# pyADiff: A simple, pure python algorithmic differentiation package¶

pyADiff is a (yet) very basic algorithmic differentiation package, which implements forward and adjoint/reverse mode differentiation. If you are looking for a fully-featured and faster library, have a look at google/jax, autograd or dco/c++ (or many more), but if you are interested in a package where you are able to quickly “look under the hood”, you may be right here.

## Basic Usage¶

Suppose we want to compute the gradient of the function $$f(x_0, x_1) = 2 x_0 x_1^2$$. This is a rather trivial task, because by simple calculus the gradient is:

$\begin{split}\nabla f(x_0, x_1) = \begin{pmatrix} 2 x_1^2 \\ 4 x_0 x_1\end{pmatrix}\end{split}$

Nevertheless we use this example illustrate the use of pyADiff.

import pyADiff as ad
# define the function f
def f(x):
return 2.*x*x**2.

x = [0.5, 2.0]
# Call the function f and the gradient function df
y = f(x)
dy = df(x)

print("f({}) = {}".format(x, y))  # prints f([0.5, 2.0]) = 4.0
print("f'({}) = {}".format(x, dy))  # prints f'([0.5, 2.0]) = [8. 4.]


Which corresponds to the evaluation of the analytic gradient.

$\begin{split}\nabla f(0.5, 2) = \begin{pmatrix} 2*2^2 \\ 4 * 0.5 * 2\end{pmatrix} = \begin{pmatrix} 8 \\ 4 \end{pmatrix}\end{split}$

## Motivation¶

My motivation to start this project arose from curiosity while listening to the lecture Computational Differentiation by Uwe Naumann at RWTH Aachen University. So basically I tried to understand the concepts from the lecture by implementing them by myself. In the end I was (positively) surprised with the outcome and decided to bundle it in a python package. Additionaly this gave me the chance to learn about python packaging, distributing, documentation, …