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 && !A->symmetric && (ftype == MAT_FACTOR_CHOLESKY||ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian CHOLESKY or ICC 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 (*B)->useordering = PETSC_TRUE; 122 PetscFunctionReturn(0); 123 } 124 125 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 126 { 127 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 128 IS isicol; 129 PetscErrorCode ierr; 130 const PetscInt *r,*ic; 131 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 132 PetscInt *bi,*bj,*ajtmp; 133 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 134 PetscReal f; 135 PetscInt nlnk,*lnk,k,**bi_ptr; 136 PetscFreeSpaceList free_space=NULL,current_space=NULL; 137 PetscBT lnkbt; 138 PetscBool missing; 139 140 PetscFunctionBegin; 141 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 142 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 143 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 144 145 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 146 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 147 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 148 149 /* get new row pointers */ 150 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 151 bi[0] = 0; 152 153 /* bdiag is location of diagonal in factor */ 154 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 155 bdiag[0] = 0; 156 157 /* linked list for storing column indices of the active row */ 158 nlnk = n + 1; 159 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 160 161 ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr); 162 163 /* initial FreeSpace size is f*(ai[n]+1) */ 164 f = info->fill; 165 if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */ 166 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 167 current_space = free_space; 168 169 for (i=0; i<n; i++) { 170 /* copy previous fill into linked list */ 171 nzi = 0; 172 nnz = ai[r[i]+1] - ai[r[i]]; 173 ajtmp = aj + ai[r[i]]; 174 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 175 nzi += nlnk; 176 177 /* add pivot rows into linked list */ 178 row = lnk[n]; 179 while (row < i) { 180 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 181 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 182 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 183 nzi += nlnk; 184 row = lnk[row]; 185 } 186 bi[i+1] = bi[i] + nzi; 187 im[i] = nzi; 188 189 /* mark bdiag */ 190 nzbd = 0; 191 nnz = nzi; 192 k = lnk[n]; 193 while (nnz-- && k < i) { 194 nzbd++; 195 k = lnk[k]; 196 } 197 bdiag[i] = bi[i] + nzbd; 198 199 /* if free space is not available, make more free space */ 200 if (current_space->local_remaining<nzi) { 201 nnz = PetscIntMultTruncate(n - i,nzi); /* estimated and max additional space needed */ 202 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 203 reallocs++; 204 } 205 206 /* copy data into free space, then initialize lnk */ 207 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 208 209 bi_ptr[i] = current_space->array; 210 current_space->array += nzi; 211 current_space->local_used += nzi; 212 current_space->local_remaining -= nzi; 213 } 214 #if defined(PETSC_USE_INFO) 215 if (ai[n] != 0) { 216 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 217 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 218 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 219 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr); 220 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 221 } else { 222 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 223 } 224 #endif 225 226 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 227 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 228 229 /* destroy list of free space and other temporary array(s) */ 230 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 231 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 232 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 233 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 234 235 /* put together the new matrix */ 236 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 237 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 238 b = (Mat_SeqAIJ*)(B)->data; 239 240 b->free_a = PETSC_TRUE; 241 b->free_ij = PETSC_TRUE; 242 b->singlemalloc = PETSC_FALSE; 243 244 ierr = PetscMalloc1(bi[n]+1,&b->a);CHKERRQ(ierr); 245 b->j = bj; 246 b->i = bi; 247 b->diag = bdiag; 248 b->ilen = 0; 249 b->imax = 0; 250 b->row = isrow; 251 b->col = iscol; 252 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 253 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 254 b->icol = isicol; 255 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 256 257 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 258 ierr = PetscLogObjectMemory((PetscObject)B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 259 b->maxnz = b->nz = bi[n]; 260 261 (B)->factortype = MAT_FACTOR_LU; 262 (B)->info.factor_mallocs = reallocs; 263 (B)->info.fill_ratio_given = f; 264 265 if (ai[n]) { 266 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 267 } else { 268 (B)->info.fill_ratio_needed = 0.0; 269 } 270 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 271 if (a->inode.size) { 272 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 273 } 274 PetscFunctionReturn(0); 275 } 276 277 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 278 { 279 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 280 IS isicol; 281 PetscErrorCode ierr; 282 const PetscInt *r,*ic,*ai=a->i,*aj=a->j,*ajtmp; 283 PetscInt i,n=A->rmap->n; 284 PetscInt *bi,*bj; 285 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 286 PetscReal f; 287 PetscInt nlnk,*lnk,k,**bi_ptr; 288 PetscFreeSpaceList free_space=NULL,current_space=NULL; 289 PetscBT lnkbt; 290 PetscBool missing; 291 292 PetscFunctionBegin; 293 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 294 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 295 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 296 297 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 298 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 299 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 300 301 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 302 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 303 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 304 bi[0] = bdiag[0] = 0; 305 306 /* linked list for storing column indices of the active row */ 307 nlnk = n + 1; 308 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 309 310 ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr); 311 312 /* initial FreeSpace size is f*(ai[n]+1) */ 313 f = info->fill; 314 if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */ 315 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 316 current_space = free_space; 317 318 for (i=0; i<n; i++) { 319 /* copy previous fill into linked list */ 320 nzi = 0; 321 nnz = ai[r[i]+1] - ai[r[i]]; 322 ajtmp = aj + ai[r[i]]; 323 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 324 nzi += nlnk; 325 326 /* add pivot rows into linked list */ 327 row = lnk[n]; 328 while (row < i) { 329 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 330 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 331 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 332 nzi += nlnk; 333 row = lnk[row]; 334 } 335 bi[i+1] = bi[i] + nzi; 336 im[i] = nzi; 337 338 /* mark bdiag */ 339 nzbd = 0; 340 nnz = nzi; 341 k = lnk[n]; 342 while (nnz-- && k < i) { 343 nzbd++; 344 k = lnk[k]; 345 } 346 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 347 348 /* if free space is not available, make more free space */ 349 if (current_space->local_remaining<nzi) { 350 /* estimated additional space needed */ 351 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(n-1,nzi)); 352 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 353 reallocs++; 354 } 355 356 /* copy data into free space, then initialize lnk */ 357 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 358 359 bi_ptr[i] = current_space->array; 360 current_space->array += nzi; 361 current_space->local_used += nzi; 362 current_space->local_remaining -= nzi; 363 } 364 365 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 366 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 367 368 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 369 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 370 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 371 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 372 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 373 374 /* put together the new matrix */ 375 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 376 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 377 b = (Mat_SeqAIJ*)(B)->data; 378 379 b->free_a = PETSC_TRUE; 380 b->free_ij = PETSC_TRUE; 381 b->singlemalloc = PETSC_FALSE; 382 383 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 384 385 b->j = bj; 386 b->i = bi; 387 b->diag = bdiag; 388 b->ilen = 0; 389 b->imax = 0; 390 b->row = isrow; 391 b->col = iscol; 392 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 393 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 394 b->icol = isicol; 395 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 396 397 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 398 ierr = PetscLogObjectMemory((PetscObject)B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 399 b->maxnz = b->nz = bdiag[0]+1; 400 401 B->factortype = MAT_FACTOR_LU; 402 B->info.factor_mallocs = reallocs; 403 B->info.fill_ratio_given = f; 404 405 if (ai[n]) { 406 B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 407 } else { 408 B->info.fill_ratio_needed = 0.0; 409 } 410 #if defined(PETSC_USE_INFO) 411 if (ai[n] != 0) { 412 PetscReal af = B->info.fill_ratio_needed; 413 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 414 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 415 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr); 416 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 417 } else { 418 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 419 } 420 #endif 421 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 422 if (a->inode.size) { 423 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 424 } 425 ierr = MatSeqAIJCheckInode_FactorLU(B);CHKERRQ(ierr); 426 PetscFunctionReturn(0); 427 } 428 429 /* 430 Trouble in factorization, should we dump the original matrix? 431 */ 432 PetscErrorCode MatFactorDumpMatrix(Mat A) 433 { 434 PetscErrorCode ierr; 435 PetscBool flg = PETSC_FALSE; 436 437 PetscFunctionBegin; 438 ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-mat_factor_dump_on_error",&flg,NULL);CHKERRQ(ierr); 439 if (flg) { 440 PetscViewer viewer; 441 char filename[PETSC_MAX_PATH_LEN]; 442 443 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 444 ierr = PetscViewerBinaryOpen(PetscObjectComm((PetscObject)A),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 445 ierr = MatView(A,viewer);CHKERRQ(ierr); 446 ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr); 447 } 448 PetscFunctionReturn(0); 449 } 450 451 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 452 { 453 Mat C =B; 454 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 455 IS isrow = b->row,isicol = b->icol; 456 PetscErrorCode ierr; 457 const PetscInt *r,*ic,*ics; 458 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 459 PetscInt i,j,k,nz,nzL,row,*pj; 460 const PetscInt *ajtmp,*bjtmp; 461 MatScalar *rtmp,*pc,multiplier,*pv; 462 const MatScalar *aa=a->a,*v; 463 PetscBool row_identity,col_identity; 464 FactorShiftCtx sctx; 465 const PetscInt *ddiag; 466 PetscReal rs; 467 MatScalar d; 468 469 PetscFunctionBegin; 470 /* MatPivotSetUp(): initialize shift context sctx */ 471 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 472 473 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 474 ddiag = a->diag; 475 sctx.shift_top = info->zeropivot; 476 for (i=0; i<n; i++) { 477 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 478 d = (aa)[ddiag[i]]; 479 rs = -PetscAbsScalar(d) - PetscRealPart(d); 480 v = aa+ai[i]; 481 nz = ai[i+1] - ai[i]; 482 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 483 if (rs>sctx.shift_top) sctx.shift_top = rs; 484 } 485 sctx.shift_top *= 1.1; 486 sctx.nshift_max = 5; 487 sctx.shift_lo = 0.; 488 sctx.shift_hi = 1.; 489 } 490 491 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 492 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 493 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 494 ics = ic; 495 496 do { 497 sctx.newshift = PETSC_FALSE; 498 for (i=0; i<n; i++) { 499 /* zero rtmp */ 500 /* L part */ 501 nz = bi[i+1] - bi[i]; 502 bjtmp = bj + bi[i]; 503 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 504 505 /* U part */ 506 nz = bdiag[i]-bdiag[i+1]; 507 bjtmp = bj + bdiag[i+1]+1; 508 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 509 510 /* load in initial (unfactored row) */ 511 nz = ai[r[i]+1] - ai[r[i]]; 512 ajtmp = aj + ai[r[i]]; 513 v = aa + ai[r[i]]; 514 for (j=0; j<nz; j++) { 515 rtmp[ics[ajtmp[j]]] = v[j]; 516 } 517 /* ZeropivotApply() */ 518 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 519 520 /* elimination */ 521 bjtmp = bj + bi[i]; 522 row = *bjtmp++; 523 nzL = bi[i+1] - bi[i]; 524 for (k=0; k < nzL; k++) { 525 pc = rtmp + row; 526 if (*pc != 0.0) { 527 pv = b->a + bdiag[row]; 528 multiplier = *pc * (*pv); 529 *pc = multiplier; 530 531 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 532 pv = b->a + bdiag[row+1]+1; 533 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 534 535 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 536 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 537 } 538 row = *bjtmp++; 539 } 540 541 /* finished row so stick it into b->a */ 542 rs = 0.0; 543 /* L part */ 544 pv = b->a + bi[i]; 545 pj = b->j + bi[i]; 546 nz = bi[i+1] - bi[i]; 547 for (j=0; j<nz; j++) { 548 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 549 } 550 551 /* U part */ 552 pv = b->a + bdiag[i+1]+1; 553 pj = b->j + bdiag[i+1]+1; 554 nz = bdiag[i] - bdiag[i+1]-1; 555 for (j=0; j<nz; j++) { 556 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 557 } 558 559 sctx.rs = rs; 560 sctx.pv = rtmp[i]; 561 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 562 if (sctx.newshift) break; /* break for-loop */ 563 rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */ 564 565 /* Mark diagonal and invert diagonal for simplier triangular solves */ 566 pv = b->a + bdiag[i]; 567 *pv = 1.0/rtmp[i]; 568 569 } /* endof for (i=0; i<n; i++) { */ 570 571 /* MatPivotRefine() */ 572 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 573 /* 574 * if no shift in this attempt & shifting & started shifting & can refine, 575 * then try lower shift 576 */ 577 sctx.shift_hi = sctx.shift_fraction; 578 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 579 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 580 sctx.newshift = PETSC_TRUE; 581 sctx.nshift++; 582 } 583 } while (sctx.newshift); 584 585 ierr = PetscFree(rtmp);CHKERRQ(ierr); 586 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 587 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 588 589 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 590 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 591 if (b->inode.size) { 592 C->ops->solve = MatSolve_SeqAIJ_Inode; 593 } else if (row_identity && col_identity) { 594 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 595 } else { 596 C->ops->solve = MatSolve_SeqAIJ; 597 } 598 C->ops->solveadd = MatSolveAdd_SeqAIJ; 599 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 600 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 601 C->ops->matsolve = MatMatSolve_SeqAIJ; 602 C->assembled = PETSC_TRUE; 603 C->preallocated = PETSC_TRUE; 604 605 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 606 607 /* MatShiftView(A,info,&sctx) */ 608 if (sctx.nshift) { 609 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 610 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); 611 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 612 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 613 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 614 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 615 } 616 } 617 PetscFunctionReturn(0); 618 } 619 620 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 621 { 622 Mat C =B; 623 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 624 IS isrow = b->row,isicol = b->icol; 625 PetscErrorCode ierr; 626 const PetscInt *r,*ic,*ics; 627 PetscInt nz,row,i,j,n=A->rmap->n,diag; 628 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 629 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 630 MatScalar *pv,*rtmp,*pc,multiplier,d; 631 const MatScalar *v,*aa=a->a; 632 PetscReal rs=0.0; 633 FactorShiftCtx sctx; 634 const PetscInt *ddiag; 635 PetscBool row_identity, col_identity; 636 637 PetscFunctionBegin; 638 /* MatPivotSetUp(): initialize shift context sctx */ 639 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 640 641 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 642 ddiag = a->diag; 643 sctx.shift_top = info->zeropivot; 644 for (i=0; i<n; i++) { 645 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 646 d = (aa)[ddiag[i]]; 647 rs = -PetscAbsScalar(d) - PetscRealPart(d); 648 v = aa+ai[i]; 649 nz = ai[i+1] - ai[i]; 650 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 651 if (rs>sctx.shift_top) sctx.shift_top = rs; 652 } 653 sctx.shift_top *= 1.1; 654 sctx.nshift_max = 5; 655 sctx.shift_lo = 0.; 656 sctx.shift_hi = 1.; 657 } 658 659 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 660 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 661 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 662 ics = ic; 663 664 do { 665 sctx.newshift = PETSC_FALSE; 666 for (i=0; i<n; i++) { 667 nz = bi[i+1] - bi[i]; 668 bjtmp = bj + bi[i]; 669 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 670 671 /* load in initial (unfactored row) */ 672 nz = ai[r[i]+1] - ai[r[i]]; 673 ajtmp = aj + ai[r[i]]; 674 v = aa + ai[r[i]]; 675 for (j=0; j<nz; j++) { 676 rtmp[ics[ajtmp[j]]] = v[j]; 677 } 678 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 679 680 row = *bjtmp++; 681 while (row < i) { 682 pc = rtmp + row; 683 if (*pc != 0.0) { 684 pv = b->a + diag_offset[row]; 685 pj = b->j + diag_offset[row] + 1; 686 multiplier = *pc / *pv++; 687 *pc = multiplier; 688 nz = bi[row+1] - diag_offset[row] - 1; 689 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 690 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 691 } 692 row = *bjtmp++; 693 } 694 /* finished row so stick it into b->a */ 695 pv = b->a + bi[i]; 696 pj = b->j + bi[i]; 697 nz = bi[i+1] - bi[i]; 698 diag = diag_offset[i] - bi[i]; 699 rs = 0.0; 700 for (j=0; j<nz; j++) { 701 pv[j] = rtmp[pj[j]]; 702 rs += PetscAbsScalar(pv[j]); 703 } 704 rs -= PetscAbsScalar(pv[diag]); 705 706 sctx.rs = rs; 707 sctx.pv = pv[diag]; 708 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 709 if (sctx.newshift) break; 710 pv[diag] = sctx.pv; 711 } 712 713 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 714 /* 715 * if no shift in this attempt & shifting & started shifting & can refine, 716 * then try lower shift 717 */ 718 sctx.shift_hi = sctx.shift_fraction; 719 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 720 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 721 sctx.newshift = PETSC_TRUE; 722 sctx.nshift++; 723 } 724 } while (sctx.newshift); 725 726 /* invert diagonal entries for simplier triangular solves */ 727 for (i=0; i<n; i++) { 728 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 729 } 730 ierr = PetscFree(rtmp);CHKERRQ(ierr); 731 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 732 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 733 734 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 735 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 736 if (row_identity && col_identity) { 737 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 738 } else { 739 C->ops->solve = MatSolve_SeqAIJ_inplace; 740 } 741 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 742 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 743 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 744 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 745 746 C->assembled = PETSC_TRUE; 747 C->preallocated = PETSC_TRUE; 748 749 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 750 if (sctx.nshift) { 751 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 752 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); 753 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 754 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 755 } 756 } 757 (C)->ops->solve = MatSolve_SeqAIJ_inplace; 758 (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 759 760 ierr = MatSeqAIJCheckInode(C);CHKERRQ(ierr); 761 PetscFunctionReturn(0); 762 } 763 764 /* 765 This routine implements inplace ILU(0) with row or/and column permutations. 766 Input: 767 A - original matrix 768 Output; 769 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 770 a->j (col index) is permuted by the inverse of colperm, then sorted 771 a->a reordered accordingly with a->j 772 a->diag (ptr to diagonal elements) is updated. 773 */ 774 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 775 { 776 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data; 777 IS isrow = a->row,isicol = a->icol; 778 PetscErrorCode ierr; 779 const PetscInt *r,*ic,*ics; 780 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 781 PetscInt *ajtmp,nz,row; 782 PetscInt *diag = a->diag,nbdiag,*pj; 783 PetscScalar *rtmp,*pc,multiplier,d; 784 MatScalar *pv,*v; 785 PetscReal rs; 786 FactorShiftCtx sctx; 787 const MatScalar *aa=a->a,*vtmp; 788 789 PetscFunctionBegin; 790 if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 791 792 /* MatPivotSetUp(): initialize shift context sctx */ 793 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 794 795 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 796 const PetscInt *ddiag = a->diag; 797 sctx.shift_top = info->zeropivot; 798 for (i=0; i<n; i++) { 799 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 800 d = (aa)[ddiag[i]]; 801 rs = -PetscAbsScalar(d) - PetscRealPart(d); 802 vtmp = aa+ai[i]; 803 nz = ai[i+1] - ai[i]; 804 for (j=0; j<nz; j++) rs += PetscAbsScalar(vtmp[j]); 805 if (rs>sctx.shift_top) sctx.shift_top = rs; 806 } 807 sctx.shift_top *= 1.1; 808 sctx.nshift_max = 5; 809 sctx.shift_lo = 0.; 810 sctx.shift_hi = 1.; 811 } 812 813 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 814 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 815 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 816 ierr = PetscArrayzero(rtmp,n+1);CHKERRQ(ierr); 817 ics = ic; 818 819 #if defined(MV) 820 sctx.shift_top = 0.; 821 sctx.nshift_max = 0; 822 sctx.shift_lo = 0.; 823 sctx.shift_hi = 0.; 824 sctx.shift_fraction = 0.; 825 826 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 827 sctx.shift_top = 0.; 828 for (i=0; i<n; i++) { 829 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 830 d = (a->a)[diag[i]]; 831 rs = -PetscAbsScalar(d) - PetscRealPart(d); 832 v = a->a+ai[i]; 833 nz = ai[i+1] - ai[i]; 834 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 835 if (rs>sctx.shift_top) sctx.shift_top = rs; 836 } 837 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 838 sctx.shift_top *= 1.1; 839 sctx.nshift_max = 5; 840 sctx.shift_lo = 0.; 841 sctx.shift_hi = 1.; 842 } 843 844 sctx.shift_amount = 0.; 845 sctx.nshift = 0; 846 #endif 847 848 do { 849 sctx.newshift = PETSC_FALSE; 850 for (i=0; i<n; i++) { 851 /* load in initial unfactored row */ 852 nz = ai[r[i]+1] - ai[r[i]]; 853 ajtmp = aj + ai[r[i]]; 854 v = a->a + ai[r[i]]; 855 /* sort permuted ajtmp and values v accordingly */ 856 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 857 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 858 859 diag[r[i]] = ai[r[i]]; 860 for (j=0; j<nz; j++) { 861 rtmp[ajtmp[j]] = v[j]; 862 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 863 } 864 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 865 866 row = *ajtmp++; 867 while (row < i) { 868 pc = rtmp + row; 869 if (*pc != 0.0) { 870 pv = a->a + diag[r[row]]; 871 pj = aj + diag[r[row]] + 1; 872 873 multiplier = *pc / *pv++; 874 *pc = multiplier; 875 nz = ai[r[row]+1] - diag[r[row]] - 1; 876 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 877 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 878 } 879 row = *ajtmp++; 880 } 881 /* finished row so overwrite it onto a->a */ 882 pv = a->a + ai[r[i]]; 883 pj = aj + ai[r[i]]; 884 nz = ai[r[i]+1] - ai[r[i]]; 885 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 886 887 rs = 0.0; 888 for (j=0; j<nz; j++) { 889 pv[j] = rtmp[pj[j]]; 890 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 891 } 892 893 sctx.rs = rs; 894 sctx.pv = pv[nbdiag]; 895 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 896 if (sctx.newshift) break; 897 pv[nbdiag] = sctx.pv; 898 } 899 900 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 901 /* 902 * if no shift in this attempt & shifting & started shifting & can refine, 903 * then try lower shift 904 */ 905 sctx.shift_hi = sctx.shift_fraction; 906 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 907 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 908 sctx.newshift = PETSC_TRUE; 909 sctx.nshift++; 910 } 911 } while (sctx.newshift); 912 913 /* invert diagonal entries for simplier triangular solves */ 914 for (i=0; i<n; i++) { 915 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 916 } 917 918 ierr = PetscFree(rtmp);CHKERRQ(ierr); 919 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 920 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 921 922 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 923 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 924 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 925 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 926 927 A->assembled = PETSC_TRUE; 928 A->preallocated = PETSC_TRUE; 929 930 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 931 if (sctx.nshift) { 932 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 933 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); 934 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 935 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 936 } 937 } 938 PetscFunctionReturn(0); 939 } 940 941 /* ----------------------------------------------------------- */ 942 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 943 { 944 PetscErrorCode ierr; 945 Mat C; 946 947 PetscFunctionBegin; 948 ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 949 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 950 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 951 952 A->ops->solve = C->ops->solve; 953 A->ops->solvetranspose = C->ops->solvetranspose; 954 955 ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr); 956 ierr = PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 957 PetscFunctionReturn(0); 958 } 959 /* ----------------------------------------------------------- */ 960 961 962 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 963 { 964 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 965 IS iscol = a->col,isrow = a->row; 966 PetscErrorCode ierr; 967 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 968 PetscInt nz; 969 const PetscInt *rout,*cout,*r,*c; 970 PetscScalar *x,*tmp,*tmps,sum; 971 const PetscScalar *b; 972 const MatScalar *aa = a->a,*v; 973 974 PetscFunctionBegin; 975 if (!n) PetscFunctionReturn(0); 976 977 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 978 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 979 tmp = a->solve_work; 980 981 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 982 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 983 984 /* forward solve the lower triangular */ 985 tmp[0] = b[*r++]; 986 tmps = tmp; 987 for (i=1; i<n; i++) { 988 v = aa + ai[i]; 989 vi = aj + ai[i]; 990 nz = a->diag[i] - ai[i]; 991 sum = b[*r++]; 992 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 993 tmp[i] = sum; 994 } 995 996 /* backward solve the upper triangular */ 997 for (i=n-1; i>=0; i--) { 998 v = aa + a->diag[i] + 1; 999 vi = aj + a->diag[i] + 1; 1000 nz = ai[i+1] - a->diag[i] - 1; 1001 sum = tmp[i]; 1002 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1003 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1004 } 1005 1006 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1007 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1008 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1009 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1010 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1011 PetscFunctionReturn(0); 1012 } 1013 1014 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1015 { 1016 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1017 IS iscol = a->col,isrow = a->row; 1018 PetscErrorCode ierr; 1019 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1020 PetscInt nz,neq,ldb,ldx; 1021 const PetscInt *rout,*cout,*r,*c; 1022 PetscScalar *x,*tmp = a->solve_work,*tmps,sum; 1023 const PetscScalar *b,*aa = a->a,*v; 1024 PetscBool isdense; 1025 1026 PetscFunctionBegin; 1027 if (!n) PetscFunctionReturn(0); 1028 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1029 if (!isdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1030 if (X != B) { 1031 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1032 if (!isdense) 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 = MatDenseGetLDA(B,&ldb);CHKERRQ(ierr); 1036 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1037 ierr = MatDenseGetLDA(X,&ldx);CHKERRQ(ierr); 1038 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1039 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1040 for (neq=0; neq<B->cmap->n; neq++) { 1041 /* forward solve the lower triangular */ 1042 tmp[0] = b[r[0]]; 1043 tmps = tmp; 1044 for (i=1; i<n; i++) { 1045 v = aa + ai[i]; 1046 vi = aj + ai[i]; 1047 nz = a->diag[i] - ai[i]; 1048 sum = b[r[i]]; 1049 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1050 tmp[i] = sum; 1051 } 1052 /* backward solve the upper triangular */ 1053 for (i=n-1; i>=0; i--) { 1054 v = aa + a->diag[i] + 1; 1055 vi = aj + a->diag[i] + 1; 1056 nz = ai[i+1] - a->diag[i] - 1; 1057 sum = tmp[i]; 1058 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1059 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1060 } 1061 b += ldb; 1062 x += ldx; 1063 } 1064 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1065 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1066 ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr); 1067 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1068 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1069 PetscFunctionReturn(0); 1070 } 1071 1072 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1073 { 1074 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1075 IS iscol = a->col,isrow = a->row; 1076 PetscErrorCode ierr; 1077 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1078 PetscInt nz,neq,ldb,ldx; 1079 const PetscInt *rout,*cout,*r,*c; 1080 PetscScalar *x,*tmp = a->solve_work,sum; 1081 const PetscScalar *b,*aa = a->a,*v; 1082 PetscBool isdense; 1083 1084 PetscFunctionBegin; 1085 if (!n) PetscFunctionReturn(0); 1086 ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1087 if (!isdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1088 if (X != B) { 1089 ierr = PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&isdense);CHKERRQ(ierr); 1090 if (!isdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1091 } 1092 ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr); 1093 ierr = MatDenseGetLDA(B,&ldb);CHKERRQ(ierr); 1094 ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr); 1095 ierr = MatDenseGetLDA(X,&ldx);CHKERRQ(ierr); 1096 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1097 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1098 for (neq=0; neq<B->cmap->n; neq++) { 1099 /* forward solve the lower triangular */ 1100 tmp[0] = b[r[0]]; 1101 v = aa; 1102 vi = aj; 1103 for (i=1; i<n; i++) { 1104 nz = ai[i+1] - ai[i]; 1105 sum = b[r[i]]; 1106 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1107 tmp[i] = sum; 1108 v += nz; vi += nz; 1109 } 1110 /* backward solve the upper triangular */ 1111 for (i=n-1; i>=0; i--) { 1112 v = aa + adiag[i+1]+1; 1113 vi = aj + adiag[i+1]+1; 1114 nz = adiag[i]-adiag[i+1]-1; 1115 sum = tmp[i]; 1116 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1117 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1118 } 1119 b += ldb; 1120 x += ldx; 1121 } 1122 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1123 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1124 ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr); 1125 ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr); 1126 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1127 PetscFunctionReturn(0); 1128 } 1129 1130 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1131 { 1132 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1133 IS iscol = a->col,isrow = a->row; 1134 PetscErrorCode ierr; 1135 const PetscInt *r,*c,*rout,*cout; 1136 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1137 PetscInt nz,row; 1138 PetscScalar *x,*tmp,*tmps,sum; 1139 const PetscScalar *b; 1140 const MatScalar *aa = a->a,*v; 1141 1142 PetscFunctionBegin; 1143 if (!n) PetscFunctionReturn(0); 1144 1145 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1146 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1147 tmp = a->solve_work; 1148 1149 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1150 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1151 1152 /* forward solve the lower triangular */ 1153 tmp[0] = b[*r++]; 1154 tmps = tmp; 1155 for (row=1; row<n; row++) { 1156 i = rout[row]; /* permuted row */ 1157 v = aa + ai[i]; 1158 vi = aj + ai[i]; 1159 nz = a->diag[i] - ai[i]; 1160 sum = b[*r++]; 1161 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1162 tmp[row] = sum; 1163 } 1164 1165 /* backward solve the upper triangular */ 1166 for (row=n-1; row>=0; row--) { 1167 i = rout[row]; /* permuted row */ 1168 v = aa + a->diag[i] + 1; 1169 vi = aj + a->diag[i] + 1; 1170 nz = ai[i+1] - a->diag[i] - 1; 1171 sum = tmp[row]; 1172 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1173 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1174 } 1175 1176 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1177 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1178 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1179 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1180 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1181 PetscFunctionReturn(0); 1182 } 1183 1184 /* ----------------------------------------------------------- */ 1185 #include <../src/mat/impls/aij/seq/ftn-kernels/fsolve.h> 1186 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1187 { 1188 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1189 PetscErrorCode ierr; 1190 PetscInt n = A->rmap->n; 1191 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1192 PetscScalar *x; 1193 const PetscScalar *b; 1194 const MatScalar *aa = a->a; 1195 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1196 PetscInt adiag_i,i,nz,ai_i; 1197 const PetscInt *vi; 1198 const MatScalar *v; 1199 PetscScalar sum; 1200 #endif 1201 1202 PetscFunctionBegin; 1203 if (!n) PetscFunctionReturn(0); 1204 1205 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1206 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1207 1208 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1209 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1210 #else 1211 /* forward solve the lower triangular */ 1212 x[0] = b[0]; 1213 for (i=1; i<n; i++) { 1214 ai_i = ai[i]; 1215 v = aa + ai_i; 1216 vi = aj + ai_i; 1217 nz = adiag[i] - ai_i; 1218 sum = b[i]; 1219 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1220 x[i] = sum; 1221 } 1222 1223 /* backward solve the upper triangular */ 1224 for (i=n-1; i>=0; i--) { 1225 adiag_i = adiag[i]; 1226 v = aa + adiag_i + 1; 1227 vi = aj + adiag_i + 1; 1228 nz = ai[i+1] - adiag_i - 1; 1229 sum = x[i]; 1230 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1231 x[i] = sum*aa[adiag_i]; 1232 } 1233 #endif 1234 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1235 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1236 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1237 PetscFunctionReturn(0); 1238 } 1239 1240 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1241 { 1242 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1243 IS iscol = a->col,isrow = a->row; 1244 PetscErrorCode ierr; 1245 PetscInt i, n = A->rmap->n,j; 1246 PetscInt nz; 1247 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1248 PetscScalar *x,*tmp,sum; 1249 const PetscScalar *b; 1250 const MatScalar *aa = a->a,*v; 1251 1252 PetscFunctionBegin; 1253 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1254 1255 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1256 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1257 tmp = a->solve_work; 1258 1259 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1260 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1261 1262 /* forward solve the lower triangular */ 1263 tmp[0] = b[*r++]; 1264 for (i=1; i<n; i++) { 1265 v = aa + ai[i]; 1266 vi = aj + ai[i]; 1267 nz = a->diag[i] - ai[i]; 1268 sum = b[*r++]; 1269 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1270 tmp[i] = sum; 1271 } 1272 1273 /* backward solve the upper triangular */ 1274 for (i=n-1; i>=0; i--) { 1275 v = aa + a->diag[i] + 1; 1276 vi = aj + a->diag[i] + 1; 1277 nz = ai[i+1] - a->diag[i] - 1; 1278 sum = tmp[i]; 1279 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1280 tmp[i] = sum*aa[a->diag[i]]; 1281 x[*c--] += tmp[i]; 1282 } 1283 1284 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1285 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1286 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1287 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1288 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1289 PetscFunctionReturn(0); 1290 } 1291 1292 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1293 { 1294 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1295 IS iscol = a->col,isrow = a->row; 1296 PetscErrorCode ierr; 1297 PetscInt i, n = A->rmap->n,j; 1298 PetscInt nz; 1299 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1300 PetscScalar *x,*tmp,sum; 1301 const PetscScalar *b; 1302 const MatScalar *aa = a->a,*v; 1303 1304 PetscFunctionBegin; 1305 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1306 1307 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1308 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1309 tmp = a->solve_work; 1310 1311 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1312 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1313 1314 /* forward solve the lower triangular */ 1315 tmp[0] = b[r[0]]; 1316 v = aa; 1317 vi = aj; 1318 for (i=1; i<n; i++) { 1319 nz = ai[i+1] - ai[i]; 1320 sum = b[r[i]]; 1321 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1322 tmp[i] = sum; 1323 v += nz; 1324 vi += nz; 1325 } 1326 1327 /* backward solve the upper triangular */ 1328 v = aa + adiag[n-1]; 1329 vi = aj + adiag[n-1]; 1330 for (i=n-1; i>=0; i--) { 1331 nz = adiag[i] - adiag[i+1] - 1; 1332 sum = tmp[i]; 1333 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1334 tmp[i] = sum*v[nz]; 1335 x[c[i]] += tmp[i]; 1336 v += nz+1; vi += nz+1; 1337 } 1338 1339 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1340 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1341 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1342 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1343 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1344 PetscFunctionReturn(0); 1345 } 1346 1347 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1348 { 1349 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1350 IS iscol = a->col,isrow = a->row; 1351 PetscErrorCode ierr; 1352 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1353 PetscInt i,n = A->rmap->n,j; 1354 PetscInt nz; 1355 PetscScalar *x,*tmp,s1; 1356 const MatScalar *aa = a->a,*v; 1357 const PetscScalar *b; 1358 1359 PetscFunctionBegin; 1360 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1361 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1362 tmp = a->solve_work; 1363 1364 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1365 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1366 1367 /* copy the b into temp work space according to permutation */ 1368 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1369 1370 /* forward solve the U^T */ 1371 for (i=0; i<n; i++) { 1372 v = aa + diag[i]; 1373 vi = aj + diag[i] + 1; 1374 nz = ai[i+1] - diag[i] - 1; 1375 s1 = tmp[i]; 1376 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1377 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1378 tmp[i] = s1; 1379 } 1380 1381 /* backward solve the L^T */ 1382 for (i=n-1; i>=0; i--) { 1383 v = aa + diag[i] - 1; 1384 vi = aj + diag[i] - 1; 1385 nz = diag[i] - ai[i]; 1386 s1 = tmp[i]; 1387 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1388 } 1389 1390 /* copy tmp into x according to permutation */ 1391 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1392 1393 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1394 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1395 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1396 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1397 1398 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1399 PetscFunctionReturn(0); 1400 } 1401 1402 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1403 { 1404 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1405 IS iscol = a->col,isrow = a->row; 1406 PetscErrorCode ierr; 1407 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1408 PetscInt i,n = A->rmap->n,j; 1409 PetscInt nz; 1410 PetscScalar *x,*tmp,s1; 1411 const MatScalar *aa = a->a,*v; 1412 const PetscScalar *b; 1413 1414 PetscFunctionBegin; 1415 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1416 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 1417 tmp = a->solve_work; 1418 1419 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1420 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1421 1422 /* copy the b into temp work space according to permutation */ 1423 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1424 1425 /* forward solve the U^T */ 1426 for (i=0; i<n; i++) { 1427 v = aa + adiag[i+1] + 1; 1428 vi = aj + adiag[i+1] + 1; 1429 nz = adiag[i] - adiag[i+1] - 1; 1430 s1 = tmp[i]; 1431 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1432 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1433 tmp[i] = s1; 1434 } 1435 1436 /* backward solve the L^T */ 1437 for (i=n-1; i>=0; i--) { 1438 v = aa + ai[i]; 1439 vi = aj + ai[i]; 1440 nz = ai[i+1] - ai[i]; 1441 s1 = tmp[i]; 1442 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1443 } 1444 1445 /* copy tmp into x according to permutation */ 1446 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1447 1448 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1449 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1450 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1451 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 1452 1453 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1454 PetscFunctionReturn(0); 1455 } 1456 1457 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1458 { 1459 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1460 IS iscol = a->col,isrow = a->row; 1461 PetscErrorCode ierr; 1462 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1463 PetscInt i,n = A->rmap->n,j; 1464 PetscInt nz; 1465 PetscScalar *x,*tmp,s1; 1466 const MatScalar *aa = a->a,*v; 1467 const PetscScalar *b; 1468 1469 PetscFunctionBegin; 1470 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1471 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1472 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1473 tmp = a->solve_work; 1474 1475 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1476 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1477 1478 /* copy the b into temp work space according to permutation */ 1479 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1480 1481 /* forward solve the U^T */ 1482 for (i=0; i<n; i++) { 1483 v = aa + diag[i]; 1484 vi = aj + diag[i] + 1; 1485 nz = ai[i+1] - diag[i] - 1; 1486 s1 = tmp[i]; 1487 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1488 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1489 tmp[i] = s1; 1490 } 1491 1492 /* backward solve the L^T */ 1493 for (i=n-1; i>=0; i--) { 1494 v = aa + diag[i] - 1; 1495 vi = aj + diag[i] - 1; 1496 nz = diag[i] - ai[i]; 1497 s1 = tmp[i]; 1498 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1499 } 1500 1501 /* copy tmp into x according to permutation */ 1502 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1503 1504 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1505 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1506 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1507 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1508 1509 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1510 PetscFunctionReturn(0); 1511 } 1512 1513 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1514 { 1515 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1516 IS iscol = a->col,isrow = a->row; 1517 PetscErrorCode ierr; 1518 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1519 PetscInt i,n = A->rmap->n,j; 1520 PetscInt nz; 1521 PetscScalar *x,*tmp,s1; 1522 const MatScalar *aa = a->a,*v; 1523 const PetscScalar *b; 1524 1525 PetscFunctionBegin; 1526 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1527 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1528 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1529 tmp = a->solve_work; 1530 1531 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1532 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1533 1534 /* copy the b into temp work space according to permutation */ 1535 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1536 1537 /* forward solve the U^T */ 1538 for (i=0; i<n; i++) { 1539 v = aa + adiag[i+1] + 1; 1540 vi = aj + adiag[i+1] + 1; 1541 nz = adiag[i] - adiag[i+1] - 1; 1542 s1 = tmp[i]; 1543 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1544 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1545 tmp[i] = s1; 1546 } 1547 1548 1549 /* backward solve the L^T */ 1550 for (i=n-1; i>=0; i--) { 1551 v = aa + ai[i]; 1552 vi = aj + ai[i]; 1553 nz = ai[i+1] - ai[i]; 1554 s1 = tmp[i]; 1555 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1556 } 1557 1558 /* copy tmp into x according to permutation */ 1559 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1560 1561 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1562 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1563 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1564 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1565 1566 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1567 PetscFunctionReturn(0); 1568 } 1569 1570 /* ----------------------------------------------------------------*/ 1571 1572 /* 1573 ilu() under revised new data structure. 1574 Factored arrays bj and ba are stored as 1575 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1576 1577 bi=fact->i is an array of size n+1, in which 1578 bi+ 1579 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1580 bi[n]: points to L(n-1,n-1)+1 1581 1582 bdiag=fact->diag is an array of size n+1,in which 1583 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1584 bdiag[n]: points to entry of U(n-1,0)-1 1585 1586 U(i,:) contains bdiag[i] as its last entry, i.e., 1587 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1588 */ 1589 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1590 { 1591 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1592 PetscErrorCode ierr; 1593 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1594 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1595 IS isicol; 1596 1597 PetscFunctionBegin; 1598 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1599 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1600 b = (Mat_SeqAIJ*)(fact)->data; 1601 1602 /* allocate matrix arrays for new data structure */ 1603 ierr = PetscMalloc3(ai[n]+1,&b->a,ai[n]+1,&b->j,n+1,&b->i);CHKERRQ(ierr); 1604 ierr = PetscLogObjectMemory((PetscObject)fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1605 1606 b->singlemalloc = PETSC_TRUE; 1607 if (!b->diag) { 1608 ierr = PetscMalloc1(n+1,&b->diag);CHKERRQ(ierr); 1609 ierr = PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1610 } 1611 bdiag = b->diag; 1612 1613 if (n > 0) { 1614 ierr = PetscArrayzero(b->a,ai[n]);CHKERRQ(ierr); 1615 } 1616 1617 /* set bi and bj with new data structure */ 1618 bi = b->i; 1619 bj = b->j; 1620 1621 /* L part */ 1622 bi[0] = 0; 1623 for (i=0; i<n; i++) { 1624 nz = adiag[i] - ai[i]; 1625 bi[i+1] = bi[i] + nz; 1626 aj = a->j + ai[i]; 1627 for (j=0; j<nz; j++) { 1628 /* *bj = aj[j]; bj++; */ 1629 bj[k++] = aj[j]; 1630 } 1631 } 1632 1633 /* U part */ 1634 bdiag[n] = bi[n]-1; 1635 for (i=n-1; i>=0; i--) { 1636 nz = ai[i+1] - adiag[i] - 1; 1637 aj = a->j + adiag[i] + 1; 1638 for (j=0; j<nz; j++) { 1639 /* *bj = aj[j]; bj++; */ 1640 bj[k++] = aj[j]; 1641 } 1642 /* diag[i] */ 1643 /* *bj = i; bj++; */ 1644 bj[k++] = i; 1645 bdiag[i] = bdiag[i+1] + nz + 1; 1646 } 1647 1648 fact->factortype = MAT_FACTOR_ILU; 1649 fact->info.factor_mallocs = 0; 1650 fact->info.fill_ratio_given = info->fill; 1651 fact->info.fill_ratio_needed = 1.0; 1652 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1653 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1654 1655 b = (Mat_SeqAIJ*)(fact)->data; 1656 b->row = isrow; 1657 b->col = iscol; 1658 b->icol = isicol; 1659 ierr = PetscMalloc1(fact->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1660 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1661 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1662 PetscFunctionReturn(0); 1663 } 1664 1665 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1666 { 1667 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1668 IS isicol; 1669 PetscErrorCode ierr; 1670 const PetscInt *r,*ic; 1671 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1672 PetscInt *bi,*cols,nnz,*cols_lvl; 1673 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1674 PetscInt i,levels,diagonal_fill; 1675 PetscBool col_identity,row_identity,missing; 1676 PetscReal f; 1677 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1678 PetscBT lnkbt; 1679 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1680 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1681 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1682 1683 PetscFunctionBegin; 1684 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); 1685 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1686 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1687 1688 levels = (PetscInt)info->levels; 1689 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1690 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1691 if (!levels && row_identity && col_identity) { 1692 /* special case: ilu(0) with natural ordering */ 1693 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1694 if (a->inode.size) { 1695 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1696 } 1697 PetscFunctionReturn(0); 1698 } 1699 1700 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1701 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1702 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1703 1704 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1705 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1706 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1707 bi[0] = bdiag[0] = 0; 1708 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1709 1710 /* create a linked list for storing column indices of the active row */ 1711 nlnk = n + 1; 1712 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1713 1714 /* initial FreeSpace size is f*(ai[n]+1) */ 1715 f = info->fill; 1716 diagonal_fill = (PetscInt)info->diagonal_fill; 1717 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1718 current_space = free_space; 1719 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1720 current_space_lvl = free_space_lvl; 1721 for (i=0; i<n; i++) { 1722 nzi = 0; 1723 /* copy current row into linked list */ 1724 nnz = ai[r[i]+1] - ai[r[i]]; 1725 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); 1726 cols = aj + ai[r[i]]; 1727 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1728 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1729 nzi += nlnk; 1730 1731 /* make sure diagonal entry is included */ 1732 if (diagonal_fill && lnk[i] == -1) { 1733 fm = n; 1734 while (lnk[fm] < i) fm = lnk[fm]; 1735 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1736 lnk[fm] = i; 1737 lnk_lvl[i] = 0; 1738 nzi++; dcount++; 1739 } 1740 1741 /* add pivot rows into the active row */ 1742 nzbd = 0; 1743 prow = lnk[n]; 1744 while (prow < i) { 1745 nnz = bdiag[prow]; 1746 cols = bj_ptr[prow] + nnz + 1; 1747 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1748 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1749 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1750 nzi += nlnk; 1751 prow = lnk[prow]; 1752 nzbd++; 1753 } 1754 bdiag[i] = nzbd; 1755 bi[i+1] = bi[i] + nzi; 1756 /* if free space is not available, make more free space */ 1757 if (current_space->local_remaining<nzi) { 1758 nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(nzi,n - i)); /* estimated and max additional space needed */ 1759 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1760 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1761 reallocs++; 1762 } 1763 1764 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1765 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1766 bj_ptr[i] = current_space->array; 1767 bjlvl_ptr[i] = current_space_lvl->array; 1768 1769 /* make sure the active row i has diagonal entry */ 1770 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); 1771 1772 current_space->array += nzi; 1773 current_space->local_used += nzi; 1774 current_space->local_remaining -= nzi; 1775 current_space_lvl->array += nzi; 1776 current_space_lvl->local_used += nzi; 1777 current_space_lvl->local_remaining -= nzi; 1778 } 1779 1780 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1781 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1782 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1783 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1784 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1785 1786 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1787 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1788 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1789 1790 #if defined(PETSC_USE_INFO) 1791 { 1792 PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1793 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 1794 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1795 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 1796 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1797 if (diagonal_fill) { 1798 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 1799 } 1800 } 1801 #endif 1802 /* put together the new matrix */ 1803 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 1804 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 1805 b = (Mat_SeqAIJ*)(fact)->data; 1806 1807 b->free_a = PETSC_TRUE; 1808 b->free_ij = PETSC_TRUE; 1809 b->singlemalloc = PETSC_FALSE; 1810 1811 ierr = PetscMalloc1(bdiag[0]+1,&b->a);CHKERRQ(ierr); 1812 1813 b->j = bj; 1814 b->i = bi; 1815 b->diag = bdiag; 1816 b->ilen = 0; 1817 b->imax = 0; 1818 b->row = isrow; 1819 b->col = iscol; 1820 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1821 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1822 b->icol = isicol; 1823 1824 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 1825 /* In b structure: Free imax, ilen, old a, old j. 1826 Allocate bdiag, solve_work, new a, new j */ 1827 ierr = PetscLogObjectMemory((PetscObject)fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1828 b->maxnz = b->nz = bdiag[0]+1; 1829 1830 (fact)->info.factor_mallocs = reallocs; 1831 (fact)->info.fill_ratio_given = f; 1832 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1833 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1834 if (a->inode.size) { 1835 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1836 } 1837 ierr = MatSeqAIJCheckInode_FactorLU(fact);CHKERRQ(ierr); 1838 PetscFunctionReturn(0); 1839 } 1840 1841 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1842 { 1843 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1844 IS isicol; 1845 PetscErrorCode ierr; 1846 const PetscInt *r,*ic; 1847 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1848 PetscInt *bi,*cols,nnz,*cols_lvl; 1849 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1850 PetscInt i,levels,diagonal_fill; 1851 PetscBool col_identity,row_identity; 1852 PetscReal f; 1853 PetscInt nlnk,*lnk,*lnk_lvl=NULL; 1854 PetscBT lnkbt; 1855 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1856 PetscFreeSpaceList free_space =NULL,current_space=NULL; 1857 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 1858 PetscBool missing; 1859 1860 PetscFunctionBegin; 1861 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); 1862 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1863 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1864 1865 f = info->fill; 1866 levels = (PetscInt)info->levels; 1867 diagonal_fill = (PetscInt)info->diagonal_fill; 1868 1869 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1870 1871 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1872 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1873 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1874 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1875 1876 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1877 if (a->inode.size) { 1878 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1879 } 1880 fact->factortype = MAT_FACTOR_ILU; 1881 (fact)->info.factor_mallocs = 0; 1882 (fact)->info.fill_ratio_given = info->fill; 1883 (fact)->info.fill_ratio_needed = 1.0; 1884 1885 b = (Mat_SeqAIJ*)(fact)->data; 1886 b->row = isrow; 1887 b->col = iscol; 1888 b->icol = isicol; 1889 ierr = PetscMalloc1((fact)->rmap->n+1,&b->solve_work);CHKERRQ(ierr); 1890 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1891 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1892 PetscFunctionReturn(0); 1893 } 1894 1895 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1896 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1897 1898 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1899 ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr); 1900 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); 1901 bi[0] = bdiag[0] = 0; 1902 1903 ierr = PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);CHKERRQ(ierr); 1904 1905 /* create a linked list for storing column indices of the active row */ 1906 nlnk = n + 1; 1907 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1908 1909 /* initial FreeSpace size is f*(ai[n]+1) */ 1910 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr); 1911 current_space = free_space; 1912 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);CHKERRQ(ierr); 1913 current_space_lvl = free_space_lvl; 1914 1915 for (i=0; i<n; i++) { 1916 nzi = 0; 1917 /* copy current row into linked list */ 1918 nnz = ai[r[i]+1] - ai[r[i]]; 1919 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); 1920 cols = aj + ai[r[i]]; 1921 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1922 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1923 nzi += nlnk; 1924 1925 /* make sure diagonal entry is included */ 1926 if (diagonal_fill && lnk[i] == -1) { 1927 fm = n; 1928 while (lnk[fm] < i) fm = lnk[fm]; 1929 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1930 lnk[fm] = i; 1931 lnk_lvl[i] = 0; 1932 nzi++; dcount++; 1933 } 1934 1935 /* add pivot rows into the active row */ 1936 nzbd = 0; 1937 prow = lnk[n]; 1938 while (prow < i) { 1939 nnz = bdiag[prow]; 1940 cols = bj_ptr[prow] + nnz + 1; 1941 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1942 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1943 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1944 nzi += nlnk; 1945 prow = lnk[prow]; 1946 nzbd++; 1947 } 1948 bdiag[i] = nzbd; 1949 bi[i+1] = bi[i] + nzi; 1950 1951 /* if free space is not available, make more free space */ 1952 if (current_space->local_remaining<nzi) { 1953 nnz = PetscIntMultTruncate(nzi,n - i); /* estimated and max additional space needed */ 1954 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1955 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1956 reallocs++; 1957 } 1958 1959 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1960 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1961 bj_ptr[i] = current_space->array; 1962 bjlvl_ptr[i] = current_space_lvl->array; 1963 1964 /* make sure the active row i has diagonal entry */ 1965 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); 1966 1967 current_space->array += nzi; 1968 current_space->local_used += nzi; 1969 current_space->local_remaining -= nzi; 1970 current_space_lvl->array += nzi; 1971 current_space_lvl->local_used += nzi; 1972 current_space_lvl->local_remaining -= nzi; 1973 } 1974 1975 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1976 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1977 1978 /* destroy list of free space and other temporary arrays */ 1979 ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr); 1980 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1981 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1982 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1983 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1984 1985 #if defined(PETSC_USE_INFO) 1986 { 1987 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1988 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr); 1989 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 1990 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);CHKERRQ(ierr); 1991 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1992 if (diagonal_fill) { 1993 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr); 1994 } 1995 } 1996 #endif 1997 1998 /* put together the new matrix */ 1999 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 2000 ierr = PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);CHKERRQ(ierr); 2001 b = (Mat_SeqAIJ*)(fact)->data; 2002 2003 b->free_a = PETSC_TRUE; 2004 b->free_ij = PETSC_TRUE; 2005 b->singlemalloc = PETSC_FALSE; 2006 2007 ierr = PetscMalloc1(bi[n],&b->a);CHKERRQ(ierr); 2008 b->j = bj; 2009 b->i = bi; 2010 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2011 b->diag = bdiag; 2012 b->ilen = 0; 2013 b->imax = 0; 2014 b->row = isrow; 2015 b->col = iscol; 2016 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2017 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2018 b->icol = isicol; 2019 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 2020 /* In b structure: Free imax, ilen, old a, old j. 2021 Allocate bdiag, solve_work, new a, new j */ 2022 ierr = PetscLogObjectMemory((PetscObject)fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2023 b->maxnz = b->nz = bi[n]; 2024 2025 (fact)->info.factor_mallocs = reallocs; 2026 (fact)->info.fill_ratio_given = f; 2027 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2028 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2029 if (a->inode.size) { 2030 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2031 } 2032 PetscFunctionReturn(0); 2033 } 2034 2035 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2036 { 2037 Mat C = B; 2038 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2039 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2040 IS ip=b->row,iip = b->icol; 2041 PetscErrorCode ierr; 2042 const PetscInt *rip,*riip; 2043 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2044 PetscInt *ai=a->i,*aj=a->j; 2045 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2046 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2047 PetscBool perm_identity; 2048 FactorShiftCtx sctx; 2049 PetscReal rs; 2050 MatScalar d,*v; 2051 2052 PetscFunctionBegin; 2053 /* MatPivotSetUp(): initialize shift context sctx */ 2054 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2055 2056 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2057 sctx.shift_top = info->zeropivot; 2058 for (i=0; i<mbs; i++) { 2059 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2060 d = (aa)[a->diag[i]]; 2061 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2062 v = aa+ai[i]; 2063 nz = ai[i+1] - ai[i]; 2064 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2065 if (rs>sctx.shift_top) sctx.shift_top = rs; 2066 } 2067 sctx.shift_top *= 1.1; 2068 sctx.nshift_max = 5; 2069 sctx.shift_lo = 0.; 2070 sctx.shift_hi = 1.; 2071 } 2072 2073 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2074 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2075 2076 /* allocate working arrays 2077 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2078 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 2079 */ 2080 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);CHKERRQ(ierr); 2081 2082 do { 2083 sctx.newshift = PETSC_FALSE; 2084 2085 for (i=0; i<mbs; i++) c2r[i] = mbs; 2086 if (mbs) il[0] = 0; 2087 2088 for (k = 0; k<mbs; k++) { 2089 /* zero rtmp */ 2090 nz = bi[k+1] - bi[k]; 2091 bjtmp = bj + bi[k]; 2092 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2093 2094 /* load in initial unfactored row */ 2095 bval = ba + bi[k]; 2096 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2097 for (j = jmin; j < jmax; j++) { 2098 col = riip[aj[j]]; 2099 if (col >= k) { /* only take upper triangular entry */ 2100 rtmp[col] = aa[j]; 2101 *bval++ = 0.0; /* for in-place factorization */ 2102 } 2103 } 2104 /* shift the diagonal of the matrix: ZeropivotApply() */ 2105 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2106 2107 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2108 dk = rtmp[k]; 2109 i = c2r[k]; /* first row to be added to k_th row */ 2110 2111 while (i < k) { 2112 nexti = c2r[i]; /* next row to be added to k_th row */ 2113 2114 /* compute multiplier, update diag(k) and U(i,k) */ 2115 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2116 uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2117 dk += uikdi*ba[ili]; /* update diag[k] */ 2118 ba[ili] = uikdi; /* -U(i,k) */ 2119 2120 /* add multiple of row i to k-th row */ 2121 jmin = ili + 1; jmax = bi[i+1]; 2122 if (jmin < jmax) { 2123 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2124 /* update il and c2r for row i */ 2125 il[i] = jmin; 2126 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2127 } 2128 i = nexti; 2129 } 2130 2131 /* copy data into U(k,:) */ 2132 rs = 0.0; 2133 jmin = bi[k]; jmax = bi[k+1]-1; 2134 if (jmin < jmax) { 2135 for (j=jmin; j<jmax; j++) { 2136 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2137 } 2138 /* add the k-th row into il and c2r */ 2139 il[k] = jmin; 2140 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2141 } 2142 2143 /* MatPivotCheck() */ 2144 sctx.rs = rs; 2145 sctx.pv = dk; 2146 ierr = MatPivotCheck(B,A,info,&sctx,i);CHKERRQ(ierr); 2147 if (sctx.newshift) break; 2148 dk = sctx.pv; 2149 2150 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2151 } 2152 } while (sctx.newshift); 2153 2154 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2155 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2156 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2157 2158 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2159 if (perm_identity) { 2160 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2161 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2162 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2163 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2164 } else { 2165 B->ops->solve = MatSolve_SeqSBAIJ_1; 2166 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2167 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2168 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2169 } 2170 2171 C->assembled = PETSC_TRUE; 2172 C->preallocated = PETSC_TRUE; 2173 2174 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2175 2176 /* MatPivotView() */ 2177 if (sctx.nshift) { 2178 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2179 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); 2180 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2181 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2182 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) { 2183 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);CHKERRQ(ierr); 2184 } 2185 } 2186 PetscFunctionReturn(0); 2187 } 2188 2189 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2190 { 2191 Mat C = B; 2192 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2193 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2194 IS ip=b->row,iip = b->icol; 2195 PetscErrorCode ierr; 2196 const PetscInt *rip,*riip; 2197 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2198 PetscInt *ai=a->i,*aj=a->j; 2199 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2200 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2201 PetscBool perm_identity; 2202 FactorShiftCtx sctx; 2203 PetscReal rs; 2204 MatScalar d,*v; 2205 2206 PetscFunctionBegin; 2207 /* MatPivotSetUp(): initialize shift context sctx */ 2208 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2209 2210 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2211 sctx.shift_top = info->zeropivot; 2212 for (i=0; i<mbs; i++) { 2213 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2214 d = (aa)[a->diag[i]]; 2215 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2216 v = aa+ai[i]; 2217 nz = ai[i+1] - ai[i]; 2218 for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]); 2219 if (rs>sctx.shift_top) sctx.shift_top = rs; 2220 } 2221 sctx.shift_top *= 1.1; 2222 sctx.nshift_max = 5; 2223 sctx.shift_lo = 0.; 2224 sctx.shift_hi = 1.; 2225 } 2226 2227 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2228 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2229 2230 /* initialization */ 2231 ierr = PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);CHKERRQ(ierr); 2232 2233 do { 2234 sctx.newshift = PETSC_FALSE; 2235 2236 for (i=0; i<mbs; i++) jl[i] = mbs; 2237 il[0] = 0; 2238 2239 for (k = 0; k<mbs; k++) { 2240 /* zero rtmp */ 2241 nz = bi[k+1] - bi[k]; 2242 bjtmp = bj + bi[k]; 2243 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2244 2245 bval = ba + bi[k]; 2246 /* initialize k-th row by the perm[k]-th row of A */ 2247 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2248 for (j = jmin; j < jmax; j++) { 2249 col = riip[aj[j]]; 2250 if (col >= k) { /* only take upper triangular entry */ 2251 rtmp[col] = aa[j]; 2252 *bval++ = 0.0; /* for in-place factorization */ 2253 } 2254 } 2255 /* shift the diagonal of the matrix */ 2256 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2257 2258 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2259 dk = rtmp[k]; 2260 i = jl[k]; /* first row to be added to k_th row */ 2261 2262 while (i < k) { 2263 nexti = jl[i]; /* next row to be added to k_th row */ 2264 2265 /* compute multiplier, update diag(k) and U(i,k) */ 2266 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2267 uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2268 dk += uikdi*ba[ili]; 2269 ba[ili] = uikdi; /* -U(i,k) */ 2270 2271 /* add multiple of row i to k-th row */ 2272 jmin = ili + 1; jmax = bi[i+1]; 2273 if (jmin < jmax) { 2274 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2275 /* update il and jl for row i */ 2276 il[i] = jmin; 2277 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2278 } 2279 i = nexti; 2280 } 2281 2282 /* shift the diagonals when zero pivot is detected */ 2283 /* compute rs=sum of abs(off-diagonal) */ 2284 rs = 0.0; 2285 jmin = bi[k]+1; 2286 nz = bi[k+1] - jmin; 2287 bcol = bj + jmin; 2288 for (j=0; j<nz; j++) { 2289 rs += PetscAbsScalar(rtmp[bcol[j]]); 2290 } 2291 2292 sctx.rs = rs; 2293 sctx.pv = dk; 2294 ierr = MatPivotCheck(B,A,info,&sctx,k);CHKERRQ(ierr); 2295 if (sctx.newshift) break; 2296 dk = sctx.pv; 2297 2298 /* copy data into U(k,:) */ 2299 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2300 jmin = bi[k]+1; jmax = bi[k+1]; 2301 if (jmin < jmax) { 2302 for (j=jmin; j<jmax; j++) { 2303 col = bj[j]; ba[j] = rtmp[col]; 2304 } 2305 /* add the k-th row into il and jl */ 2306 il[k] = jmin; 2307 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2308 } 2309 } 2310 } while (sctx.newshift); 2311 2312 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2313 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2314 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2315 2316 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2317 if (perm_identity) { 2318 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2319 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2320 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2321 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2322 } else { 2323 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2324 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2325 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2326 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2327 } 2328 2329 C->assembled = PETSC_TRUE; 2330 C->preallocated = PETSC_TRUE; 2331 2332 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2333 if (sctx.nshift) { 2334 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2335 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2336 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2337 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);CHKERRQ(ierr); 2338 } 2339 } 2340 PetscFunctionReturn(0); 2341 } 2342 2343 /* 2344 icc() under revised new data structure. 2345 Factored arrays bj and ba are stored as 2346 U(0,:),...,U(i,:),U(n-1,:) 2347 2348 ui=fact->i is an array of size n+1, in which 2349 ui+ 2350 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2351 ui[n]: points to U(n-1,n-1)+1 2352 2353 udiag=fact->diag is an array of size n,in which 2354 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2355 2356 U(i,:) contains udiag[i] as its last entry, i.e., 2357 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2358 */ 2359 2360 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2361 { 2362 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2363 Mat_SeqSBAIJ *b; 2364 PetscErrorCode ierr; 2365 PetscBool perm_identity,missing; 2366 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2367 const PetscInt *rip,*riip; 2368 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2369 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2370 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2371 PetscReal fill =info->fill,levels=info->levels; 2372 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2373 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2374 PetscBT lnkbt; 2375 IS iperm; 2376 2377 PetscFunctionBegin; 2378 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); 2379 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2380 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2381 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2382 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2383 2384 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2385 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2386 ui[0] = 0; 2387 2388 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2389 if (!levels && perm_identity) { 2390 for (i=0; i<am; i++) { 2391 ncols = ai[i+1] - a->diag[i]; 2392 ui[i+1] = ui[i] + ncols; 2393 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2394 } 2395 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2396 cols = uj; 2397 for (i=0; i<am; i++) { 2398 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2399 ncols = ai[i+1] - a->diag[i] -1; 2400 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2401 *cols++ = i; /* diagonal is located as the last entry of U(i,:) */ 2402 } 2403 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2404 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2405 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2406 2407 /* initialization */ 2408 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2409 2410 /* jl: linked list for storing indices of the pivot rows 2411 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2412 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2413 for (i=0; i<am; i++) { 2414 jl[i] = am; il[i] = 0; 2415 } 2416 2417 /* create and initialize a linked list for storing column indices of the active row k */ 2418 nlnk = am + 1; 2419 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2420 2421 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2422 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2423 current_space = free_space; 2424 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space_lvl);CHKERRQ(ierr); 2425 current_space_lvl = free_space_lvl; 2426 2427 for (k=0; k<am; k++) { /* for each active row k */ 2428 /* initialize lnk by the column indices of row rip[k] of A */ 2429 nzk = 0; 2430 ncols = ai[rip[k]+1] - ai[rip[k]]; 2431 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); 2432 ncols_upper = 0; 2433 for (j=0; j<ncols; j++) { 2434 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2435 if (riip[i] >= k) { /* only take upper triangular entry */ 2436 ajtmp[ncols_upper] = i; 2437 ncols_upper++; 2438 } 2439 } 2440 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2441 nzk += nlnk; 2442 2443 /* update lnk by computing fill-in for each pivot row to be merged in */ 2444 prow = jl[k]; /* 1st pivot row */ 2445 2446 while (prow < k) { 2447 nextprow = jl[prow]; 2448 2449 /* merge prow into k-th row */ 2450 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2451 jmax = ui[prow+1]; 2452 ncols = jmax-jmin; 2453 i = jmin - ui[prow]; 2454 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2455 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2456 j = *(uj - 1); 2457 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2458 nzk += nlnk; 2459 2460 /* update il and jl for prow */ 2461 if (jmin < jmax) { 2462 il[prow] = jmin; 2463 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2464 } 2465 prow = nextprow; 2466 } 2467 2468 /* if free space is not available, make more free space */ 2469 if (current_space->local_remaining<nzk) { 2470 i = am - k + 1; /* num of unfactored rows */ 2471 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2472 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2473 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2474 reallocs++; 2475 } 2476 2477 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2478 if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2479 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2480 2481 /* add the k-th row into il and jl */ 2482 if (nzk > 1) { 2483 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2484 jl[k] = jl[i]; jl[i] = k; 2485 il[k] = ui[k] + 1; 2486 } 2487 uj_ptr[k] = current_space->array; 2488 uj_lvl_ptr[k] = current_space_lvl->array; 2489 2490 current_space->array += nzk; 2491 current_space->local_used += nzk; 2492 current_space->local_remaining -= nzk; 2493 2494 current_space_lvl->array += nzk; 2495 current_space_lvl->local_used += nzk; 2496 current_space_lvl->local_remaining -= nzk; 2497 2498 ui[k+1] = ui[k] + nzk; 2499 } 2500 2501 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2502 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2503 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2504 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2505 2506 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2507 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2508 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2509 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2510 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2511 2512 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2513 2514 /* put together the new matrix in MATSEQSBAIJ format */ 2515 b = (Mat_SeqSBAIJ*)(fact)->data; 2516 b->singlemalloc = PETSC_FALSE; 2517 2518 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2519 2520 b->j = uj; 2521 b->i = ui; 2522 b->diag = udiag; 2523 b->free_diag = PETSC_TRUE; 2524 b->ilen = 0; 2525 b->imax = 0; 2526 b->row = perm; 2527 b->col = perm; 2528 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2529 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2530 b->icol = iperm; 2531 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2532 2533 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2534 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2535 2536 b->maxnz = b->nz = ui[am]; 2537 b->free_a = PETSC_TRUE; 2538 b->free_ij = PETSC_TRUE; 2539 2540 fact->info.factor_mallocs = reallocs; 2541 fact->info.fill_ratio_given = fill; 2542 if (ai[am] != 0) { 2543 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2544 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2545 } else { 2546 fact->info.fill_ratio_needed = 0.0; 2547 } 2548 #if defined(PETSC_USE_INFO) 2549 if (ai[am] != 0) { 2550 PetscReal af = fact->info.fill_ratio_needed; 2551 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2552 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2553 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2554 } else { 2555 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2556 } 2557 #endif 2558 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2559 PetscFunctionReturn(0); 2560 } 2561 2562 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2563 { 2564 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2565 Mat_SeqSBAIJ *b; 2566 PetscErrorCode ierr; 2567 PetscBool perm_identity,missing; 2568 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2569 const PetscInt *rip,*riip; 2570 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2571 PetscInt nlnk,*lnk,*lnk_lvl=NULL,d; 2572 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2573 PetscReal fill =info->fill,levels=info->levels; 2574 PetscFreeSpaceList free_space =NULL,current_space=NULL; 2575 PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL; 2576 PetscBT lnkbt; 2577 IS iperm; 2578 2579 PetscFunctionBegin; 2580 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); 2581 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2582 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2583 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2584 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2585 2586 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2587 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2588 ui[0] = 0; 2589 2590 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2591 if (!levels && perm_identity) { 2592 2593 for (i=0; i<am; i++) { 2594 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2595 udiag[i] = ui[i]; 2596 } 2597 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2598 cols = uj; 2599 for (i=0; i<am; i++) { 2600 aj = a->j + a->diag[i]; 2601 ncols = ui[i+1] - ui[i]; 2602 for (j=0; j<ncols; j++) *cols++ = *aj++; 2603 } 2604 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2605 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2606 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2607 2608 /* initialization */ 2609 ierr = PetscMalloc1(am+1,&ajtmp);CHKERRQ(ierr); 2610 2611 /* jl: linked list for storing indices of the pivot rows 2612 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2613 ierr = PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);CHKERRQ(ierr); 2614 for (i=0; i<am; i++) { 2615 jl[i] = am; il[i] = 0; 2616 } 2617 2618 /* create and initialize a linked list for storing column indices of the active row k */ 2619 nlnk = am + 1; 2620 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2621 2622 /* initial FreeSpace size is fill*(ai[am]+1) */ 2623 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2624 current_space = free_space; 2625 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space_lvl);CHKERRQ(ierr); 2626 current_space_lvl = free_space_lvl; 2627 2628 for (k=0; k<am; k++) { /* for each active row k */ 2629 /* initialize lnk by the column indices of row rip[k] of A */ 2630 nzk = 0; 2631 ncols = ai[rip[k]+1] - ai[rip[k]]; 2632 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); 2633 ncols_upper = 0; 2634 for (j=0; j<ncols; j++) { 2635 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2636 if (riip[i] >= k) { /* only take upper triangular entry */ 2637 ajtmp[ncols_upper] = i; 2638 ncols_upper++; 2639 } 2640 } 2641 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2642 nzk += nlnk; 2643 2644 /* update lnk by computing fill-in for each pivot row to be merged in */ 2645 prow = jl[k]; /* 1st pivot row */ 2646 2647 while (prow < k) { 2648 nextprow = jl[prow]; 2649 2650 /* merge prow into k-th row */ 2651 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2652 jmax = ui[prow+1]; 2653 ncols = jmax-jmin; 2654 i = jmin - ui[prow]; 2655 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2656 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2657 j = *(uj - 1); 2658 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2659 nzk += nlnk; 2660 2661 /* update il and jl for prow */ 2662 if (jmin < jmax) { 2663 il[prow] = jmin; 2664 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2665 } 2666 prow = nextprow; 2667 } 2668 2669 /* if free space is not available, make more free space */ 2670 if (current_space->local_remaining<nzk) { 2671 i = am - k + 1; /* num of unfactored rows */ 2672 i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2673 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2674 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2675 reallocs++; 2676 } 2677 2678 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2679 if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2680 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2681 2682 /* add the k-th row into il and jl */ 2683 if (nzk > 1) { 2684 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2685 jl[k] = jl[i]; jl[i] = k; 2686 il[k] = ui[k] + 1; 2687 } 2688 uj_ptr[k] = current_space->array; 2689 uj_lvl_ptr[k] = current_space_lvl->array; 2690 2691 current_space->array += nzk; 2692 current_space->local_used += nzk; 2693 current_space->local_remaining -= nzk; 2694 2695 current_space_lvl->array += nzk; 2696 current_space_lvl->local_used += nzk; 2697 current_space_lvl->local_remaining -= nzk; 2698 2699 ui[k+1] = ui[k] + nzk; 2700 } 2701 2702 #if defined(PETSC_USE_INFO) 2703 if (ai[am] != 0) { 2704 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2705 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2706 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2707 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2708 } else { 2709 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2710 } 2711 #endif 2712 2713 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2714 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2715 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2716 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2717 2718 /* destroy list of free space and other temporary array(s) */ 2719 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2720 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2721 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2722 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2723 2724 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2725 2726 /* put together the new matrix in MATSEQSBAIJ format */ 2727 2728 b = (Mat_SeqSBAIJ*)fact->data; 2729 b->singlemalloc = PETSC_FALSE; 2730 2731 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2732 2733 b->j = uj; 2734 b->i = ui; 2735 b->diag = udiag; 2736 b->free_diag = PETSC_TRUE; 2737 b->ilen = 0; 2738 b->imax = 0; 2739 b->row = perm; 2740 b->col = perm; 2741 2742 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2743 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2744 2745 b->icol = iperm; 2746 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2747 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2748 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2749 b->maxnz = b->nz = ui[am]; 2750 b->free_a = PETSC_TRUE; 2751 b->free_ij = PETSC_TRUE; 2752 2753 fact->info.factor_mallocs = reallocs; 2754 fact->info.fill_ratio_given = fill; 2755 if (ai[am] != 0) { 2756 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2757 } else { 2758 fact->info.fill_ratio_needed = 0.0; 2759 } 2760 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2761 PetscFunctionReturn(0); 2762 } 2763 2764 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2765 { 2766 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2767 Mat_SeqSBAIJ *b; 2768 PetscErrorCode ierr; 2769 PetscBool perm_identity,missing; 2770 PetscReal fill = info->fill; 2771 const PetscInt *rip,*riip; 2772 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2773 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2774 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2775 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2776 PetscBT lnkbt; 2777 IS iperm; 2778 2779 PetscFunctionBegin; 2780 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); 2781 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2782 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2783 2784 /* check whether perm is the identity mapping */ 2785 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2786 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2787 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2788 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2789 2790 /* initialization */ 2791 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2792 ierr = PetscMalloc1(am+1,&udiag);CHKERRQ(ierr); 2793 ui[0] = 0; 2794 2795 /* jl: linked list for storing indices of the pivot rows 2796 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2797 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2798 for (i=0; i<am; i++) { 2799 jl[i] = am; il[i] = 0; 2800 } 2801 2802 /* create and initialize a linked list for storing column indices of the active row k */ 2803 nlnk = am + 1; 2804 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2805 2806 /* initial FreeSpace size is fill*(ai[am]+am)/2 */ 2807 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);CHKERRQ(ierr); 2808 current_space = free_space; 2809 2810 for (k=0; k<am; k++) { /* for each active row k */ 2811 /* initialize lnk by the column indices of row rip[k] of A */ 2812 nzk = 0; 2813 ncols = ai[rip[k]+1] - ai[rip[k]]; 2814 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); 2815 ncols_upper = 0; 2816 for (j=0; j<ncols; j++) { 2817 i = riip[*(aj + ai[rip[k]] + j)]; 2818 if (i >= k) { /* only take upper triangular entry */ 2819 cols[ncols_upper] = i; 2820 ncols_upper++; 2821 } 2822 } 2823 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2824 nzk += nlnk; 2825 2826 /* update lnk by computing fill-in for each pivot row to be merged in */ 2827 prow = jl[k]; /* 1st pivot row */ 2828 2829 while (prow < k) { 2830 nextprow = jl[prow]; 2831 /* merge prow into k-th row */ 2832 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2833 jmax = ui[prow+1]; 2834 ncols = jmax-jmin; 2835 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2836 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2837 nzk += nlnk; 2838 2839 /* update il and jl for prow */ 2840 if (jmin < jmax) { 2841 il[prow] = jmin; 2842 j = *uj_ptr; 2843 jl[prow] = jl[j]; 2844 jl[j] = prow; 2845 } 2846 prow = nextprow; 2847 } 2848 2849 /* if free space is not available, make more free space */ 2850 if (current_space->local_remaining<nzk) { 2851 i = am - k + 1; /* num of unfactored rows */ 2852 i = PetscIntMultTruncate(i,PetscMin(nzk,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2853 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2854 reallocs++; 2855 } 2856 2857 /* copy data into free space, then initialize lnk */ 2858 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2859 2860 /* add the k-th row into il and jl */ 2861 if (nzk > 1) { 2862 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2863 jl[k] = jl[i]; jl[i] = k; 2864 il[k] = ui[k] + 1; 2865 } 2866 ui_ptr[k] = current_space->array; 2867 2868 current_space->array += nzk; 2869 current_space->local_used += nzk; 2870 current_space->local_remaining -= nzk; 2871 2872 ui[k+1] = ui[k] + nzk; 2873 } 2874 2875 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2876 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2877 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2878 2879 /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */ 2880 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 2881 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2882 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2883 2884 /* put together the new matrix in MATSEQSBAIJ format */ 2885 2886 b = (Mat_SeqSBAIJ*)fact->data; 2887 b->singlemalloc = PETSC_FALSE; 2888 b->free_a = PETSC_TRUE; 2889 b->free_ij = PETSC_TRUE; 2890 2891 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 2892 2893 b->j = uj; 2894 b->i = ui; 2895 b->diag = udiag; 2896 b->free_diag = PETSC_TRUE; 2897 b->ilen = 0; 2898 b->imax = 0; 2899 b->row = perm; 2900 b->col = perm; 2901 2902 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2903 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2904 2905 b->icol = iperm; 2906 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2907 2908 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 2909 ierr = PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2910 2911 b->maxnz = b->nz = ui[am]; 2912 2913 fact->info.factor_mallocs = reallocs; 2914 fact->info.fill_ratio_given = fill; 2915 if (ai[am] != 0) { 2916 /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */ 2917 fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am); 2918 } else { 2919 fact->info.fill_ratio_needed = 0.0; 2920 } 2921 #if defined(PETSC_USE_INFO) 2922 if (ai[am] != 0) { 2923 PetscReal af = fact->info.fill_ratio_needed; 2924 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 2925 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 2926 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 2927 } else { 2928 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 2929 } 2930 #endif 2931 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2932 PetscFunctionReturn(0); 2933 } 2934 2935 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2936 { 2937 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2938 Mat_SeqSBAIJ *b; 2939 PetscErrorCode ierr; 2940 PetscBool perm_identity,missing; 2941 PetscReal fill = info->fill; 2942 const PetscInt *rip,*riip; 2943 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2944 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2945 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2946 PetscFreeSpaceList free_space=NULL,current_space=NULL; 2947 PetscBT lnkbt; 2948 IS iperm; 2949 2950 PetscFunctionBegin; 2951 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); 2952 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 2953 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 2954 2955 /* check whether perm is the identity mapping */ 2956 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2957 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2958 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2959 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2960 2961 /* initialization */ 2962 ierr = PetscMalloc1(am+1,&ui);CHKERRQ(ierr); 2963 ui[0] = 0; 2964 2965 /* jl: linked list for storing indices of the pivot rows 2966 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2967 ierr = PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);CHKERRQ(ierr); 2968 for (i=0; i<am; i++) { 2969 jl[i] = am; il[i] = 0; 2970 } 2971 2972 /* create and initialize a linked list for storing column indices of the active row k */ 2973 nlnk = am + 1; 2974 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2975 2976 /* initial FreeSpace size is fill*(ai[am]+1) */ 2977 ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);CHKERRQ(ierr); 2978 current_space = free_space; 2979 2980 for (k=0; k<am; k++) { /* for each active row k */ 2981 /* initialize lnk by the column indices of row rip[k] of A */ 2982 nzk = 0; 2983 ncols = ai[rip[k]+1] - ai[rip[k]]; 2984 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); 2985 ncols_upper = 0; 2986 for (j=0; j<ncols; j++) { 2987 i = riip[*(aj + ai[rip[k]] + j)]; 2988 if (i >= k) { /* only take upper triangular entry */ 2989 cols[ncols_upper] = i; 2990 ncols_upper++; 2991 } 2992 } 2993 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2994 nzk += nlnk; 2995 2996 /* update lnk by computing fill-in for each pivot row to be merged in */ 2997 prow = jl[k]; /* 1st pivot row */ 2998 2999 while (prow < k) { 3000 nextprow = jl[prow]; 3001 /* merge prow into k-th row */ 3002 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3003 jmax = ui[prow+1]; 3004 ncols = jmax-jmin; 3005 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3006 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3007 nzk += nlnk; 3008 3009 /* update il and jl for prow */ 3010 if (jmin < jmax) { 3011 il[prow] = jmin; 3012 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3013 } 3014 prow = nextprow; 3015 } 3016 3017 /* if free space is not available, make more free space */ 3018 if (current_space->local_remaining<nzk) { 3019 i = am - k + 1; /* num of unfactored rows */ 3020 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3021 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3022 reallocs++; 3023 } 3024 3025 /* copy data into free space, then initialize lnk */ 3026 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3027 3028 /* add the k-th row into il and jl */ 3029 if (nzk-1 > 0) { 3030 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3031 jl[k] = jl[i]; jl[i] = k; 3032 il[k] = ui[k] + 1; 3033 } 3034 ui_ptr[k] = current_space->array; 3035 3036 current_space->array += nzk; 3037 current_space->local_used += nzk; 3038 current_space->local_remaining -= nzk; 3039 3040 ui[k+1] = ui[k] + nzk; 3041 } 3042 3043 #if defined(PETSC_USE_INFO) 3044 if (ai[am] != 0) { 3045 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3046 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);CHKERRQ(ierr); 3047 ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr); 3048 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);CHKERRQ(ierr); 3049 } else { 3050 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 3051 } 3052 #endif 3053 3054 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3055 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3056 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3057 3058 /* destroy list of free space and other temporary array(s) */ 3059 ierr = PetscMalloc1(ui[am]+1,&uj);CHKERRQ(ierr); 3060 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3061 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3062 3063 /* put together the new matrix in MATSEQSBAIJ format */ 3064 3065 b = (Mat_SeqSBAIJ*)fact->data; 3066 b->singlemalloc = PETSC_FALSE; 3067 b->free_a = PETSC_TRUE; 3068 b->free_ij = PETSC_TRUE; 3069 3070 ierr = PetscMalloc1(ui[am]+1,&b->a);CHKERRQ(ierr); 3071 3072 b->j = uj; 3073 b->i = ui; 3074 b->diag = 0; 3075 b->ilen = 0; 3076 b->imax = 0; 3077 b->row = perm; 3078 b->col = perm; 3079 3080 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3081 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3082 3083 b->icol = iperm; 3084 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3085 3086 ierr = PetscMalloc1(am+1,&b->solve_work);CHKERRQ(ierr); 3087 ierr = PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3088 b->maxnz = b->nz = ui[am]; 3089 3090 fact->info.factor_mallocs = reallocs; 3091 fact->info.fill_ratio_given = fill; 3092 if (ai[am] != 0) { 3093 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3094 } else { 3095 fact->info.fill_ratio_needed = 0.0; 3096 } 3097 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3098 PetscFunctionReturn(0); 3099 } 3100 3101 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3102 { 3103 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3104 PetscErrorCode ierr; 3105 PetscInt n = A->rmap->n; 3106 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3107 PetscScalar *x,sum; 3108 const PetscScalar *b; 3109 const MatScalar *aa = a->a,*v; 3110 PetscInt i,nz; 3111 3112 PetscFunctionBegin; 3113 if (!n) PetscFunctionReturn(0); 3114 3115 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3116 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 3117 3118 /* forward solve the lower triangular */ 3119 x[0] = b[0]; 3120 v = aa; 3121 vi = aj; 3122 for (i=1; i<n; i++) { 3123 nz = ai[i+1] - ai[i]; 3124 sum = b[i]; 3125 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3126 v += nz; 3127 vi += nz; 3128 x[i] = sum; 3129 } 3130 3131 /* backward solve the upper triangular */ 3132 for (i=n-1; i>=0; i--) { 3133 v = aa + adiag[i+1] + 1; 3134 vi = aj + adiag[i+1] + 1; 3135 nz = adiag[i] - adiag[i+1]-1; 3136 sum = x[i]; 3137 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3138 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3139 } 3140 3141 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3142 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3143 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 3144 PetscFunctionReturn(0); 3145 } 3146 3147 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3148 { 3149 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3150 IS iscol = a->col,isrow = a->row; 3151 PetscErrorCode ierr; 3152 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3153 const PetscInt *rout,*cout,*r,*c; 3154 PetscScalar *x,*tmp,sum; 3155 const PetscScalar *b; 3156 const MatScalar *aa = a->a,*v; 3157 3158 PetscFunctionBegin; 3159 if (!n) PetscFunctionReturn(0); 3160 3161 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3162 ierr = VecGetArrayWrite(xx,&x);CHKERRQ(ierr); 3163 tmp = a->solve_work; 3164 3165 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3166 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3167 3168 /* forward solve the lower triangular */ 3169 tmp[0] = b[r[0]]; 3170 v = aa; 3171 vi = aj; 3172 for (i=1; i<n; i++) { 3173 nz = ai[i+1] - ai[i]; 3174 sum = b[r[i]]; 3175 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3176 tmp[i] = sum; 3177 v += nz; vi += nz; 3178 } 3179 3180 /* backward solve the upper triangular */ 3181 for (i=n-1; i>=0; i--) { 3182 v = aa + adiag[i+1]+1; 3183 vi = aj + adiag[i+1]+1; 3184 nz = adiag[i]-adiag[i+1]-1; 3185 sum = tmp[i]; 3186 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3187 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3188 } 3189 3190 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3191 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3192 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3193 ierr = VecRestoreArrayWrite(xx,&x);CHKERRQ(ierr); 3194 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3195 PetscFunctionReturn(0); 3196 } 3197 3198 /* 3199 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 3200 */ 3201 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3202 { 3203 Mat B = *fact; 3204 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3205 IS isicol; 3206 PetscErrorCode ierr; 3207 const PetscInt *r,*ic; 3208 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3209 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3210 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3211 PetscInt nlnk,*lnk; 3212 PetscBT lnkbt; 3213 PetscBool row_identity,icol_identity; 3214 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3215 const PetscInt *ics; 3216 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3217 PetscReal dt =info->dt,shift=info->shiftamount; 3218 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3219 PetscBool missing; 3220 3221 PetscFunctionBegin; 3222 if (dt == PETSC_DEFAULT) dt = 0.005; 3223 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3224 3225 /* ------- symbolic factorization, can be reused ---------*/ 3226 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3227 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3228 adiag=a->diag; 3229 3230 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3231 3232 /* bdiag is location of diagonal in factor */ 3233 ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3234 ierr = PetscMalloc1(n+1,&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3235 3236 /* allocate row pointers bi */ 3237 ierr = PetscMalloc1(2*n+2,&bi);CHKERRQ(ierr); 3238 3239 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3240 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3241 nnz_max = ai[n]+2*n*dtcount+2; 3242 3243 ierr = PetscMalloc1(nnz_max+1,&bj);CHKERRQ(ierr); 3244 ierr = PetscMalloc1(nnz_max+1,&ba);CHKERRQ(ierr); 3245 3246 /* put together the new matrix */ 3247 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr); 3248 ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr); 3249 b = (Mat_SeqAIJ*)B->data; 3250 3251 b->free_a = PETSC_TRUE; 3252 b->free_ij = PETSC_TRUE; 3253 b->singlemalloc = PETSC_FALSE; 3254 3255 b->a = ba; 3256 b->j = bj; 3257 b->i = bi; 3258 b->diag = bdiag; 3259 b->ilen = 0; 3260 b->imax = 0; 3261 b->row = isrow; 3262 b->col = iscol; 3263 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3264 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3265 b->icol = isicol; 3266 3267 ierr = PetscMalloc1(n+1,&b->solve_work);CHKERRQ(ierr); 3268 ierr = PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3269 b->maxnz = nnz_max; 3270 3271 B->factortype = MAT_FACTOR_ILUDT; 3272 B->info.factor_mallocs = 0; 3273 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3274 /* ------- end of symbolic factorization ---------*/ 3275 3276 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3277 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3278 ics = ic; 3279 3280 /* linked list for storing column indices of the active row */ 3281 nlnk = n + 1; 3282 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3283 3284 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3285 ierr = PetscMalloc2(n,&im,n,&jtmp);CHKERRQ(ierr); 3286 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3287 ierr = PetscMalloc2(n,&rtmp,n,&vtmp);CHKERRQ(ierr); 3288 ierr = PetscArrayzero(rtmp,n);CHKERRQ(ierr); 3289 3290 bi[0] = 0; 3291 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3292 bdiag_rev[n] = bdiag[0]; 3293 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3294 for (i=0; i<n; i++) { 3295 /* copy initial fill into linked list */ 3296 nzi = ai[r[i]+1] - ai[r[i]]; 3297 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); 3298 nzi_al = adiag[r[i]] - ai[r[i]]; 3299 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3300 ajtmp = aj + ai[r[i]]; 3301 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3302 3303 /* load in initial (unfactored row) */ 3304 aatmp = a->a + ai[r[i]]; 3305 for (j=0; j<nzi; j++) { 3306 rtmp[ics[*ajtmp++]] = *aatmp++; 3307 } 3308 3309 /* add pivot rows into linked list */ 3310 row = lnk[n]; 3311 while (row < i) { 3312 nzi_bl = bi[row+1] - bi[row] + 1; 3313 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3314 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3315 nzi += nlnk; 3316 row = lnk[row]; 3317 } 3318 3319 /* copy data from lnk into jtmp, then initialize lnk */ 3320 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3321 3322 /* numerical factorization */ 3323 bjtmp = jtmp; 3324 row = *bjtmp++; /* 1st pivot row */ 3325 while (row < i) { 3326 pc = rtmp + row; 3327 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3328 multiplier = (*pc) * (*pv); 3329 *pc = multiplier; 3330 if (PetscAbsScalar(*pc) > dt) { /* apply tolerance dropping rule */ 3331 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3332 pv = ba + bdiag[row+1] + 1; 3333 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3334 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3335 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 3336 } 3337 row = *bjtmp++; 3338 } 3339 3340 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3341 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3342 nzi_bl = 0; j = 0; 3343 while (jtmp[j] < i) { /* Note: jtmp is sorted */ 3344 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3345 nzi_bl++; j++; 3346 } 3347 nzi_bu = nzi - nzi_bl -1; 3348 while (j < nzi) { 3349 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3350 j++; 3351 } 3352 3353 bjtmp = bj + bi[i]; 3354 batmp = ba + bi[i]; 3355 /* apply level dropping rule to L part */ 3356 ncut = nzi_al + dtcount; 3357 if (ncut < nzi_bl) { 3358 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3359 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3360 } else { 3361 ncut = nzi_bl; 3362 } 3363 for (j=0; j<ncut; j++) { 3364 bjtmp[j] = jtmp[j]; 3365 batmp[j] = vtmp[j]; 3366 } 3367 bi[i+1] = bi[i] + ncut; 3368 nzi = ncut + 1; 3369 3370 /* apply level dropping rule to U part */ 3371 ncut = nzi_au + dtcount; 3372 if (ncut < nzi_bu) { 3373 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3374 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3375 } else { 3376 ncut = nzi_bu; 3377 } 3378 nzi += ncut; 3379 3380 /* mark bdiagonal */ 3381 bdiag[i+1] = bdiag[i] - (ncut + 1); 3382 bdiag_rev[n-i-1] = bdiag[i+1]; 3383 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3384 bjtmp = bj + bdiag[i]; 3385 batmp = ba + bdiag[i]; 3386 *bjtmp = i; 3387 *batmp = diag_tmp; /* rtmp[i]; */ 3388 if (*batmp == 0.0) { 3389 *batmp = dt+shift; 3390 } 3391 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3392 3393 bjtmp = bj + bdiag[i+1]+1; 3394 batmp = ba + bdiag[i+1]+1; 3395 for (k=0; k<ncut; k++) { 3396 bjtmp[k] = jtmp[nzi_bl+1+k]; 3397 batmp[k] = vtmp[nzi_bl+1+k]; 3398 } 3399 3400 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3401 } /* for (i=0; i<n; i++) */ 3402 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]); 3403 3404 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3405 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3406 3407 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3408 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3409 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3410 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3411 3412 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3413 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3414 3415 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3416 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3417 if (row_identity && icol_identity) { 3418 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3419 } else { 3420 B->ops->solve = MatSolve_SeqAIJ; 3421 } 3422 3423 B->ops->solveadd = 0; 3424 B->ops->solvetranspose = 0; 3425 B->ops->solvetransposeadd = 0; 3426 B->ops->matsolve = 0; 3427 B->assembled = PETSC_TRUE; 3428 B->preallocated = PETSC_TRUE; 3429 PetscFunctionReturn(0); 3430 } 3431 3432 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3433 /* 3434 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 3435 */ 3436 3437 PetscErrorCode MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3438 { 3439 PetscErrorCode ierr; 3440 3441 PetscFunctionBegin; 3442 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3443 PetscFunctionReturn(0); 3444 } 3445 3446 /* 3447 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3448 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3449 */ 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 MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3455 { 3456 Mat C =fact; 3457 Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data; 3458 IS isrow = b->row,isicol = b->icol; 3459 PetscErrorCode ierr; 3460 const PetscInt *r,*ic,*ics; 3461 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3462 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3463 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3464 PetscReal dt=info->dt,shift=info->shiftamount; 3465 PetscBool row_identity, col_identity; 3466 3467 PetscFunctionBegin; 3468 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3469 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3470 ierr = PetscMalloc1(n+1,&rtmp);CHKERRQ(ierr); 3471 ics = ic; 3472 3473 for (i=0; i<n; i++) { 3474 /* initialize rtmp array */ 3475 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3476 bjtmp = bj + bi[i]; 3477 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3478 rtmp[i] = 0.0; 3479 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3480 bjtmp = bj + bdiag[i+1] + 1; 3481 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3482 3483 /* load in initial unfactored row of A */ 3484 nz = ai[r[i]+1] - ai[r[i]]; 3485 ajtmp = aj + ai[r[i]]; 3486 v = aa + ai[r[i]]; 3487 for (j=0; j<nz; j++) { 3488 rtmp[ics[*ajtmp++]] = v[j]; 3489 } 3490 3491 /* numerical factorization */ 3492 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3493 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3494 k = 0; 3495 while (k < nzl) { 3496 row = *bjtmp++; 3497 pc = rtmp + row; 3498 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3499 multiplier = (*pc) * (*pv); 3500 *pc = multiplier; 3501 if (PetscAbsScalar(multiplier) > dt) { 3502 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3503 pv = b->a + bdiag[row+1] + 1; 3504 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3505 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3506 ierr = PetscLogFlops(1+2.0*nz);CHKERRQ(ierr); 3507 } 3508 k++; 3509 } 3510 3511 /* finished row so stick it into b->a */ 3512 /* L-part */ 3513 pv = b->a + bi[i]; 3514 pj = bj + bi[i]; 3515 nzl = bi[i+1] - bi[i]; 3516 for (j=0; j<nzl; j++) { 3517 pv[j] = rtmp[pj[j]]; 3518 } 3519 3520 /* diagonal: invert diagonal entries for simplier triangular solves */ 3521 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3522 b->a[bdiag[i]] = 1.0/rtmp[i]; 3523 3524 /* U-part */ 3525 pv = b->a + bdiag[i+1] + 1; 3526 pj = bj + bdiag[i+1] + 1; 3527 nzu = bdiag[i] - bdiag[i+1] - 1; 3528 for (j=0; j<nzu; j++) { 3529 pv[j] = rtmp[pj[j]]; 3530 } 3531 } 3532 3533 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3534 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3535 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3536 3537 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3538 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3539 if (row_identity && col_identity) { 3540 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3541 } else { 3542 C->ops->solve = MatSolve_SeqAIJ; 3543 } 3544 C->ops->solveadd = 0; 3545 C->ops->solvetranspose = 0; 3546 C->ops->solvetransposeadd = 0; 3547 C->ops->matsolve = 0; 3548 C->assembled = PETSC_TRUE; 3549 C->preallocated = PETSC_TRUE; 3550 3551 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3552 PetscFunctionReturn(0); 3553 } 3554