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An automatic differentiation library for Python+NumPy.

Project description


An automatic differentiation library for Python+NumPy

How To Use

There are four public elements of the API:

  • AutoDiff is a context manager and must be entered with a with statement. The __enter__ method returns a new version of x that must be used to instead of the x passed as a parameter to the AutoDiff constructor.

  • value, jacobian, get_value_and_jacobian, these functions, which must be called in an AutoDiff context, extract the value, Jacobian, or both from a dependent variable.

If you are using get_value_and_jacobian, x must be a 2D column vector, and the value you must be parsing for the derivative must also be a 2D column vector. In most other cases, how to convert to a Jacobian Matrix is non-obvious. If you wish to deal with those cases see the paragraph after the example.


import auto_diff
import numpy as np

# Define a function f
# f can have other constant arguments, if they are constant wrt x
# Define the input vector, x

with auto_diff.AutoDiff(x) as x:
    f_eval = f(x, u)
    y, Jf = auto_diff.get_value_and_jacobian(f_eval)

# y is the value of f(x, u) and Jf is the Jacobian of f with respect to x.

We can also differentiate functions from arbitrarily shaped numpy arrays to arbitrarily shaped outputs. Let y = f(x), where x is a numpy array of shape x.shape, and y is is the output of the function we wish to differentiate, f.

We can then access a numpy array of shape (*y.shape, *x.shape), by accessing y.der. This represents the gradients of each component of y with respect to x. To find the gradient of the norm of a vector x, for example one can do

import auto_diff
import numpy as np
x = np.array([[np.pi], [3.0], [17.0]])

with auto_diff.AutoDiff(x) as x:


  • You must import numpy and use that object, rather then do something like from numpy import ..., where ... is either * or just function names.

Crashes, Bug Reports, and Feedback: Email

There are missing features right now. I'm working on them, feel free to email me if you want something prioritized.


A version of NumPy >= 1.17 may be required. Bugs on older versions have always raised errors, so there should be nothing to worry about.

Author: Parth Nobel (Github: /PTNobel, Version: 0.3

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