Math::MatrixReal v2.04
http://leto.net/code/Math-MatrixReal/

Contents of this file:
----------------------
    -   Legal stuff
    -   Requirements
    -   What does it do
    -   Preliminary steps for use with Perl prior to version 5.002
    -   How to install it
    -   Version history
    -   Credits
    -   Final note

Legal stuff:
------------
Copyright (c) 1996, 1997 by Steffen Beyer.
              1999 by Rodolphe Ortalo.
	      2001-2008 by Jonathan Leto.
All rights reserved.
This package is free software; you can redistribute it and/or
modify it under the same terms as Perl itself.

Requirements:
-------------
Perl version 5.003 or higher capable of "overloading" (overload.pm).

What does it do:
----------------

Math::MatrixReal - Matrix of Reals

Implements the data type "matrix of reals" (and consequently also
"vector of reals") which can be used almost like any other basic
Perl type thanks to OPERATOR OVERLOADING, i.e.,

    $A = $matrix1 * $matrix2;
    $B = $A ** 2;
    $C = $A + 2*B;
    $D = $C - $B/2;
    $inverse = $C ** -1;
    $inverse = 1/$C;
    
does what you would like it to do.

Also features many important operations and methods: matrix norm,
matrix transposition, matrix inverse, determinant of a matrix, order
and numerical condition of a matrix, scalar product of vectors, vector
product of vectors, vector length, projection of row and column vectors,
a comfortable way for reading in a matrix from a file, the keyboard or
your code, and many more.

Allows to solve linear equation systems using an efficient algorithm
known as "L-R-decomposition" and several approximative (iterative) methods.

Features an implementation of Kleene's algorithm to compute the minimal
costs for all paths in a graph with weighted edges (the "weights" being
the costs associated with each edge).

Allows to solve the eigensystem of a real symmetric matrix, using
Householder transformation and QL decomposition.

New Module::Build Installation Instructions
------------------------------------------------

Since Math::MatrixReal 2.03, Module::Build is used for the build process, but
a Makefile.PL is still generated for older installations. If you do not have Module::Build, please
read the "Old Installation Instructions".

The build and install Math::MatrixReal run the commands

	perl Build.PL
	./Build
	./Build test
	./Build install

Or, if you're on a platform (like DOS or Windows) that doesn't require
the "./" notation, you can do this:

        perl Build.PL
        Build
        Build test
        Build install


Old Installation Instructions (should still work):
-------------------------------------------------

Preliminary steps for use with Perl prior to version 5.002:
-----------------------------------------------------------

Edit the "Makefile.PL" file in this package and change the line

    'VERSION_FROM'	=> 'MatrixReal.pm',

to

    'VERSION'		=> '2.04',


How to install it:
------------------

Please unpack and build this package OUTSIDE the Perl source and distribution
tree!!

 1) Change directory to the directory that has been created by unpacking this
    package ("Math-MatrixReal-1.3/").

 2) Type "perl Makefile.PL".
    (Or whatever the name and path of your Perl 5 binary is)
    Alternatively you can type, e.g., "perl Makefile.PL PREFIX=/home/doe"
    to install the module in the home directory, e.g. John Doe...

 3) Type "make".

 3.5) Optionally, type "make test" to test the build and/or benchmark
    your system a little.

 4) Type "make install".


Version history:
----------------

Version 1.0 was the initial release.

Version 1.1 fixed a bug in the "kleene()" method.

Version 1.2 changed the "new()" and "new_from_string()" methods so
that they don't fail anymore if an empty class name is given to them
(instead, "Math::MatrixReal" is used as the default).

The documentation of the "new_from_string()" method was also slightly
changed because it had proven to be incomplete and misleading.

Version 1.3 included the eigenvalues/eigenvectors computation methods,
added by Rodolphe Ortalo. Some test/bench programs were added also,
especially for these methods.

Please see the CHANGES file for newer version history.

(NOTE:  The change from 1.9 to version 2.01 was not a major change, 
we just didn't start out with leading zeroes in the original versioning,
and ran out of decimal digits for minor updates.)

Credits:
--------

As always, many thanks to Andreas Koenig <andreas.koenig@mind.de>
for his relentless support and efforts as upload manager of the CPAN!

Also many thanks to Stu Smith <stu@cs.uml.edu> for raising the questions
concerning the "new_from_string()" method (whose documentation was mis-
leading and incomplete)!

Many thanks to Steffen Beyer himself for being very open to third-party
additions. (Of course, this acknowledgment is due to Rodolphe. :-)

Final note:
-----------

Please send all comments/bugs/patches to Jonathan Leto <jonathan@leto.net>,
as I have taken over module maintainer-ship as of version 1.4.

Original Final note:

If you need any assistance or have any comments, problems, suggestions,
findings, complaints, questions, insights, compliments or donations to give ;-)
then please don't hesitate to send me a mail:

sb@engelschall.com (Steffen Beyer)

You can also contact me if you think it's relevant (e.g. especially
for compliments or donations ;-)):

ortalo@laas.fr (Rodolphe Ortalo)

In fact I'd be glad if you could drop me an e-mail when you are using this
package, so I can see how much interest exists in it and how much time is
reasonable to spend on its further development.

Therefore, I would also be glad to know what you liked and what you disliked
about this package!

And I would also be very interested to know what your application is in
which you found this package to be useful, just to get an idea what can
all be done with it and in which direction it should be developed further.

Many thanks in advance!!

