Discrete Riccati Equation and Lyapunov Equation Solvers
=======================================================

This small package contains two Python routines for solving the
discrete-time Riccati Equation (DARE) and the discrete-time
Lyapunov Equation.  These routines were developed in support
of a controls-related research project.  Both solvers were
developed into a minimally functional set of routines to 
satisfy the project for which they were originally meant. 
However, this functionality may be sufficient for other users
as well.  Note that the pydare package does not include 
routines for solving continuous versions of these two equation
sets.

Requirements
============

	* NumPy - http://numpy.scipy.org/
	* A Python interpretter compatible with NumPy
	
The routines were tested under Python 2.5 and 2.6.

Additionally, this package can take advantage of (but does not
require):

    * Slycot - https://github.com/avventi/Slycot

Methods - DARE
==============

The DareSolver class has four separate implementations of 
DARE solvers:

	* Direct using a Schur method
	* An iterative cyclic reduction method
	* An iterative Newton's method
    * Direct using SLICOT SB02OD implementation (via Slycot)
	
More information is available using
	
	>>> help(pydare.DareSolver)
	
Methods - Discrete Lyapunov
===========================

Three functions are provided for solving the discrete-time Lyapunov 
equation:

	* An iterative solver
	* Direct using a Schur method based on an Octave implementation
    * Direct using SLICOT SB03MD implementation (via Slycot)

More information is available using

	>>> help(pydare.dylap)
	
Usage - DARE
============

A solver object is initialized by passing A, B, Q, and R matrices (NumPy matrix 
objects) to the constructor.  The default solver is the direct Schur method.  To
select other methods, the following members of the solver object can be set:

	>>> solver.iterative = True   # To utilize the iterative Newton method
	
	>>> solver.use_cyclic = True  # To utilize the cyclic reduction method
	
Finally, the solve() method will return the calculated solution if the solver
was successful.

Testing
=======

An extremely basic test suite is included in the 'test' directory.  These tests
are present mainly to ensure minimal functionality.  If Slycot is not
installed, the Slycot-associated tests will fail.

Support
=======

This package is not officially "supported," but additions and corrections can be
added by sending specifics to Jeff Armstrong at jeff@rainbow-100.com.  As this
package is functional to the point where it is acceptable for its original 
purpose, future additions are somewhat unlikely.

Also, this package is released under a free software license, so anyone should
feel free to distribute changes as they see fit as long as the distribution is
compatible with the GNU General Public License Version 3 or higher.

Copyright
=========

Copyright (C) 2010 Jeffrey Armstrong <jeff@rainbow-100.com>
http://jeff.rainbow-100.com/

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program 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 General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.

A full version of the license terms is available in LICENSE.