SuperLU_DIST
4.0
superlu_dist on CPU and GPU clusters
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Elimination tree computation and layout routines. More...
Functions | |
int | sp_symetree_dist (int_t *acolst, int_t *acolend, int_t *arow, int_t n, int_t *parent) |
Symmetric elimination tree. More... | |
int | sp_coletree_dist (int_t *acolst, int_t *acolend, int_t *arow, int_t nr, int_t nc, int_t *parent) |
Nonsymmetric elimination tree. More... | |
int_t * | TreePostorder_dist (int_t n, int_t *parent) |
Elimination tree computation and layout routines.
Implementation of disjoint set union routines. Elements are integers in 0..n-1, and the names of the sets themselves are of type int.
Calls are: initialize_disjoint_sets (n) initial call. s = make_set (i) returns a set containing only i. s = link (t, u) returns s = t union u, destroying t and u. s = find (i) return name of set containing i. finalize_disjoint_sets final call.
This implementation uses path compression but not weighted union. See Tarjan's book for details. John Gilbert, CMI, 1987.
Implemented path-halving by XL 7/5/95.
int sp_coletree_dist | ( | int_t * | acolst, |
int_t * | acolend, | ||
int_t * | arow, | ||
int_t | nr, | ||
int_t | nc, | ||
int_t * | parent | ||
) |
Nonsymmetric elimination tree.
Find the elimination tree for A'*A. This uses something similar to Liu's algorithm. It runs in time O(nz(A)*log n) and does not form A'*A.
Input: Sparse matrix A. Numeric values are ignored, so any explicit zeros are treated as nonzero. Output: Integer array of parents representing the elimination tree of the symbolic product A'*A. Each vertex is a column of A, and nc means a root of the elimination forest.
John R. Gilbert, Xerox, 10 Dec 1990 Based on code by JRG dated 1987, 1988, and 1990.
Symmetric elimination tree.
p = spsymetree (A);
Find the elimination tree for symmetric matrix A. This uses Liu's algorithm, and runs in time O(nz*log n).
Input: Square sparse matrix A. No check is made for symmetry; elements below and on the diagonal are ignored. Numeric values are ignored, so any explicit zeros are treated as nonzero. Output: Integer array of parents representing the etree, with n meaning a root of the elimination forest. Note: This routine uses only the upper triangle, while sparse Cholesky (as in spchol.c) uses only the lower. Matlab's dense Cholesky uses only the upper. This routine could be modified to use the lower triangle either by transposing the matrix or by traversing it by rows with auxiliary pointer and link arrays.
John R. Gilbert, Xerox, 10 Dec 1990 Based on code by JRG dated 1987, 1988, and 1990. Modified by X.S. Li, November 1999.