AutoDiffCC 1.1.0

An AutoDifferentiation Library

Click here to see full documentation

Final Project - AutoDiffCC Python Package

CS207: Systems Development for Computational Science in Fall 2019

Group 22

• Alex Spiride
• Maja Garbulinska
• Matthew Finney
• Zhiying Xu

Overview

With the evolution of science and the growing computational possibilities, differentiation plays a critical role in a wide range of scientific and industrial applications of computer science. However, the precise computation of symbolic derivatives is computationally expensive, and not even possible in all situations, whereas the finite differencing method is not always accurate or stable. Automatic differentiation, however, provides a computationally efficient way to calculate derivatives, particularly of complex functions, for applications where accuracy and performance at scale are important.

Our package AutoDiffCC provides is an easy to use package that computes derivates of scalar and vector functions using the concept of automatic differentation.

We invite you to take a look at our repo and use AutoDiffCC!

Installation Guide

AutoDiffCC supports package installation via pip. Users can install the package in the command line with the following command.

pip install autodiffcc

How To Use

To use AutoDiffCC you first have to import it. If you already have it installed, you can do it by just running:

# Import the autodiffcc package
>>> import autodiffcc as ad 

Basic Applications

There are several ways in which you can take advantage of AutoDiffCC. Below we present some examples.

Example 1

A simple example using overloaded operators is described below. If you would like to evaluate f = x * x at x = 2, first initiate an AD object x with x = ad.AD(val=2.0, der=1.0), where 2 is the value and 1 is the derivative. Then simply define your function f = x * x and enjoy the results. You can see this example implemented below.

# Overload basic arithmetic operations
>>> x = ad.AD(val=2.0, der=1.0) 
>>> f = x * x
>>> print(f.val, f.der)
4.0 4.0

Alternatively, you can just proceed as follows:

>>> def f(x):
>>>   return x*x
>>> dfdx = differentiate(f)
>>> dfdx(x=2.0)
4.0 # this is the derivative value at x=2 

Example 2

To use more complex function like cos(x) follow this example using our built-in module ADmath:

>>> x = AD(val=3.0, der=1.0)
>>> ADmath.cos(x) 
(array(-0.9899924966004454), array(-0.1411200080598672))

Again, you can also do:

>>> def f(x):
>>>   return ADmath.cos(x) 
>>> dfdx = differentiate(f)
>>> dfdx( x=3.0)
-0.1411200080598672 # this is the derivative value evaluated at 3.0.

Offered Extentions

Root Finding

Our package offers three root finding methods. The bisection method, the newton-fourier method and the newton-raphson method.

Example 1

# Import the autodiffcc package
>>> import autodiffcc as ad

# Find the foot of a function with two variables using the bisection method

>>> def f(x, y):
>>>    return x + y - 100
>>> interval = [[1, 2], [3, 100]]
>>> my_root = ad.find_root(function=f, method='bisection', interval=interval)
>>> print(my_root)
[1.999999999999993, 98.0]

Example 2

# Import the autodiffcc package
>>> import autodiffcc as ad
    >>> interval = [[3, -3], [3, -3]]
    >>> my_root = ad.find_root(lambda x, y: (2 * x + y - 2, y + 2), interval=interval, method='newton-fourier', max_iter=150)
    >>> print(my_root)
    [ 2. -2.]

Example 3

# Import the autodiffcc package
>>> import autodiffcc as ad
    >>> def f1var(x):
    >>>     return (x + 2) * (x - 3)

    >>> my_root = ad.find_root(function=f1var, method='newton', start_values=1, threshold=1e-8)
    >>> print(my_root)
    3.

Expression parsing

Example 1

Another extension we offer is expression parsing. The below are two examples of parsing string expressions to function objects fn corresponding to the expressions.

# Import the autodiffcc package 
>>> import autodiffcc as ad
>>> from autodiffcc.parser import expressioncc

>>> x = ad.AD(2, der = [1, 0])
>>> y = ad.AD(3, der = [0, 1])

# Use expressioncc to parse a normal expression
>>> fn = expressioncc('x+y+1', ['x', 'y']).get_fn()
>>> print(fn(x,y).val)
6.0
>>> print(fn(x,y).der)
[1. 1.]

# Use expressioncc to parse an equation (left - right)
>>> fn = expressioncc('x = -y-1', ['x', 'y']).get_fn()
>>> print(fn(x,y).val)
6.0
>>> print(fn(x,y).der)
[1. 1.]

Resources

We would like to acknowledge Glenfletcher as his contribution was used in our package.

• Glenfletcher 2014. , DOI: https://github.com/glenfletcher/Equation/tree/master/Equation