPivotSetUp(): initialize shift context sctx */ 638 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 639 640 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 641 ddiag = a->diag; 642 sctx.shift_top = info->zeropivot; 643 for (i=0; i<n; i++) { 644 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 645 d = (aa)[ddiag[i]]; 646 rs = -PetscAbsScalar(d) - PetscRealPart(d); 647 v = aa+ai[i]; 648 nz = ai[i+1] - ai[i]; 649 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 650 if (rs>sctx.shift_top) sctx.shift_top = rs; 651 } 652 sctx.shift_top *= 1.1; 653 sctx.nshift_max = 5; 654 sctx.shift_lo = 0.; 655 sctx.shift_hi = 1.; 656 } 657 658 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 659 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 660 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 661 ics = ic; 662 663 do { 664 sctx.newshift = PETSC_FALSE; 665 for (i=0; i<n; i++) { 666 nz = bi[i+1] - bi[i]; 667 bjtmp = bj + bi[i]; 668 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 669 670 /* load in initial (unfactored row) */ 671 nz = ai[r[i]+1] - ai[r[i]]; 672 ajtmp = aj + ai[r[i]]; 673 v = aa + ai[r[i]]; 674 for (j=0; j<nz; j++) { 675 rtmp[ics[ajtmp[j]]] = v[j]; 676 } 677 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 678 679 row = *bjtmp++; 680 while (row < i) { 681 pc = rtmp + row; 682 if (*pc != 0.0) { 683 pv = b->a + diag_offset[row]; 684 pj = b->j + diag_offset[row] + 1; 685 multiplier = *pc / *pv++; 686 *pc = multiplier; 687 nz = bi[row+1] - diag_offset[row] - 1; 688 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 689 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 690 } 691 row = *bjtmp++; 692 } 693 /* finished row so stick it into b->a */ 694 pv = b->a + bi[i]; 695 pj = b->j + bi[i]; 696 nz = bi[i+1] - bi[i]; 697 diag = diag_offset[i] - bi[i]; 698 rs = 0.0; 699 for (j=0; j<nz; j++) { 700 pv[j] = rtmp[pj[j]]; 701 rs += PetscAbsScalar(pv[j]); 702 } 703 rs -= PetscAbsScalar(pv[diag]); 704 705 sctx.rs = rs; 706 sctx.pv = pv[diag]; 707 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 708 if (sctx.newshift) break; 709 pv[diag] = sctx.pv; 710 } 711 712 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 713 /* 714 * if no shift in this attempt & shifting & started shifting & can refine, 715 * then try lower shift 716 */ 717 sctx.shift_hi = sctx.shift_fraction; 718 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 719 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 720 sctx.newshift = PETSC_TRUE; 721 sctx.nshift++; 722 } 723 } while (sctx.newshift); 724 725 /* invert diagonal entries for simplier triangular solves */ 726 for (i=0; i<n; i++) { 727 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 728 } 729 ierr = PetscFree(rtmp);CHKERRQ(ierr); 730 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 731 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 732 733 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 734 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 735 if (row_identity && col_identity) { 736 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 737 } else { 738 C->ops->solve = MatSolve_SeqAIJ_inplace; 739 } 740 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 741 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 742 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 743 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 744 745 C->assembled = PETSC_TRUE; 746 C->preallocated = PETSC_TRUE; 747 748 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 749 if (sctx.nshift) { 750 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 751 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); 752 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 753 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 754 } 755 } 756 (C)->ops->solve = MatSolve_SeqAIJ_inplace; 757 (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 758 759 ierr = MatSeqAIJCheckInode(C);CHKERRQ(ierr); 760 PetscFunctionReturn(0); 761 } 762 763 /* 764 This routine implements inplace ILU(0) with row or/and column permutations. 765 Input: 766 A - original matrix 767 Output; 768 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 769 a->j (col index) is permuted by the inverse of colperm, then sorted 770 a->a reordered accordingly with a->j 771 a->diag (ptr to diagonal elements) is updated. 772 */ 773 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 774 { 775 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data; 776 IS isrow = a->row,isicol = a->icol; 777 PetscErrorCode ierr; 778 const PetscInt *r,*ic,*ics; 779 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 780 PetscInt *ajtmp,nz,row; 781 PetscInt *diag = a->diag,nbdiag,*pj; 782 PetscScalar *rtmp,*pc,multiplier,d; 783 MatScalar *pv,*v; 784 PetscReal rs; 785 FactorShiftCtx sctx; 786 const MatScalar *aa=a->a,*vtmp; 787 788 PetscFunctionBegin; 789 if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 790 791 /* MatPivotSetUp(): initialize shift context sctx */ 792 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 793 794 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 795 const PetscInt *ddiag = a->diag; 796 sctx.shift_top = info->zeropivot; 797 for (i=0; i<n; i++) { 798 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 799 d = (aa)[ddiag[i]]; 800 rs = -PetscAbsScalar(d) - PetscRealPart(d); 801 vtmp = aa+ai[i]; 802 nz = ai[i+1] - ai[i]; 803 for (j=0; j<nz; j++) rs += PetscAbsScalar(vtmp[j]); 804 if (rs>sctx.shift_top) sctx.shift_top = rs; 805 } 806 sctx.shift_top *= 1.1; 807 sctx.nshift_max = 5; 808 sctx.shift_lo = 0.; 809 sctx.shift_hi = 1.; 810 } 811 812 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 813 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 814 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 815 ierr = PetscArrayzero(rtmp,n+1);CHKERRQ(ierr); 816 ics = ic; 817 818 #if defined(MV) 819 sctx.shift_top = 0.; 820 sctx.nshift_max = 0; 821 sctx.shift_lo = 0.; 822 sctx.shift_hi = 0.; 823 sctx.shift_fraction = 0.; 824 825 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 826 sctx.shift_top = 0.; 827 for (i=0; i<n; i++) { 828 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 829 d = (a->a)[diag[i]]; 830 rs = -PetscAbsScalar(d) - PetscRealPart(d); 831 v = a->a+ai[i]; 832 nz = ai[i+1] - ai[i]; 833 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 834 if (rs>sctx.shift_top) sctx.shift_top = rs; 835 } 836 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 837 sctx.shift_top *= 1.1; 838 sctx.nshift_max = 5; 839 sctx.shift_lo = 0.; 840 sctx.shift_hi = 1.; 841 } 842 843 sctx.shift_amount = 0.; 844 sctx.nshift = 0; 845 #endif 846 847 do { 848 sctx.newshift = PETSC_FALSE; 849 for (i=0; i<n; i++) { 850 /* load in initial unfactored row */ 851 nz = ai[r[i]+1] - ai[r[i]]; 852 ajtmp = aj + ai[r[i]]; 853 v = a->a + ai[r[i]]; 854 /* sort permuted ajtmp and values v accordingly */ 855 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 856 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 857 858 diag[r[i]] = ai[r[i]]; 859 for (j=0; j<nz; j++) { 860 rtmp[ajtmp[j]] = v[j]; 861 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 862 } 863 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 864 865 row = *ajtmp++; 866 while (row < i) { 867 pc = rtmp + row; 868 if (*pc != 0.0) { 869 pv = a->a + diag[r[row]]; 870 pj = aj + diag[r[row]] + 1; 871 872 multiplier = *pc / *pv++; 873 *pc = multiplier; 874 nz = ai[r[row]+1] - diag[r[row]] - 1; 875 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 876 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 877 } 878 row = *ajtmp++; 879 } 880 /* finished row so overwrite it onto a->a */ 881 pv = a->a + ai[r[i]]; 882 pj = aj + ai[r[i]]; 883 nz = ai[r[i]+1] - ai[r[i]]; 884 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 885 886 rs = 0.0; 887 for (j=0; j<nz; j++) { 888 pv[j] = rtmp[pj[j]]; 889 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 890 } 891 892 sctx.rs = rs; 893 sctx.pv = pv[nbdiag]; 894 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 895 if (sctx.newshift) break; 896 pv[nbdiag] = sctx.pv; 897 } 898 899 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 900 /* 901 * if no shift in this attempt & shifting & started shifting & can refine, 902 * then try lower shift 903 */ 904 sctx.shift_hi = sctx.shift_fraction; 905 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 906 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 907 sctx.newshift = PETSC_TRUE; 908 sctx.nshift++; 909 } 910 } while (sctx.newshift); 911 912 /* invert diagonal entries for simplier triangular solves */ 913 for (i=0; i<n; i++) { 914 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 915 } 916 917 ierr = PetscFree(rtmp);CHKERRQ(ierr); 918 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 919 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 920 921 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 922 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 923 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 924 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 925 926 A->assembled = PETSC_TRUE; 927 A->preallocated = PETSC_TRUE; 928 929 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 930 if (sctx.nshift) { 931 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 932 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); 933 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 934 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 935 } 936 } 937 PetscFunctionReturn(0); 938 } 939 940 /* ----------------------------------------------------------- */ 941 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 942 { 943 PetscErrorCode ierr; 944 Mat C; 945 946 PetscFunctionBegin; 947 ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 948 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 949 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 950 951 A->ops->solve = C->ops->solve; 952 A->ops->solvetranspose = C->ops->solvetranspose; 953 954 ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr); 955 ierr = PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 956 PetscFunctionReturn(0); 957 } 958 /* ----------------------------------------------------------- */ 959 960 961 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 962 { 963 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 964 IS iscol = a->col,isrow = a->row; 965 PetscErrorCode ierr; 966 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 967 PetscInt nz; 968 const PetscInt *rout,*cout,*r,*c; 969 PetscScalar *x,*tmp,*tmps,sum; 970 const PetscScalar *b; 971 const MatScalar *aa = a->a,*v; 972 973 PetscFunctionBegin; 974 if (!n) PetscFunctionReturn(0); 975 976 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 977 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 978 tmp = a->solve_work; 979 980 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 981 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 982 983 /* forward solve the lower triangular */ 984 tmp[0] = b[*r++]; 985 tmps = tmp; 986 for (i=1; i<n; i++) { 987 v = aa + ai[i]; 988 vi = aj + ai[i]; 989 nz = a->diag[i] - ai[i]; 990 sum = b[*r++]; 991 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 992 tmp[i] = sum; 993 } 994 995 /* backward solve the upper triangular */ 996 for (i=n-1; i>=0; i--) { 997 v = aa + a->diag[i] + 1; 998 vi = aj + a->diag[i] + 1; 999 nz = ai[i+1] - a->diag[i] - 1; 1000 sum = tmp[i]; 1001 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1002 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1003 } 1004 1005 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1006 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1007 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1008 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1009 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1010 PetscFunctionReturn(0); 1011 } 1012 1013 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1014 { 1015 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1016 IS iscol = a->col,isrow = a->row; 1017 PetscErrorCode ierr; 1018 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1019 PetscInt nz,neq; 1020 const PetscInt *rout,*cout,*r,*c; 1021 PetscScalar *x,*tmp,*tmps,sum; 1022 const PetscScalar *aa = a->a,*v; 1023 const PetscScalar *b; 1024 PetscBool bisdense,xisdense; 1025 1026 PetscFunctionBegin; 1027 if (!n) PetscFunctionReturn(0); 1028 1029 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1030 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1031 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1032 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1033 1034 ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr); 1035 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1036 1037 tmp = a->solve_work; 1038 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1039 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1040 1041 for (neq=0; neq<B->cmap->n; neq++) { 1042 /* forward solve the lower triangular */ 1043 tmp[0] = b[r[0]]; 1044 tmps = tmp; 1045 for (i=1; i<n; i++) { 1046 v = aa + ai[i]; 1047 vi = aj + ai[i]; 1048 nz = a->diag[i] - ai[i]; 1049 sum = b[r[i]]; 1050 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1051 tmp[i] = sum; 1052 } 1053 /* backward solve the upper triangular */ 1054 for (i=n-1; i>=0; i--) { 1055 v = aa + a->diag[i] + 1; 1056 vi = aj + a->diag[i] + 1; 1057 nz = ai[i+1] - a->diag[i] - 1; 1058 sum = tmp[i]; 1059 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1060 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1061 } 1062 1063 b += n; 1064 x += n; 1065 } 1066 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1067 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1068 ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr); 1069 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1070 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1071 PetscFunctionReturn(0); 1072 } 1073 1074 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1075 { 1076 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1077 IS iscol = a->col,isrow = a->row; 1078 PetscErrorCode ierr; 1079 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1080 PetscInt nz,neq; 1081 const PetscInt *rout,*cout,*r,*c; 1082 PetscScalar *x,*tmp,sum; 1083 const PetscScalar *b; 1084 const PetscScalar *aa = a->a,*v; 1085 PetscBool bisdense,xisdense; 1086 1087 PetscFunctionBegin; 1088 if (!n) PetscFunctionReturn(0); 1089 1090 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1091 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1092 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1093 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1094 1095 ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr); 1096 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1097 1098 tmp = a->solve_work; 1099 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1100 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1101 1102 for (neq=0; neq<B->cmap->n; neq++) { 1103 /* forward solve the lower triangular */ 1104 tmp[0] = b[r[0]]; 1105 v = aa; 1106 vi = aj; 1107 for (i=1; i<n; i++) { 1108 nz = ai[i+1] - ai[i]; 1109 sum = b[r[i]]; 1110 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1111 tmp[i] = sum; 1112 v += nz; vi += nz; 1113 } 1114 1115 /* backward solve the upper triangular */ 1116 for (i=n-1; i>=0; i--) { 1117 v = aa + adiag[i+1]+1; 1118 vi = aj + adiag[i+1]+1; 1119 nz = adiag[i]-adiag[i+1]-1; 1120 sum = tmp[i]; 1121 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1122 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1123 } 1124 1125 b += n; 1126 x += n; 1127 } 1128 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1129 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1130 ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr); 1131 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1132 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1133 PetscFunctionReturn(0); 1134 } 1135 1136 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1137 { 1138 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1139 IS iscol = a->col,isrow = a->row; 1140 PetscErrorCode ierr; 1141 const PetscInt *r,*c,*rout,*cout; 1142 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1143 PetscInt nz,row; 1144 PetscScalar *x,*tmp,*tmps,sum; 1145 const PetscScalar *b; 1146 const MatScalar *aa = a->a,*v; 1147 1148 PetscFunctionBegin; 1149 if (!n) PetscFunctionReturn(0); 1150 1151 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1152 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1153 tmp = a->solve_work; 1154 1155 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1156 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1157 1158 /* forward solve the lower triangular */ 1159 tmp[0] = b[*r++]; 1160 tmps = tmp; 1161 for (row=1; row<n; row++) { 1162 i = rout[row]; /* permuted row */ 1163 v = aa + ai[i]; 1164 vi = aj + ai[i]; 1165 nz = a->diag[i] - ai[i]; 1166 sum = b[*r++]; 1167 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1168 tmp[row] = sum; 1169 } 1170 1171 /* backward solve the upper triangular */ 1172 for (row=n-1; row>=0; row--) { 1173 i = rout[row]; /* permuted row */ 1174 v = aa + a->diag[i] + 1; 1175 vi = aj + a->diag[i] + 1; 1176 nz = ai[i+1] - a->diag[i] - 1; 1177 sum = tmp[row]; 1178 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1179 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1180 } 1181 1182 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1183 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1184 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1185 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1186 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1187 PetscFunctionReturn(0); 1188 } 1189 1190 /* ----------------------------------------------------------- */ 1191 #include <../src/mat/impls/aij/seq/ftn-kernels/fsolve.h> 1192 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1193 { 1194 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1195 PetscErrorCode ierr; 1196 PetscInt n = A->rmap->n; 1197 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1198 PetscScalar *x; 1199 const PetscScalar *b; 1200 const MatScalar *aa = a->a; 1201 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1202 PetscInt adiag_i,i,nz,ai_i; 1203 const PetscInt *vi; 1204 const MatScalar *v; 1205 PetscScalar sum; 1206 #endif 1207 1208 PetscFunctionBegin; 1209 if (!n) PetscFunctionReturn(0); 1210 1211 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1212 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1213 1214 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1215 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1216 #else 1217 /* forward solve the lower triangular */ 1218 x[0] = b[0]; 1219 for (i=1; i<n; i++) { 1220 ai_i = ai[i]; 1221 v = aa + ai_i; 1222 vi = aj + ai_i; 1223 nz = adiag[i] - ai_i; 1224 sum = b[i]; 1225 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1226 x[i] = sum; 1227 } 1228 1229 /* backward solve the upper triangular */ 1230 for (i=n-1; i>=0; i--) { 1231 adiag_i = adiag[i]; 1232 v = aa + adiag_i + 1; 1233 vi = aj + adiag_i + 1; 1234 nz = ai[i+1] - adiag_i - 1; 1235 sum = x[i]; 1236 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1237 x[i] = sum*aa[adiag_i]; 1238 } 1239 #endif 1240 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1241 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1242 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1243 PetscFunctionReturn(0); 1244 } 1245 1246 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1247 { 1248 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1249 IS iscol = a->col,isrow = a->row; 1250 PetscErrorCode ierr; 1251 PetscInt i, n = A->rmap->n,j; 1252 PetscInt nz; 1253 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1254 PetscScalar *x,*tmp,sum; 1255 const PetscScalar *b; 1256 const MatScalar *aa = a->a,*v; 1257 1258 PetscFunctionBegin; 1259 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1260 1261 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1262 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1263 tmp = a->solve_work; 1264 1265 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1266 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1267 1268 /* forward solve the lower triangular */ 1269 tmp[0] = b[*r++]; 1270 for (i=1; i<n; i++) { 1271 v = aa + ai[i]; 1272 vi = aj + ai[i]; 1273 nz = a->diag[i] - ai[i]; 1274 sum = b[*r++]; 1275 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1276 tmp[i] = sum; 1277 } 1278 1279 /* backward solve the upper triangular */ 1280 for (i=n-1; i>=0; i--) { 1281 v = aa + a->diag[i] + 1; 1282 vi = aj + a->diag[i] + 1; 1283 nz = ai[i+1] - a->diag[i] - 1; 1284 sum = tmp[i]; 1285 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1286 tmp[i] = sum*aa[a->diag[i]]; 1287 x[*c--] += tmp[i]; 1288 } 1289 1290 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1291 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1292 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1293 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1294 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1295 PetscFunctionReturn(0); 1296 } 1297 1298 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1299 { 1300 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1301 IS iscol = a->col,isrow = a->row; 1302 PetscErrorCode ierr; 1303 PetscInt i, n = A->rmap->n,j; 1304 PetscInt nz; 1305 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1306 PetscScalar *x,*tmp,sum; 1307 const PetscScalar *b; 1308 const MatScalar *aa = a->a,*v; 1309 1310 PetscFunctionBegin; 1311 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1312 1313 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1314 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1315 tmp = a->solve_work; 1316 1317 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1318 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1319 1320 /* forward solve the lower triangular */ 1321 tmp[0] = b[r[0]]; 1322 v = aa; 1323 vi = aj; 1324 for (i=1; i<n; i++) { 1325 nz = ai[i+1] - ai[i]; 1326 sum = b[r[i]]; 1327 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1328 tmp[i] = sum; 1329 v += nz; 1330 vi += nz; 1331 } 1332 1333 /* backward solve the upper triangular */ 1334 v = aa + adiag[n-1]; 1335 vi = aj + adiag[n-1]; 1336 for (i=n-1; i>=0; i--) { 1337 nz = adiag[i] - adiag[i+1] - 1; 1338 sum = tmp[i]; 1339 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1340 tmp[i] = sum*v[nz]; 1341 x[c[i]] += tmp[i]; 1342 v += nz+1; vi += nz+1; 1343 } 1344 1345 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1346 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1347 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1348 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1349 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1350 PetscFunctionReturn(0); 1351 } 1352 1353 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1354 { 1355 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1356 IS iscol = a->col,isrow = a->row; 1357 PetscErrorCode ierr; 1358 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1359 PetscInt i,n = A->rmap->n,j; 1360 PetscInt nz; 1361 PetscScalar *x,*tmp,s1; 1362 const MatScalar *aa = a->a,*v; 1363 const PetscScalar *b; 1364 1365 PetscFunctionBegin; 1366 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1367 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1368 tmp = a->solve_work; 1369 1370 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1371 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1372 1373 /* copy the b into temp work space according to permutation */ 1374 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1375 1376 /* forward solve the U^T */ 1377 for (i=0; i<n; i++) { 1378 v = aa + diag[i]; 1379 vi = aj + diag[i] + 1; 1380 nz = ai[i+1] - diag[i] - 1; 1381 s1 = tmp[i]; 1382 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1383 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1384 tmp[i] = s1; 1385 } 1386 1387 /* backward solve the L^T */ 1388 for (i=n-1; i>=0; i--) { 1389 v = aa + diag[i] - 1; 1390 vi = aj + diag[i] - 1; 1391 nz = diag[i] - ai[i]; 1392 s1 = tmp[i]; 1393 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1394 } 1395 1396 /* copy tmp into x according to permutation */ 1397 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1398 1399 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1400 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1401 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1402 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1403 1404 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1405 PetscFunctionReturn(0); 1406 } 1407 1408 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1409 { 1410 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1411 IS iscol = a->col,isrow = a->row; 1412 PetscErrorCode ierr; 1413 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1414 PetscInt i,n = A->rmap->n,j; 1415 PetscInt nz; 1416 PetscScalar *x,*tmp,s1; 1417 const MatScalar *aa = a->a,*v; 1418 const PetscScalar *b; 1419 1420 PetscFunctionBegin; 1421 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1422 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1423 tmp = a->solve_work; 1424 1425 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1426 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1427 1428 /* copy the b into temp work space according to permutation */ 1429 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1430 1431 /* forward solve the U^T */ 1432 for (i=0; i<n; i++) { 1433 v = aa + adiag[i+1] + 1; 1434 vi = aj + adiag[i+1] + 1; 1435 nz = adiag[i] - adiag[i+1] - 1; 1436 s1 = tmp[i]; 1437 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1438 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1439 tmp[i] = s1; 1440 } 1441 1442 /* backward solve the L^T */ 1443 for (i=n-1; i>=0; i--) { 1444 v = aa + ai[i]; 1445 vi = aj + ai[i]; 1446 nz = ai[i+1] - ai[i]; 1447 s1 = tmp[i]; 1448 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1449 } 1450 1451 /* copy tmp into x according to permutation */ 1452 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1453 1454 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1455 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1456 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1457 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1458 1459 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1460 PetscFunctionReturn(0); 1461 } 1462 1463 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1464 { 1465 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1466 IS iscol = a->col,isrow = a->row; 1467 PetscErrorCode ierr; 1468 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1469 PetscInt i,n = A->rmap->n,j; 1470 PetscInt nz; 1471 PetscScalar *x,*tmp,s1; 1472 const MatScalar *aa = a->a,*v; 1473 const PetscScalar *b; 1474 1475 PetscFunctionBegin; 1476 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1477 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1478 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1479 tmp = a->solve_work; 1480 1481 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1482 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1483 1484 /* copy the b into temp work space according to permutation */ 1485 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1486 1487 /* forward solve the U^T */ 1488 for (i=0; i<n; i++) { 1489 v = aa + diag[i]; 1490 vi = aj + diag[i] + 1; 1491 nz = ai[i+1] - diag[i] - 1; 1492 s1 = tmp[i]; 1493 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1494 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1495 tmp[i] = s1; 1496 } 1497 1498 /* backward solve the L^T */ 1499 for (i=n-1; i>=0; i--) { 1500 v = aa + diag[i] - 1; 1501 vi = aj + diag[i] - 1; 1502 nz = diag[i] - ai[i]; 1503 s1 = tmp[i]; 1504 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1505 } 1506 1507 /* copy tmp into x according to permutation */ 1508 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1509 1510 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1511 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1512 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1513 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1514 1515 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1516 PetscFunctionReturn(0); 1517 } 1518 1519 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1520 { 1521 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1522 IS iscol = a->col,isrow = a->row; 1523 PetscErrorCode ierr; 1524 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1525 PetscInt i,n = A->rmap->n,j; 1526 PetscInt nz; 1527 PetscScalar *x,*tmp,s1; 1528 const MatScalar *aa = a->a,*v; 1529 const PetscScalar *b; 1530 1531 PetscFunctionBegin; 1532 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1533 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1534 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1535 tmp = a->solve_work; 1536 1537 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1538 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1539 1540 /* copy the b into temp work space according to permutation */ 1541 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1542 1543 /* forward solve the U^T */ 1544 for (i=0; i<n; i++) { 1545 v = aa + adiag[i+1] + 1; 1546 vi = aj + adiag[i+1] + 1; 1547 nz = adiag[i] - adiag[i+1] - 1; 1548 s1 = tmp[i]; 1549 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1550 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1551 tmp[i] = s1; 1552 } 1553 1554 1555 /* backward solve the L^T */ 1556 for (i=n-1; i>=0; i--) { 1557 v = aa + ai[i]; 1558 vi = aj + ai[i]; 1559 nz = ai[i+1] - ai[i]; 1560 s1 = tmp[i]; 1561 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1562 } 1563 1564 /* copy tmp into x according to permutation */ 1565 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1566 1567 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1568 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1569 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1570 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1571 1572 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1573 PetscFunctionReturn(0); 1574 } 1575 1576 /* ----------------------------------------------------------------*/ 1577 1578 /* 1579 ilu() under revised new data structure. 1580 Factored arrays bj and ba are stored as 1581 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1582 1583 bi=fact->i is an array of size n+1, in which 1584 bi+ 1585 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1586 bi[n]: points to L(n-1,n-1)+1 1587 1588 bdiag=fact->diag is an array of size n+1,in which 1589 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1590 bdiag[n]: points to entry of U(n-1,0)-1 1591 1592 U(i,:) contains bdiag[i] as its last entry, i.e., 1593 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1594 */ 1595 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1596 { 1597 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1598 PetscErrorCode ierr; 1599 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1600 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1601 IS isicol; 1602 1603 PetscFunctionBegin; 1604 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1605 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1606 b = (Mat_SeqAIJ*)(fact)->data; 1607 1608 /* allocate matrix arrays for new data structure */ 1609 ierr = PetscMalloc3(ai[n]+1,&b->a,ai[n]+1,&b->j,n+1,&b->i);CHKERRQ(ierr); 1610 ierr = PetscLogObjectMemory((PetscObject)fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1611 1612 b->singlemalloc = PETSC_TRUE; 1613 if (!b->diag) { 1614 ierr = PetscMalloc1(n+1,&b->diag);CHKERRQ(ierr); 1615 ierr = PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1616 } 1617 bdiag = b->diag; 1618 1619 if (n > 0) { 1620 ierr = PetscArrayzero(b->a,ai[n]);CHKERRQ(ierr); 1621 } 1622 1623 /* set bi and bj with new data structure */ 1624 bi = b->i; 1625 bj = b->j; 1626 1627 /* L part */ 1628 bi[0] = 0; 1629 for (i=0; i<n; i++) { 1630 nz = adiag[i] - ai[i]; 1631 bi[i+1] = bi[i] + nz; 1632 aj = a->j + ai[i]; 1633 for (j=0; j<nz; j++) { 1634 /* *bj = aj[j]; bj++; */ 1635 bj[k++] = aj[j]; 1636 } 1637 } 1638 1639 /* U part */ 1640 bdiag[n] = bi[n]-1; 1641 for (i=n-1; i>=0; i--) { 1642 nz = ai[i+1] - adiag[i] - 1; 1643 aj = a->j + adiag[i] + 1; 1644 for (j=0; j<nz; j++) { 1645 /* *bj = aj[j]; bj++; */ 1646 bj[k++] = aj[j]; 1647 } 1648 /* diag[i] */ 1649 /* *bj = i; bj++; */ 1650 bj[k++] = i; 1651 bdiag[i] = bdiag[i+1] + nz + 1; 1652 } 1653 1654 fact->factortype = MAT_FACTOR_ILU; 1655 fact->info.factor_mallocs = 0; 1656 fact->info.fill_ratio_given = info->fill; 1657 fact->info.fill_ratio_needed = 1.0; 1658 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1659 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1660 1661 b = (Mat_SeqAIJ*)(fact)->data; 1662 b->row = isrow; 1663 b->col = iscol; 1664 b->icol = isicol; 1665 ierr = PetscMalloc1(fact->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1666 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1667 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1668 PetscFunctionReturn(0); 1669 } 1670 1671 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1672 { 1673 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1674 IS isicol; 1675 PetscErrorCode ierr; 1676 const PetscInt *r,*ic; 1677 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1678 PetscInt *bi,*cols,nnz,*cols_lvl; 1679 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1680 PetscInt i,levels,diagonal_fill; 1681 PetscBool col_identity,row_identity,missing; 1682 PetscReal f; 1683 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1684 PetscBT lnkbt; 1685 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1686 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1687 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1688 1689 PetscFunctionBegin; 1690 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); 1691 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1692 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1693 1694 levels = (PetscInt)info->levels; 1695 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1696 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1697 if (!levels && row_identity && col_identity) { 1698 /* special case: ilu(0) with natural ordering */ 1699 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1700 if (a->inode.size) { 1701 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1702 } 1703 PetscFunctionReturn(0); 1704 } 1705 1706 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1707 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1708 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1709 1710 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1711 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1712 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1713 bi[0] = bdiag[0] = 0; 1714 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1715 1716 /* create a linked list for storing column indices of the active row */ 1717 nlnk = n + 1; 1718 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1719 1720 /* initial FreeSpace size is f*(ai[n]+1) */ 1721 f = info->fill; 1722 diagonal_fill = (PetscInt)info->diagonal_fill; 1723 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1724 current_space = free_space; 1725 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1726 current_space_lvl = free_space_lvl; 1727 for (i=0; i<n; i++) { 1728 nzi = 0; 1729 /* copy current row into linked list */ 1730 nnz = ai[r[i]+1] - ai[r[i]]; 1731 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); 1732 cols = aj + ai[r[i]]; 1733 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1734 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1735 nzi += nlnk; 1736 1737 /* make sure diagonal entry is included */ 1738 if (diagonal_fill && lnk[i] == -1) { 1739 fm = n; 1740 while (lnk[fm] < i) fm = lnk[fm]; 1741 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1742 lnk[fm] = i; 1743 lnk_lvl[i] = 0; 1744 nzi++; dcount++; 1745 } 1746 1747 /* add pivot rows into the active row */ 1748 nzbd = 0; 1749 prow = lnk[n]; 1750 while (prow < i) { 1751 nnz = bdiag[prow]; 1752 cols = bj_ptr[prow] + nnz + 1; 1753 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1754 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1755 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1756 nzi += nlnk; 1757 prow = lnk[prow]; 1758 nzbd++; 1759 } 1760 bdiag[i] = nzbd; 1761 bi[i+1] = bi[i] + nzi; 1762 /* if free space is not available, make more free space */ 1763 if (current_space->local_remaining<nzi) { 1764 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(nzi,n - i)); /* estimated and max additional space needed */ 1765 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1766 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1767 reallocs++; 1768 } 1769 1770 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1771 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1772 bj_ptr[i] = current_space->array; 1773 bjlvl_ptr[i] = current_space_lvl->array; 1774 1775 /* make sure the active row i has diagonal entry */ 1776 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); 1777 1778 current_space->array += nzi; 1779 current_space->local_used += nzi; 1780 current_space->local_remaining -= nzi; 1781 current_space_lvl->array += nzi; 1782 current_space_lvl->local_used += nzi; 1783 current_space_lvl->local_remaining -= nzi; 1784 } 1785 1786 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1787 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1788 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1789 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1790 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1791 1792 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1793 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1794 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1795 1796 #if defined(PETSC_USE_INFO) 1797 { 1798 PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1799 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 1800 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1801 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 1802 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1803 if (diagonal_fill) { 1804 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 1805 } 1806 } 1807 #endif 1808 /* put together the new matrix */ 1809 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 1810 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 1811 b = (Mat_SeqAIJ*)(fact)->data; 1812 1813 b->free_a = PETSC_TRUE; 1814 b->free_ij = PETSC_TRUE; 1815 b->singlemalloc = PETSC_FALSE; 1816 1817 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 1818 1819 b->j = bj; 1820 b->i = bi; 1821 b->diag = bdiag; 1822 b->ilen = 0; 1823 b->imax = 0; 1824 b->row = isrow; 1825 b->col = iscol; 1826 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1827 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1828 b->icol = isicol; 1829 1830 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 1831 /* In b structure: Free imax, ilen, old a, old j. 1832 Allocate bdiag, solve_work, new a, new j */ 1833 ierr = PetscLogObjectMemory((PetscObject)fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1834 b->maxnz = b->nz = bdiag[0]+1; 1835 1836 (fact)->info.factor_mallocs = reallocs; 1837 (fact)->info.fill_ratio_given = f; 1838 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1839 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1840 if (a->inode.size) { 1841 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1842 } 1843 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1844 PetscFunctionReturn(0); 1845 } 1846 1847 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1848 { 1849 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1850 IS isicol; 1851 PetscErrorCode ierr; 1852 const PetscInt *r,*ic; 1853 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1854 PetscInt *bi,*cols,nnz,*cols_lvl; 1855 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1856 PetscInt i,levels,diagonal_fill; 1857 PetscBool col_identity,row_identity; 1858 PetscReal f; 1859 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1860 PetscBT lnkbt; 1861 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1862 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1863 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1864 PetscBool missing; 1865 1866 PetscFunctionBegin; 1867 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); 1868 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1869 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1870 1871 f = info->fill; 1872 levels = (PetscInt)info->levels; 1873 diagonal_fill = (PetscInt)info->diagonal_fill; 1874 1875 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1876 1877 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1878 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1879 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1880 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1881 1882 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1883 if (a->inode.size) { 1884 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1885 } 1886 fact->factortype = MAT_FACTOR_ILU; 1887 (fact)->info.factor_mallocs = 0; 1888 (fact)->info.fill_ratio_given = info->fill; 1889 (fact)->info.fill_ratio_needed = 1.0; 1890 1891 b = (Mat_SeqAIJ*)(fact)->data; 1892 b->row = isrow; 1893 b->col = iscol; 1894 b->icol = isicol; 1895 ierr = PetscMalloc1((fact)->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1896 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1897 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1898 PetscFunctionReturn(0); 1899 } 1900 1901 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1902 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1903 1904 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1905 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1906 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1907 bi[0] = bdiag[0] = 0; 1908 1909 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1910 1911 /* create a linked list for storing column indices of the active row */ 1912 nlnk = n + 1; 1913 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1914 1915 /* initial FreeSpace size is f*(ai[n]+1) */ 1916 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1917 current_space = free_space; 1918 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1919 current_space_lvl = free_space_lvl; 1920 1921 for (i=0; i<n; i++) { 1922 nzi = 0; 1923 /* copy current row into linked list */ 1924 nnz = ai[r[i]+1] - ai[r[i]]; 1925 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); 1926 cols = aj + ai[r[i]]; 1927 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1928 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1929 nzi += nlnk; 1930 1931 /* make sure diagonal entry is included */ 1932 if (diagonal_fill && lnk[i] == -1) { 1933 fm = n; 1934 while (lnk[fm] < i) fm = lnk[fm]; 1935 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1936 lnk[fm] = i; 1937 lnk_lvl[i] = 0; 1938 nzi++; dcount++; 1939 } 1940 1941 /* add pivot rows into the active row */ 1942 nzbd = 0; 1943 prow = lnk[n]; 1944 while (prow < i) { 1945 nnz = bdiag[prow]; 1946 cols = bj_ptr[prow] + nnz + 1; 1947 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1948 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1949 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1950 nzi += nlnk; 1951 prow = lnk[prow]; 1952 nzbd++; 1953 } 1954 bdiag[i] = nzbd; 1955 bi[i+1] = bi[i] + nzi; 1956 1957 /* if free space is not available, make more free space */ 1958 if (current_space->local_remaining<nzi) { 1959 nnz = PetscIntMultTruncate(nzi,n - i); /* estimated and max additional space needed */ 1960 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1961 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1962 reallocs++; 1963 } 1964 1965 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1966 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1967 bj_ptr[i] = current_space->array; 1968 bjlvl_ptr[i] = current_space_lvl->array; 1969 1970 /* make sure the active row i has diagonal entry */ 1971 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); 1972 1973 current_space->array += nzi; 1974 current_space->local_used += nzi; 1975 current_space->local_remaining -= nzi; 1976 current_space_lvl->array += nzi; 1977 current_space_lvl->local_used += nzi; 1978 current_space_lvl->local_remaining -= nzi; 1979 } 1980 1981 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1982 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1983 1984 /* destroy list of free space and other temporary arrays */ 1985 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1986 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1987 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1988 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1989 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1990 1991 #if defined(PETSC_USE_INFO) 1992 { 1993 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1994 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 1995 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1996 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 1997 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1998 if (diagonal_fill) { 1999 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 2000 } 2001 } 2002 #endif 2003 2004 /* put together the new matrix */ 2005 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 2006 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 2007 b = (Mat_SeqAIJ*)(fact)->data; 2008 2009 b->free_a = PETSC_TRUE; 2010 b->free_ij = PETSC_TRUE; 2011 b->singlemalloc = PETSC_FALSE; 2012 2013 ierr = PetscMalloc1(bi[n],&b->a);CHKERRQ(ierr); 2014 b->j = bj; 2015 b->i = bi; 2016 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2017 b->diag = bdiag; 2018 b->ilen = 0; 2019 b->imax = 0; 2020 b->row = isrow; 2021 b->col = iscol; 2022 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2023 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2024 b->icol = isicol; 2025 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 2026 /* In b structure: Free imax, ilen, old a, old j. 2027 Allocate bdiag, solve_work, new a, new j */ 2028 ierr = PetscLogObjectMemory((PetscObject)fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2029 b->maxnz = b->nz = bi[n]; 2030 2031 (fact)->info.factor_mallocs = reallocs; 2032 (fact)->info.fill_ratio_given = f; 2033 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2034 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2035 if (a->inode.size) { 2036 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2037 } 2038 PetscFunctionReturn(0); 2039 } 2040 2041 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2042 { 2043 Mat C = B; 2044 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2045 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2046 IS ip=b->row,iip = b->icol; 2047 PetscErrorCode ierr; 2048 const PetscInt *rip,*riip; 2049 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2050 PetscInt *ai=a->i,*aj=a->j; 2051 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2052 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2053 PetscBool perm_identity; 2054 FactorShiftCtx sctx; 2055 PetscReal rs; 2056 MatScalar d,*v; 2057 2058 PetscFunctionBegin; 2059 /* MatPivotSetUp(): initialize shift context sctx */ 2060 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2061 2062 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2063 sctx.shift_top = info->zeropivot; 2064 for (i=0; i<mbs; i++) { 2065 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2066 d = (aa)[a->diag[i]]; 2067 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2068 v = aa+ai[i]; 2069 nz = ai[i+1] - ai[i]; 2070 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2071 if (rs>sctx.shift_top) sctx.shift_top = rs; 2072 } 2073 sctx.shift_top *= 1.1; 2074 sctx.nshift_max = 5; 2075 sctx.shift_lo = 0.; 2076 sctx.shift_hi = 1.; 2077 } 2078 2079 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2080 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2081 2082 /* allocate working arrays 2083 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2084 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 2085 */ 2086 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);CHKERRQ(ierr); 2087 2088 do { 2089 sctx.newshift = PETSC_FALSE; 2090 2091 for (i=0; i<mbs; i++) c2r[i] = mbs; 2092 if (mbs) il[0] = 0; 2093 2094 for (k = 0; k<mbs; k++) { 2095 /* zero rtmp */ 2096 nz = bi[k+1] - bi[k]; 2097 bjtmp = bj + bi[k]; 2098 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2099 2100 /* load in initial unfactored row */ 2101 bval = ba + bi[k]; 2102 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2103 for (j = jmin; j < jmax; j++) { 2104 col = riip[aj[j]]; 2105 if (col >= k) { /* only take upper triangular entry */ 2106 rtmp[col] = aa[j]; 2107 *bval++ = 0.0; /* for in-place factorization */ 2108 } 2109 } 2110 /* shift the diagonal of the matrix: ZeropivotApply() */ 2111 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2112 2113 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2114 dk = rtmp[k]; 2115 i = c2r[k]; /* first row to be added to k_th row */ 2116 2117 while (i < k) { 2118 nexti = c2r[i]; /* next row to be added to k_th row */ 2119 2120 /* compute multiplier, update diag(k) and U(i,k) */ 2121 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2122 uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2123 dk += uikdi*ba[ili]; /* update diag[k] */ 2124 ba[ili] = uikdi; /* -U(i,k) */ 2125 2126 /* add multiple of row i to k-th row */ 2127 jmin = ili + 1; jmax = bi[i+1]; 2128 if (jmin < jmax) { 2129 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2130 /* update il and c2r for row i */ 2131 il[i] = jmin; 2132 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2133 } 2134 i = nexti; 2135 } 2136 2137 /* copy data into U(k,:) */ 2138 rs = 0.0; 2139 jmin = bi[k]; jmax = bi[k+1]-1; 2140 if (jmin < jmax) { 2141 for (j=jmin; j<jmax; j++) { 2142 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2143 } 2144 /* add the k-th row into il and c2r */ 2145 il[k] = jmin; 2146 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2147 } 2148 2149 /* MatPivotCheck() */ 2150 sctx.rs = rs; 2151 sctx.pv = dk; 2152 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 2153 if (sctx.newshift) break; 2154 dk = sctx.pv; 2155 2156 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2157 } 2158 } while (sctx.newshift); 2159 2160 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2161 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2162 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2163 2164 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2165 if (perm_identity) { 2166 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2167 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2168 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2169 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2170 } else { 2171 B->ops->solve = MatSolve_SeqSBAIJ_1; 2172 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2173 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2174 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2175 } 2176 2177 C->assembled = PETSC_TRUE; 2178 C->preallocated = PETSC_TRUE; 2179 2180 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2181 2182 /* MatPivotView() */ 2183 if (sctx.nshift) { 2184 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2185 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); 2186 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2187 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2188 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 2189 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 2190 } 2191 } 2192 PetscFunctionReturn(0); 2193 } 2194 2195 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2196 { 2197 Mat C = B; 2198 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2199 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2200 IS ip=b->row,iip = b->icol; 2201 PetscErrorCode ierr; 2202 const PetscInt *rip,*riip; 2203 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2204 PetscInt *ai=a->i,*aj=a->j; 2205 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2206 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2207 PetscBool perm_identity; 2208 FactorShiftCtx sctx; 2209 PetscReal rs; 2210 MatScalar d,*v; 2211 2212 PetscFunctionBegin; 2213 /* MatPivotSetUp(): initialize shift context sctx */ 2214 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2215 2216 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2217 sctx.shift_top = info->zeropivot; 2218 for (i=0; i<mbs; i++) { 2219 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2220 d = (aa)[a->diag[i]]; 2221 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2222 v = aa+ai[i]; 2223 nz = ai[i+1] - ai[i]; 2224 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2225 if (rs>sctx.shift_top) sctx.shift_top = rs; 2226 } 2227 sctx.shift_top *= 1.1; 2228 sctx.nshift_max = 5; 2229 sctx.shift_lo = 0.; 2230 sctx.shift_hi = 1.; 2231 } 2232 2233 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2234 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2235 2236 /* initialization */ 2237 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);CHKERRQ(ierr); 2238 2239 do { 2240 sctx.newshift = PETSC_FALSE; 2241 2242 for (i=0; i<mbs; i++) jl[i] = mbs; 2243 il[0] = 0; 2244 2245 for (k = 0; k<mbs; k++) { 2246 /* zero rtmp */ 2247 nz = bi[k+1] - bi[k]; 2248 bjtmp = bj + bi[k]; 2249 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2250 2251 bval = ba + bi[k]; 2252 /* initialize k-th row by the perm[k]-th row of A */ 2253 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2254 for (j = jmin; j < jmax; j++) { 2255 col = riip[aj[j]]; 2256 if (col >= k) { /* only take upper triangular entry */ 2257 rtmp[col] = aa[j]; 2258 *bval++ = 0.0; /* for in-place factorization */ 2259 } 2260 } 2261 /* shift the diagonal of the matrix */ 2262 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2263 2264 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2265 dk = rtmp[k]; 2266 i = jl[k]; /* first row to be added to k_th row */ 2267 2268 while (i < k) { 2269 nexti = jl[i]; /* next row to be added to k_th row */ 2270 2271 /* compute multiplier, update diag(k) and U(i,k) */ 2272 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2273 uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2274 dk += uikdi*ba[ili]; 2275 ba[ili] = uikdi; /* -U(i,k) */ 2276 2277 /* add multiple of row i to k-th row */ 2278 jmin = ili + 1; jmax = bi[i+1]; 2279 if (jmin < jmax) { 2280 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2281 /* update il and jl for row i */ 2282 il[i] = jmin; 2283 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2284 } 2285 i = nexti; 2286 } 2287 2288 /* shift the diagonals when zero pivot is detected */ 2289 /* compute rs=sum of abs(off-diagonal) */ 2290 rs = 0.0; 2291 jmin = bi[k]+1; 2292 nz = bi[k+1] - jmin; 2293 bcol = bj + jmin; 2294 for (j=0; j<nz; j++) { 2295 rs += PetscAbsScalar(rtmp[bcol[j]]); 2296 } 2297 2298 sctx.rs = rs; 2299 sctx.pv = dk; 2300 ierr = MatPivotCheck(B,A,info,&sctx,k);CHKERRQ(ierr); 2301 if (sctx.newshift) break; 2302 dk = sctx.pv; 2303 2304 /* copy data into U(k,:) */ 2305 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2306 jmin = bi[k]+1; jmax = bi[k+1]; 2307 if (jmin < jmax) { 2308 for (j=jmin; j<jmax; j++) { 2309 col = bj[j]; ba[j] = rtmp[col]; 2310 } 2311 /* add the k-th row into il and jl */ 2312 il[k] = jmin; 2313 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2314 } 2315 } 2316 } while (sctx.newshift); 2317 2318 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2319 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2320 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2321 2322 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2323 if (perm_identity) { 2324 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2325 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2326 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2327 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2328 } else { 2329 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2330 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2331 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2332 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2333 } 2334 2335 C->assembled = PETSC_TRUE; 2336 C->preallocated = PETSC_TRUE; 2337 2338 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2339 if (sctx.nshift) { 2340 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2341 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2342 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2343 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2344 } 2345 } 2346 PetscFunctionReturn(0); 2347 } 2348 2349 /* 2350 icc() under revised new data structure. 2351 Factored arrays bj and ba are stored as 2352 U(0,:),...,U(i,:),U(n-1,:) 2353 2354 ui=fact->i is an array of size n+1, in which 2355 ui+ 2356 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2357 ui[n]: points to U(n-1,n-1)+1 2358 2359 udiag=fact->diag is an array of size n,in which 2360 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2361 2362 U(i,:) contains udiag[i] as its last entry, i.e., 2363 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2364 */ 2365 2366 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2367 { 2368 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2369 Mat_SeqSBAIJ *b; 2370 PetscErrorCode ierr; 2371 PetscBool perm_identity,missing; 2372 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2373 const PetscInt *rip,*riip; 2374 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2375 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2376 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2377 PetscReal fill =info->fill,levels=info->levels; 2378 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2379 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2380 PetscBT lnkbt; 2381 IS iperm; 2382 2383 PetscFunctionBegin; 2384 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); 2385 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2386 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2387 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2388 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2389 2390 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2391 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2392 ui[0] = 0; 2393 2394 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2395 if (!levels && perm_identity) { 2396 for (i=0; i<am; i++) { 2397 ncols = ai[i+1] - a->diag[i]; 2398 ui[i+1] = ui[i] + ncols; 2399 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2400 } 2401 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2402 cols = uj; 2403 for (i=0; i<am; i++) { 2404 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2405 ncols = ai[i+1] - a->diag[i] -1; 2406 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2407 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2408 } 2409 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2410 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2411 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2412 2413 /* initialization */ 2414 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2415 2416 /* jl: linked list for storing indices of the pivot rows 2417 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2418 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2419 for (i=0; i<am; i++) { 2420 jl[i] = am; il[i] = 0; 2421 } 2422 2423 /* create and initialize a linked list for storing column indices of the active row k */ 2424 nlnk = am + 1; 2425 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2426 2427 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2428 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2429 current_space = free_space; 2430 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space_lvl);CHKERRQ(ierr); 2431 current_space_lvl = free_space_lvl; 2432 2433 for (k=0; k<am; k++) { /* for each active row k */ 2434 /* initialize lnk by the column indices of row rip[k] of A */ 2435 nzk = 0; 2436 ncols = ai[rip[k]+1] - ai[rip[k]]; 2437 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); 2438 ncols_upper = 0; 2439 for (j=0; j<ncols; j++) { 2440 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2441 if (riip[i] >= k) { /* only take upper triangular entry */ 2442 ajtmp[ncols_upper] = i; 2443 ncols_upper++; 2444 } 2445 } 2446 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2447 nzk += nlnk; 2448 2449 /* update lnk by computing fill-in for each pivot row to be merged in */ 2450 prow = jl[k]; /* 1st pivot row */ 2451 2452 while (prow < k) { 2453 nextprow = jl[prow]; 2454 2455 /* merge prow into k-th row */ 2456 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2457 jmax = ui[prow+1]; 2458 ncols = jmax-jmin; 2459 i = jmin - ui[prow]; 2460 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2461 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2462 j = *(uj - 1); 2463 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2464 nzk += nlnk; 2465 2466 /* update il and jl for prow */ 2467 if (jmin < jmax) { 2468 il[prow] = jmin; 2469 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2470 } 2471 prow = nextprow; 2472 } 2473 2474 /* if free space is not available, make more free space */ 2475 if (current_space->local_remaining<nzk) { 2476 i = am - k + 1; /* num of unfactored rows */ 2477 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2478 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2479 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2480 reallocs++; 2481 } 2482 2483 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2484 if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2485 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2486 2487 /* add the k-th row into il and jl */ 2488 if (nzk > 1) { 2489 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2490 jl[k] = jl[i]; jl[i] = k; 2491 il[k] = ui[k] + 1; 2492 } 2493 uj_ptr[k] = current_space->array; 2494 uj_lvl_ptr[k] = current_space_lvl->array; 2495 2496 current_space->array += nzk; 2497 current_space->local_used += nzk; 2498 current_space->local_remaining -= nzk; 2499 2500 current_space_lvl->array += nzk; 2501 current_space_lvl->local_used += nzk; 2502 current_space_lvl->local_remaining -= nzk; 2503 2504 ui[k+1] = ui[k] + nzk; 2505 } 2506 2507 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2508 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2509 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2510 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2511 2512 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2513 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2514 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2515 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2516 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2517 2518 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2519 2520 /* put together the new matrix in MATSEQSBAIJ format */ 2521 b = (Mat_SeqSBAIJ*)(fact)->data; 2522 b->singlemalloc = PETSC_FALSE; 2523 2524 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2525 2526 b->j = uj; 2527 b->i = ui; 2528 b->diag = udiag; 2529 b->free_diag = PETSC_TRUE; 2530 b->ilen = 0; 2531 b->imax = 0; 2532 b->row = perm; 2533 b->col = perm; 2534 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2535 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2536 b->icol = iperm; 2537 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2538 2539 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2540 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2541 2542 b->maxnz = b->nz = ui[am]; 2543 b->free_a = PETSC_TRUE; 2544 b->free_ij = PETSC_TRUE; 2545 2546 fact->info.factor_mallocs = reallocs; 2547 fact->info.fill_ratio_given = fill; 2548 if (ai[am] != 0) { 2549 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2550 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2551 } else { 2552 fact->info.fill_ratio_needed = 0.0; 2553 } 2554 #if defined(PETSC_USE_INFO) 2555 if (ai[am] != 0) { 2556 PetscReal af = fact->info.fill_ratio_needed; 2557 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2558 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2559 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2560 } else { 2561 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2562 } 2563 #endif 2564 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2565 PetscFunctionReturn(0); 2566 } 2567 2568 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2569 { 2570 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2571 Mat_SeqSBAIJ *b; 2572 PetscErrorCode ierr; 2573 PetscBool perm_identity,missing; 2574 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2575 const PetscInt *rip,*riip; 2576 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2577 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2578 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2579 PetscReal fill =info->fill,levels=info->levels; 2580 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2581 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2582 PetscBT lnkbt; 2583 IS iperm; 2584 2585 PetscFunctionBegin; 2586 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); 2587 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2588 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2589 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2590 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2591 2592 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2593 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2594 ui[0] = 0; 2595 2596 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2597 if (!levels && perm_identity) { 2598 2599 for (i=0; i<am; i++) { 2600 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2601 udiag[i] = ui[i]; 2602 } 2603 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2604 cols = uj; 2605 for (i=0; i<am; i++) { 2606 aj = a->j + a->diag[i]; 2607 ncols = ui[i+1] - ui[i]; 2608 for (j=0; j<ncols; j++) *cols++ = *aj++; 2609 } 2610 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2611 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2612 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2613 2614 /* initialization */ 2615 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2616 2617 /* jl: linked list for storing indices of the pivot rows 2618 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2619 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2620 for (i=0; i<am; i++) { 2621 jl[i] = am; il[i] = 0; 2622 } 2623 2624 /* create and initialize a linked list for storing column indices of the active row k */ 2625 nlnk = am + 1; 2626 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2627 2628 /* initial FreeSpace size is fill*(ai[am]+1) */ 2629 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2630 current_space = free_space; 2631 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space_lvl);CHKERRQ(ierr); 2632 current_space_lvl = free_space_lvl; 2633 2634 for (k=0; k<am; k++) { /* for each active row k */ 2635 /* initialize lnk by the column indices of row rip[k] of A */ 2636 nzk = 0; 2637 ncols = ai[rip[k]+1] - ai[rip[k]]; 2638 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); 2639 ncols_upper = 0; 2640 for (j=0; j<ncols; j++) { 2641 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2642 if (riip[i] >= k) { /* only take upper triangular entry */ 2643 ajtmp[ncols_upper] = i; 2644 ncols_upper++; 2645 } 2646 } 2647 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2648 nzk += nlnk; 2649 2650 /* update lnk by computing fill-in for each pivot row to be merged in */ 2651 prow = jl[k]; /* 1st pivot row */ 2652 2653 while (prow < k) { 2654 nextprow = jl[prow]; 2655 2656 /* merge prow into k-th row */ 2657 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2658 jmax = ui[prow+1]; 2659 ncols = jmax-jmin; 2660 i = jmin - ui[prow]; 2661 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2662 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2663 j = *(uj - 1); 2664 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2665 nzk += nlnk; 2666 2667 /* update il and jl for prow */ 2668 if (jmin < jmax) { 2669 il[prow] = jmin; 2670 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2671 } 2672 prow = nextprow; 2673 } 2674 2675 /* if free space is not available, make more free space */ 2676 if (current_space->local_remaining<nzk) { 2677 i = am - k + 1; /* num of unfactored rows */ 2678 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2679 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2680 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2681 reallocs++; 2682 } 2683 2684 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2685 if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2686 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2687 2688 /* add the k-th row into il and jl */ 2689 if (nzk > 1) { 2690 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2691 jl[k] = jl[i]; jl[i] = k; 2692 il[k] = ui[k] + 1; 2693 } 2694 uj_ptr[k] = current_space->array; 2695 uj_lvl_ptr[k] = current_space_lvl->array; 2696 2697 current_space->array += nzk; 2698 current_space->local_used += nzk; 2699 current_space->local_remaining -= nzk; 2700 2701 current_space_lvl->array += nzk; 2702 current_space_lvl->local_used += nzk; 2703 current_space_lvl->local_remaining -= nzk; 2704 2705 ui[k+1] = ui[k] + nzk; 2706 } 2707 2708 #if defined(PETSC_USE_INFO) 2709 if (ai[am] != 0) { 2710 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2711 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2712 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2713 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2714 } else { 2715 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2716 } 2717 #endif 2718 2719 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2720 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2721 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2722 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2723 2724 /* destroy list of free space and other temporary array(s) */ 2725 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2726 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2727 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2728 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2729 2730 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2731 2732 /* put together the new matrix in MATSEQSBAIJ format */ 2733 2734 b = (Mat_SeqSBAIJ*)fact->data; 2735 b->singlemalloc = PETSC_FALSE; 2736 2737 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2738 2739 b->j = uj; 2740 b->i = ui; 2741 b->diag = udiag; 2742 b->free_diag = PETSC_TRUE; 2743 b->ilen = 0; 2744 b->imax = 0; 2745 b->row = perm; 2746 b->col = perm; 2747 2748 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2749 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2750 2751 b->icol = iperm; 2752 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2753 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2754 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2755 b->maxnz = b->nz = ui[am]; 2756 b->free_a = PETSC_TRUE; 2757 b->free_ij = PETSC_TRUE; 2758 2759 fact->info.factor_mallocs = reallocs; 2760 fact->info.fill_ratio_given = fill; 2761 if (ai[am] != 0) { 2762 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2763 } else { 2764 fact->info.fill_ratio_needed = 0.0; 2765 } 2766 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2767 PetscFunctionReturn(0); 2768 } 2769 2770 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2771 { 2772 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2773 Mat_SeqSBAIJ *b; 2774 PetscErrorCode ierr; 2775 PetscBool perm_identity,missing; 2776 PetscReal fill = info->fill; 2777 const PetscInt *rip,*riip; 2778 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2779 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2780 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2781 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2782 PetscBT lnkbt; 2783 IS iperm; 2784 2785 PetscFunctionBegin; 2786 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); 2787 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2788 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2789 2790 /* check whether perm is the identity mapping */ 2791 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2792 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2793 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2794 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2795 2796 /* initialization */ 2797 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2798 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2799 ui[0] = 0; 2800 2801 /* jl: linked list for storing indices of the pivot rows 2802 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2803 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2804 for (i=0; i<am; i++) { 2805 jl[i] = am; il[i] = 0; 2806 } 2807 2808 /* create and initialize a linked list for storing column indices of the active row k */ 2809 nlnk = am + 1; 2810 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2811 2812 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2813 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2814 current_space = free_space; 2815 2816 for (k=0; k<am; k++) { /* for each active row k */ 2817 /* initialize lnk by the column indices of row rip[k] of A */ 2818 nzk = 0; 2819 ncols = ai[rip[k]+1] - ai[rip[k]]; 2820 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); 2821 ncols_upper = 0; 2822 for (j=0; j<ncols; j++) { 2823 i = riip[*(aj + ai[rip[k]] + j)]; 2824 if (i >= k) { /* only take upper triangular entry */ 2825 cols[ncols_upper] = i; 2826 ncols_upper++; 2827 } 2828 } 2829 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2830 nzk += nlnk; 2831 2832 /* update lnk by computing fill-in for each pivot row to be merged in */ 2833 prow = jl[k]; /* 1st pivot row */ 2834 2835 while (prow < k) { 2836 nextprow = jl[prow]; 2837 /* merge prow into k-th row */ 2838 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2839 jmax = ui[prow+1]; 2840 ncols = jmax-jmin; 2841 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2842 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2843 nzk += nlnk; 2844 2845 /* update il and jl for prow */ 2846 if (jmin < jmax) { 2847 il[prow] = jmin; 2848 j = *uj_ptr; 2849 jl[prow] = jl[j]; 2850 jl[j] = prow; 2851 } 2852 prow = nextprow; 2853 } 2854 2855 /* if free space is not available, make more free space */ 2856 if (current_space->local_remaining<nzk) { 2857 i = am - k + 1; /* num of unfactored rows */ 2858 i = PetscIntMultTruncate(i,PetscMin(nzk,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2859 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2860 reallocs++; 2861 } 2862 2863 /* copy data into free space, then initialize lnk */ 2864 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2865 2866 /* add the k-th row into il and jl */ 2867 if (nzk > 1) { 2868 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2869 jl[k] = jl[i]; jl[i] = k; 2870 il[k] = ui[k] + 1; 2871 } 2872 ui_ptr[k] = current_space->array; 2873 2874 current_space->array += nzk; 2875 current_space->local_used += nzk; 2876 current_space->local_remaining -= nzk; 2877 2878 ui[k+1] = ui[k] + nzk; 2879 } 2880 2881 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2882 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2883 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2884 2885 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2886 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2887 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2888 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2889 2890 /* put together the new matrix in MATSEQSBAIJ format */ 2891 2892 b = (Mat_SeqSBAIJ*)fact->data; 2893 b->singlemalloc = PETSC_FALSE; 2894 b->free_a = PETSC_TRUE; 2895 b->free_ij = PETSC_TRUE; 2896 2897 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2898 2899 b->j = uj; 2900 b->i = ui; 2901 b->diag = udiag; 2902 b->free_diag = PETSC_TRUE; 2903 b->ilen = 0; 2904 b->imax = 0; 2905 b->row = perm; 2906 b->col = perm; 2907 2908 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2909 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2910 2911 b->icol = iperm; 2912 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2913 2914 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2915 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2916 2917 b->maxnz = b->nz = ui[am]; 2918 2919 fact->info.factor_mallocs = reallocs; 2920 fact->info.fill_ratio_given = fill; 2921 if (ai[am] != 0) { 2922 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2923 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2924 } else { 2925 fact->info.fill_ratio_needed = 0.0; 2926 } 2927 #if defined(PETSC_USE_INFO) 2928 if (ai[am] != 0) { 2929 PetscReal af = fact->info.fill_ratio_needed; 2930 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2931 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2932 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2933 } else { 2934 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2935 } 2936 #endif 2937 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2938 PetscFunctionReturn(0); 2939 } 2940 2941 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2942 { 2943 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2944 Mat_SeqSBAIJ *b; 2945 PetscErrorCode ierr; 2946 PetscBool perm_identity,missing; 2947 PetscReal fill = info->fill; 2948 const PetscInt *rip,*riip; 2949 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2950 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2951 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2952 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2953 PetscBT lnkbt; 2954 IS iperm; 2955 2956 PetscFunctionBegin; 2957 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); 2958 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2959 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2960 2961 /* check whether perm is the identity mapping */ 2962 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2963 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2964 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2965 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2966 2967 /* initialization */ 2968 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2969 ui[0] = 0; 2970 2971 /* jl: linked list for storing indices of the pivot rows 2972 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2973 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2974 for (i=0; i<am; i++) { 2975 jl[i] = am; il[i] = 0; 2976 } 2977 2978 /* create and initialize a linked list for storing column indices of the active row k */ 2979 nlnk = am + 1; 2980 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2981 2982 /* initial FreeSpace size is fill*(ai[am]+1) */ 2983 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2984 current_space = free_space; 2985 2986 for (k=0; k<am; k++) { /* for each active row k */ 2987 /* initialize lnk by the column indices of row rip[k] of A */ 2988 nzk = 0; 2989 ncols = ai[rip[k]+1] - ai[rip[k]]; 2990 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); 2991 ncols_upper = 0; 2992 for (j=0; j<ncols; j++) { 2993 i = riip[*(aj + ai[rip[k]] + j)]; 2994 if (i >= k) { /* only take upper triangular entry */ 2995 cols[ncols_upper] = i; 2996 ncols_upper++; 2997 } 2998 } 2999 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3000 nzk += nlnk; 3001 3002 /* update lnk by computing fill-in for each pivot row to be merged in */ 3003 prow = jl[k]; /* 1st pivot row */ 3004 3005 while (prow < k) { 3006 nextprow = jl[prow]; 3007 /* merge prow into k-th row */ 3008 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3009 jmax = ui[prow+1]; 3010 ncols = jmax-jmin; 3011 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3012 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3013 nzk += nlnk; 3014 3015 /* update il and jl for prow */ 3016 if (jmin < jmax) { 3017 il[prow] = jmin; 3018 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3019 } 3020 prow = nextprow; 3021 } 3022 3023 /* if free space is not available, make more free space */ 3024 if (current_space->local_remaining<nzk) { 3025 i = am - k + 1; /* num of unfactored rows */ 3026 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3027 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3028 reallocs++; 3029 } 3030 3031 /* copy data into free space, then initialize lnk */ 3032 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3033 3034 /* add the k-th row into il and jl */ 3035 if (nzk-1 > 0) { 3036 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3037 jl[k] = jl[i]; jl[i] = k; 3038 il[k] = ui[k] + 1; 3039 } 3040 ui_ptr[k] = current_space->array; 3041 3042 current_space->array += nzk; 3043 current_space->local_used += nzk; 3044 current_space->local_remaining -= nzk; 3045 3046 ui[k+1] = ui[k] + nzk; 3047 } 3048 3049 #if defined(PETSC_USE_INFO) 3050 if (ai[am] != 0) { 3051 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3052 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 3053 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 3054 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 3055 } else { 3056 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 3057 } 3058 #endif 3059 3060 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3061 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3062 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3063 3064 /* destroy list of free space and other temporary array(s) */ 3065 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 3066 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3067 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3068 3069 /* put together the new matrix in MATSEQSBAIJ format */ 3070 3071 b = (Mat_SeqSBAIJ*)fact->data; 3072 b->singlemalloc = PETSC_FALSE; 3073 b->free_a = PETSC_TRUE; 3074 b->free_ij = PETSC_TRUE; 3075 3076 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 3077 3078 b->j = uj; 3079 b->i = ui; 3080 b->diag = 0; 3081 b->ilen = 0; 3082 b->imax = 0; 3083 b->row = perm; 3084 b->col = perm; 3085 3086 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3087 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3088 3089 b->icol = iperm; 3090 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3091 3092 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 3093 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3094 b->maxnz = b->nz = ui[am]; 3095 3096 fact->info.factor_mallocs = reallocs; 3097 fact->info.fill_ratio_given = fill; 3098 if (ai[am] != 0) { 3099 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3100 } else { 3101 fact->info.fill_ratio_needed = 0.0; 3102 } 3103 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3104 PetscFunctionReturn(0); 3105 } 3106 3107 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3108 { 3109 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3110 PetscErrorCode ierr; 3111 PetscInt n = A->rmap->n; 3112 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3113 PetscScalar *x,sum; 3114 const PetscScalar *b; 3115 const MatScalar *aa = a->a,*v; 3116 PetscInt i,nz; 3117 3118 PetscFunctionBegin; 3119 if (!n) PetscFunctionReturn(0); 3120 3121 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3122 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 3123 3124 /* forward solve the lower triangular */ 3125 x[0] = b[0]; 3126 v = aa; 3127 vi = aj; 3128 for (i=1; i<n; i++) { 3129 nz = ai[i+1] - ai[i]; 3130 sum = b[i]; 3131 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3132 v += nz; 3133 vi += nz; 3134 x[i] = sum; 3135 } 3136 3137 /* backward solve the upper triangular */ 3138 for (i=n-1; i>=0; i--) { 3139 v = aa + adiag[i+1] + 1; 3140 vi = aj + adiag[i+1] + 1; 3141 nz = adiag[i] - adiag[i+1]-1; 3142 sum = x[i]; 3143 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3144 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3145 } 3146 3147 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3148 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3149 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 3150 PetscFunctionReturn(0); 3151 } 3152 3153 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3154 { 3155 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3156 IS iscol = a->col,isrow = a->row; 3157 PetscErrorCode ierr; 3158 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3159 const PetscInt *rout,*cout,*r,*c; 3160 PetscScalar *x,*tmp,sum; 3161 const PetscScalar *b; 3162 const MatScalar *aa = a->a,*v; 3163 3164 PetscFunctionBegin; 3165 if (!n) PetscFunctionReturn(0); 3166 3167 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3168 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 3169 tmp = a->solve_work; 3170 3171 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3172 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3173 3174 /* forward solve the lower triangular */ 3175 tmp[0] = b[r[0]]; 3176 v = aa; 3177 vi = aj; 3178 for (i=1; i<n; i++) { 3179 nz = ai[i+1] - ai[i]; 3180 sum = b[r[i]]; 3181 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3182 tmp[i] = sum; 3183 v += nz; vi += nz; 3184 } 3185 3186 /* backward solve the upper triangular */ 3187 for (i=n-1; i>=0; i--) { 3188 v = aa + adiag[i+1]+1; 3189 vi = aj + adiag[i+1]+1; 3190 nz = adiag[i]-adiag[i+1]-1; 3191 sum = tmp[i]; 3192 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3193 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3194 } 3195 3196 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3197 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3198 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3199 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 3200 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3201 PetscFunctionReturn(0); 3202 } 3203 3204 /* 3205 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 3206 */ 3207 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3208 { 3209 Mat B = *fact; 3210 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3211 IS isicol; 3212 PetscErrorCode ierr; 3213 const PetscInt *r,*ic; 3214 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3215 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3216 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3217 PetscInt nlnk,*lnk; 3218 PetscBT lnkbt; 3219 PetscBool row_identity,icol_identity; 3220 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3221 const PetscInt *ics; 3222 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3223 PetscReal dt =info->dt,shift=info->shiftamount; 3224 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3225 PetscBool missing; 3226 3227 PetscFunctionBegin; 3228 if (dt == PETSC_DEFAULT) dt = 0.005; 3229 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3230 3231 /* ------- symbolic factorization, can be reused ---------*/ 3232 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3233 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3234 adiag=a->diag; 3235 3236 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3237 3238 /* bdiag is location of diagonal in factor */ 3239 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3240 ierr = PetscMalloc1(n+1,&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3241 3242 /* allocate row pointers bi */ 3243 ierr = PetscMalloc1(2*n+2,&bi);CHKERRQ(ierr); 3244 3245 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3246 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3247 nnz_max = ai[n]+2*n*dtcount+2; 3248 3249 ierr = PetscMalloc1(nnz_max+1,&bj);CHKERRQ(ierr); 3250 ierr = PetscMalloc1(nnz_max+1,&ba);CHKERRQ(ierr); 3251 3252 /* put together the new matrix */ 3253 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 3254 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 3255 b = (Mat_SeqAIJ*)B->data; 3256 3257 b->free_a = PETSC_TRUE; 3258 b->free_ij = PETSC_TRUE; 3259 b->singlemalloc = PETSC_FALSE; 3260 3261 b->a = ba; 3262 b->j = bj; 3263 b->i = bi; 3264 b->diag = bdiag; 3265 b->ilen = 0; 3266 b->imax = 0; 3267 b->row = isrow; 3268 b->col = iscol; 3269 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3270 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3271 b->icol = isicol; 3272 3273 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 3274 ierr = PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3275 b->maxnz = nnz_max; 3276 3277 B->factortype = MAT_FACTOR_ILUDT; 3278 B->info.factor_mallocs = 0; 3279 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3280 /* ------- end of symbolic factorization ---------*/ 3281 3282 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3283 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3284 ics = ic; 3285 3286 /* linked list for storing column indices of the active row */ 3287 nlnk = n + 1; 3288 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3289 3290 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3291 ierr = PetscMalloc2(n,&im,n,&jtmp);CHKERRQ(ierr); 3292 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3293 ierr = PetscMalloc2(n,&rtmp,n,&vtmp);CHKERRQ(ierr); 3294 ierr = PetscArrayzero(rtmp,n);CHKERRQ(ierr); 3295 3296 bi[0] = 0; 3297 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3298 bdiag_rev[n] = bdiag[0]; 3299 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3300 for (i=0; i<n; i++) { 3301 /* copy initial fill into linked list */ 3302 nzi = ai[r[i]+1] - ai[r[i]]; 3303 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); 3304 nzi_al = adiag[r[i]] - ai[r[i]]; 3305 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3306 ajtmp = aj + ai[r[i]]; 3307 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3308 3309 /* load in initial (unfactored row) */ 3310 aatmp = a->a + ai[r[i]]; 3311 for (j=0; j<nzi; j++) { 3312 rtmp[ics[*ajtmp++]] = *aatmp++; 3313 } 3314 3315 /* add pivot rows into linked list */ 3316 row = lnk[n]; 3317 while (row < i) { 3318 nzi_bl = bi[row+1] - bi[row] + 1; 3319 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3320 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3321 nzi += nlnk; 3322 row = lnk[row]; 3323 } 3324 3325 /* copy data from lnk into jtmp, then initialize lnk */ 3326 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3327 3328 /* numerical factorization */ 3329 bjtmp = jtmp; 3330 row = *bjtmp++; /* 1st pivot row */ 3331 while (row < i) { 3332 pc = rtmp + row; 3333 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3334 multiplier = (*pc) * (*pv); 3335 *pc = multiplier; 3336 if (PetscAbsScalar(*pc) > dt) { /* apply tolerance dropping rule */ 3337 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3338 pv = ba + bdiag[row+1] + 1; 3339 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3340 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3341 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3342 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 3343 } 3344 row = *bjtmp++; 3345 } 3346 3347 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3348 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3349 nzi_bl = 0; j = 0; 3350 while (jtmp[j] < i) { /* Note: jtmp is sorted */ 3351 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3352 nzi_bl++; j++; 3353 } 3354 nzi_bu = nzi - nzi_bl -1; 3355 while (j < nzi) { 3356 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3357 j++; 3358 } 3359 3360 bjtmp = bj + bi[i]; 3361 batmp = ba + bi[i]; 3362 /* apply level dropping rule to L part */ 3363 ncut = nzi_al + dtcount; 3364 if (ncut < nzi_bl) { 3365 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3366 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3367 } else { 3368 ncut = nzi_bl; 3369 } 3370 for (j=0; j<ncut; j++) { 3371 bjtmp[j] = jtmp[j]; 3372 batmp[j] = vtmp[j]; 3373 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3374 } 3375 bi[i+1] = bi[i] + ncut; 3376 nzi = ncut + 1; 3377 3378 /* apply level dropping rule to U part */ 3379 ncut = nzi_au + dtcount; 3380 if (ncut < nzi_bu) { 3381 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3382 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3383 } else { 3384 ncut = nzi_bu; 3385 } 3386 nzi += ncut; 3387 3388 /* mark bdiagonal */ 3389 bdiag[i+1] = bdiag[i] - (ncut + 1); 3390 bdiag_rev[n-i-1] = bdiag[i+1]; 3391 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3392 bjtmp = bj + bdiag[i]; 3393 batmp = ba + bdiag[i]; 3394 *bjtmp = i; 3395 *batmp = diag_tmp; /* rtmp[i]; */ 3396 if (*batmp == 0.0) { 3397 *batmp = dt+shift; 3398 /* printf(" row %d add shift %g\n",i,shift); */ 3399 } 3400 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3401 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3402 3403 bjtmp = bj + bdiag[i+1]+1; 3404 batmp = ba + bdiag[i+1]+1; 3405 for (k=0; k<ncut; k++) { 3406 bjtmp[k] = jtmp[nzi_bl+1+k]; 3407 batmp[k] = vtmp[nzi_bl+1+k]; 3408 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3409 } 3410 /* printf("\n"); */ 3411 3412 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3413 /* 3414 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3415 printf(" ----------------------------\n"); 3416 */ 3417 } /* for (i=0; i<n; i++) */ 3418 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3419 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]); 3420 3421 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3422 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3423 3424 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3425 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3426 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3427 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3428 3429 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3430 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3431 3432 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3433 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3434 if (row_identity && icol_identity) { 3435 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3436 } else { 3437 B->ops->solve = MatSolve_SeqAIJ; 3438 } 3439 3440 B->ops->solveadd = 0; 3441 B->ops->solvetranspose = 0; 3442 B->ops->solvetransposeadd = 0; 3443 B->ops->matsolve = 0; 3444 B->assembled = PETSC_TRUE; 3445 B->preallocated = PETSC_TRUE; 3446 PetscFunctionReturn(0); 3447 } 3448 3449 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3450 /* 3451 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 3452 */ 3453 3454 PetscErrorCode MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3455 { 3456 PetscErrorCode ierr; 3457 3458 PetscFunctionBegin; 3459 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3460 PetscFunctionReturn(0); 3461 } 3462 3463 /* 3464 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3465 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3466 */ 3467 /* 3468 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 3469 */ 3470 3471 PetscErrorCode MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3472 { 3473 Mat C =fact; 3474 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 3475 IS isrow = b->row,isicol = b->icol; 3476 PetscErrorCode ierr; 3477 const PetscInt *r,*ic,*ics; 3478 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3479 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3480 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3481 PetscReal dt=info->dt,shift=info->shiftamount; 3482 PetscBool row_identity, col_identity; 3483 3484 PetscFunctionBegin; 3485 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3486 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3487 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 3488 ics = ic; 3489 3490 for (i=0; i<n; i++) { 3491 /* initialize rtmp array */ 3492 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3493 bjtmp = bj + bi[i]; 3494 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3495 rtmp[i] = 0.0; 3496 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3497 bjtmp = bj + bdiag[i+1] + 1; 3498 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3499 3500 /* load in initial unfactored row of A */ 3501 /* printf("row %d\n",i); */ 3502 nz = ai[r[i]+1] - ai[r[i]]; 3503 ajtmp = aj + ai[r[i]]; 3504 v = aa + ai[r[i]]; 3505 for (j=0; j<nz; j++) { 3506 rtmp[ics[*ajtmp++]] = v[j]; 3507 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3508 } 3509 /* printf("\n"); */ 3510 3511 /* numerical factorization */ 3512 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3513 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3514 k = 0; 3515 while (k < nzl) { 3516 row = *bjtmp++; 3517 /* printf(" prow %d\n",row); */ 3518 pc = rtmp + row; 3519 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3520 multiplier = (*pc) * (*pv); 3521 *pc = multiplier; 3522 if (PetscAbsScalar(multiplier) > dt) { 3523 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3524 pv = b->a + bdiag[row+1] + 1; 3525 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3526 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3527 ierr = PetscLogFlops(1+2*nz);CHKERRQ(ierr); 3528 } 3529 k++; 3530 } 3531 3532 /* finished row so stick it into b->a */ 3533 /* L-part */ 3534 pv = b->a + bi[i]; 3535 pj = bj + bi[i]; 3536 nzl = bi[i+1] - bi[i]; 3537 for (j=0; j<nzl; j++) { 3538 pv[j] = rtmp[pj[j]]; 3539 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3540 } 3541 3542 /* diagonal: invert diagonal entries for simplier triangular solves */ 3543 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3544 b->a[bdiag[i]] = 1.0/rtmp[i]; 3545 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3546 3547 /* U-part */ 3548 pv = b->a + bdiag[i+1] + 1; 3549 pj = bj + bdiag[i+1] + 1; 3550 nzu = bdiag[i] - bdiag[i+1] - 1; 3551 for (j=0; j<nzu; j++) { 3552 pv[j] = rtmp[pj[j]]; 3553 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3554 } 3555 /* printf("\n"); */ 3556 } 3557 3558 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3559 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3560 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3561 3562 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3563 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3564 if (row_identity && col_identity) { 3565 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3566 } else { 3567 C->ops->solve = MatSolve_SeqAIJ; 3568 } 3569 C->ops->solveadd = 0; 3570 C->ops->solvetranspose = 0; 3571 C->ops->solvetransposeadd = 0; 3572 C->ops->matsolve = 0; 3573 C->assembled = PETSC_TRUE; 3574 C->preallocated = PETSC_TRUE; 3575 3576 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3577 PetscFunctionReturn(0); 3578 } 3579