1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
NOTE: Files in this subdirectory are NOT part of the GLPK package, but
are used with GLPK.
The original code was modified according to GLPK requirements by
Andrew Makhorin <mao@gnu.org>.
************************************************************************
COLAMD/SYMAMD Version 2.7, Copyright (C) 1998-2007, Timothy A. Davis,
All Rights Reserved.
Description:
colamd: an approximate minimum degree column ordering algorithm,
for LU factorization of symmetric or unsymmetric matrices,
QR factorization, least squares, interior point methods for
linear programming problems, and other related problems.
symamd: an approximate minimum degree ordering algorithm for
Cholesky factorization of symmetric matrices.
Purpose:
Colamd computes a permutation Q such that the Cholesky factorization
of (AQ)'(AQ) has less fill-in and requires fewer floating point
operations than A'A. This also provides a good ordering for sparse
partial pivoting methods, P(AQ) = LU, where Q is computed prior to
numerical factorization, and P is computed during numerical
factorization via conventional partial pivoting with row
interchanges. Colamd is the column ordering method used in SuperLU,
part of the ScaLAPACK library. It is also available as built-in
function in MATLAB Version 6, available from MathWorks, Inc.
(http://www.mathworks.com). This routine can be used in place of
colmmd in MATLAB.
Symamd computes a permutation P of a symmetric matrix A such that
the Cholesky factorization of PAP' has less fill-in and requires
fewer floating point operations than A. Symamd constructs a matrix
M such that M'M has the same nonzero pattern of A, and then orders
the columns of M using colmmd. The column ordering of M is then
returned as the row and column ordering P of A.
Authors:
The authors of the code itself are Stefan I. Larimore and Timothy A.
Davis (davis at cise.ufl.edu), University of Florida. The algorithm
was developed in collaboration with John Gilbert, Xerox PARC, and
Esmond Ng, Oak Ridge National Laboratory.
Acknowledgements:
This work was supported by the National Science Foundation, under
grants DMS-9504974 and DMS-9803599.
License:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public License
as published by the Free Software Foundation; either version 2.1 of
the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
USA.
Permission is hereby granted to use or copy this program under the
terms of the GNU LGPL, provided that the Copyright, this License,
and the Availability of the original version is retained on all
copies. User documentation of any code that uses this code or any
modified version of this code must cite the Copyright, this License,
the Availability note, and "Used by permission." Permission to
modify the code and to distribute modified code is granted, provided
the Copyright, this License, and the Availability note are retained,
and a notice that the code was modified is included.
COLAMD is also available under alternate licenses, contact T. Davis
for details.
Availability:
The colamd/symamd library is available at:
http://www.cise.ufl.edu/research/sparse/colamd/
References:
T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, An approximate
column minimum degree ordering algorithm, ACM Transactions on
Mathematical Software, vol. 30, no. 3., pp. 353-376, 2004.
T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng, Algorithm 836:
COLAMD, an approximate column minimum degree ordering algorithm, ACM
Transactions on Mathematical Software, vol. 30, no. 3., pp. 377-380,
2004.
|
