An automatic differentiation library for Python+NumPy.
An automatic differentiation library for Python+NumPy
How To Use
There are four public elements of the API:
AutoDiffis 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
get_value_and_jacobian, these functions, which must be called in an
AutoDiffcontext, 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
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
y is is the output of the function we wish to differentiate,
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: print(np.linalg.norm(x).der)
- You must import numpy and use that object, rather then do something like
from numpy import ..., where
*or just function names.
Crashes, Bug Reports, and Feedback:
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, email@example.com) Version: 0.3
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