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.