COIN-OR::LEMON - Graph Library

source: glpk-cmake/src/colamd/README @ 1:c445c931472f

Last change on this file since 1:c445c931472f was 1:c445c931472f, checked in by Alpar Juttner <alpar@…>, 10 years ago

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