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.