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Automatic differentiation with dual numbers

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AutoDiff

Developed by: Will Claybaugh, Bruce Xiong, Erin Williams
Group #3, CS207 Fall 2018

Introduction

Autodiff finds the derivatives of a function (to machine precision!) at the same time it finds the value of the function.

import autodiff.autodiff as ad

x = ad.DualNumber('x', 2)
y = ad.DualNumber('y', 3)

out = x/y
out.value # 0.66666, the value of 2 divided by 3
out.derivatives #{x: 1/3, y: -2/(3**2)}, the gradient of x/y at (2,3)

Autodiff works for functions and expressions with any number of inputs. Just pass those functions DualNumbers instead of regular ints/floats (and upgrade any math module functions to their autodiff equvalents)

Installation

Autodiff is on PyPi and can be installed using the command pip install AutoDiff-group3. To import, use import autodiff.autodiff as ad.

Autodiff can also be installed by downloading from github. Becuase it has no dependencies, you can simply add the repo folder to your python path (import sys sys.path.insert(0, '/path_to_repo/')) and import as normal.

Examples

Using autodiff is very simple:

import autodiff.autodiff as ad

def f(a,b):
    return 3*a/b*ad.sin(a*b+2)

out = f(ad.DualNumber('x',2),ad.DualNumber('y',3))

print(out.value)
1.978716

print(out.derivatives['x'])
0.116358

print(out.derivatives['y'])
-1.24157

# get the value and derifative of f at a different point
out = f(ad.DualNumber('x',0),ad.DualNumber('y',1))

A Python 3 notebook containing more in-depth examples and usage is available HERE

Documentation

Click HERE for full documentation.

Dependencies

Click HERE for a full listing of dependencies.

License

Click HERE to view our MIT License.

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