Elimination tree computation and layout routines. More...
Include dependency graph for etree.c:
Functions | |
| static int_t * | mxCallocInt (int_t n) |
| static void | initialize_disjoint_sets (int_t n, int_t **pp) |
| static int_t | make_set (int_t i, int_t *pp) |
| static int_t | link (int_t s, int_t t, int_t *pp) |
| static int_t | find (int_t i, int_t *pp) |
| static void | finalize_disjoint_sets (int_t *pp) |
| 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... | |
| static void | etdfs (int_t v, int_t first_kid[], int_t next_kid[], int_t post[], int_t *postnum) |
| static void | nr_etdfs (int_t n, int_t *parent, int_t *first_kid, int_t *next_kid, int_t *post, int_t postnum) |
| int_t * | TreePostorder_dist (int_t n, int_t *parent) |
Variables | |
| static int_t * | first_kid |
| Depth-first search from vertext. More... | |
| static int_t * | next_kid |
| static int_t * | post |
| static int_t | postnum |
Detailed Description
Elimination tree computation and layout routines.
Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt at the top-level directory.
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.
Function Documentation
◆ etdfs()
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◆ finalize_disjoint_sets()
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◆ find()
◆ initialize_disjoint_sets()
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◆ link()
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◆ make_set()
◆ mxCallocInt()
◆ nr_etdfs()
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◆ sp_coletree_dist()
| 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.
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◆ sp_symetree_dist()
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.
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◆ TreePostorder_dist()
Variable Documentation
◆ first_kid
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Depth-first search from vertext.
q = TreePostorder_dist (n, p);
Postorder a tree.
Input:
p is a vector of parent pointers for a forest whose
vertices are the integers 0 to n-1; p[root]==n.
Output:
q is a vector indexed by 0..n-1 such that q[i] is the
i-th vertex in a postorder numbering of the tree.
( 2/7/95 modified by X.Li:
q is a vector indexed by 0:n-1 such that vertex i is the
q[i]-th vertex in a postorder numbering of the tree.
That is, this is the inverse of the previous q. )
In the child structure, lower-numbered children are represented
first, so that a tree which is already numbered in postorder
will not have its order changed.
Written by John Gilbert, Xerox, 10 Dec 1990.
Based on code written by John Gilbert at CMI in 1987.
◆ next_kid
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◆ post
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◆ postnum
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