ShallowWater
============

This is a simple implementation of the Shallow Water equations in Python using numpy or Theano for computation. 

The equations were taken from the relevant wikipedia article.
http://en.wikipedia.org/wiki/Shallow_water_equations

The time stepping scheme is simple Euler

To see results run shallowwater_simple.demo()
>>> from shallowwater_simple import demo
>>> demo()

depends on numpy and matplotlib for plotting

Theano
------

This code also demonstrates the use of Theano. It is being used to test how 
effective theano might be for the solution of partial differential equations
and their derivatives. 

Code Structure
--------------

The main code is split into three files:
shallowwater_base :
    Contains shallowwater solution code that is numpy/theano agnostic. 
    This code is written very close to the mathematical solution.
    It supports two files

shallowwater_python : 
    Uses shallowwater_base, numpy, and python iterators to solve the equations
    
shallowwater_theano : 
    Uses shallowwater_base and the theano project to generate code.

There is an additional file for clarity

shallowwater_simple :
    Is a simple, self contained solution equivalent to shallowwater_python. 
    This file is simple and independent from the rest of the code. 
    It is intended to serve as a clear example of the problem to be solved and
    is a great place to start if just arriving at this code.