ADPY

ADPY
====

##Description


ADPY is a Python library for algorithmic differentiation (http://en.wikipedia.org/wiki/Automatic_differentiation).
It aims to provide an easy way to extract partial derivatives of vector valued function (Jacobian matrix). In addition it allows to created callable function for obtaining function values using computational graphs.  

Features:

* optimize numerical evaluation by using computational graph
* create callable function from Sympy expressions (calls lambdify once and creates a computational graph) 
* extract partial derivatives using forward or reverse algorithmic differentiation
* bonus: a small nonlinear solver using all advantages mentioned above



##How to use

Due the small amount of features the handling is quite easy.         
        
For the easiest use you need a callable function which takes a list of float numbers and returns a list.

        def f(x):
        	return [x[0]**2,2*x[1]]

You need a valid values for x which cause no singularities while evaluating the function.

		x1 = [1.,2.]

Initialize the ADFUN object.

		from ADPY import adfun
		adpy_test  = adfun(f,x1)

Now you have a callable function with computational graph optimization.

			y1 = adpy_test(x1)

If you want to use derivatives just do
	
		adpy_test.init_reverse_jac()

or

		adpy_test.init_forward_jac()

Now you can evaluate them using

		J_forward = adpy_test.jac_reverse(x1)

or

		J_forward = adpy_test.jac_forward(x1)


For more information see the attached examples.

##Install

clone git

        git clone https://github.com/zwenson/ADPY
and run setup.py

        python setup.py install

or use easy_install

        easy_install ADPY

##How it works

Without going in to detail. It uses an overloaded class "adfloat" to record a list of the mathematical operations required to obtain the result. This list is then translated in to python expressions and made executable. The list is also used to perform automatic differentiation.


##To do
* more testing
* add more operations
* maybe add Hessian matrix? 
* add Taylor arithmetic?