An automatic differentiation library for Python+NumPy.
Project description
auto_diff
An automatic differentiation library for Python+NumPy
How To Use
There are five 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 theAutoDiff
constructor. 
value
,jacobian
,get_value_and_jacobian
, these functions, which must be called in anAutoDiff
context, extract the value, Jacobian, or both from a dependent variable. 
get_value_and_jacobians
, if multiple vectors are passed in as arguments toAutoDiff
, this method returns a tuple of Jacobians wrt to the different variables.
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
nonobvious. If you wish to deal with those cases see the paragraph after the
example.
auto_diff
also supports using sparse matrices instead of ndarray
s to store the Jacobians.
Simple use the SparseAutoDiff
context manager instead of AutoDiff
.
Also if you use SparseAutoDiff
, you need to verify that your code and none of nonNumPy dependencies use the np.ndarray
constructor for a floating point vector.
If using SparseAutoDiff
, get_value_and_jacobian
, jacobian
, and get_value_and_jacobians
return scipy.sparse.lil_matrix
es instead of ndarray
s.
Example
import auto_diff import numpy as np # Define a function f # f can have other 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.
If you need both the Jacobian wrt to x and u,
with auto_diff.AutoDiff(x, u) as (x, u): f_eval = f(x, u) y, (Jfx, Jfu) = auto_diff.get_value_and_jacobians(f_eval) # y is the value of f(x, u), Jfx is the Jacobian of f with respect to x, and # Jfu is the Jacobian of f with respect to u.
Finally, if f
and x
are very highdimensional, then we can use SparseAutoDiff
to save memory.
with auto_diff.SparseAutoDiff(x, u) as (x, u): f_eval = f(x, u) y, (Jfx, Jfu) = auto_diff.get_value_and_jacobians(f_eval) # y is the value of f(x, u), Jfx is the Jacobian of f with respect to x, and # Jfu is the Jacobian of f with respect to u. # Jfx and Jfu are instances of scipy.sparse.lil_matrix.
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: print(np.linalg.norm(x).der)
Restrictions
 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 parthnobel@berkeley.edu
There are missing features right now. I'm working on them, feel free to email me if you want something prioritized.
Prerequisite
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, parthnobel@berkeley.edu) Version: 0.3
Project details
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Filename, size  File type  Python version  Upload date  Hashes 

Filename, size auto_diff0.4.0py3noneany.whl (20.2 kB)  File type Wheel  Python version py3  Upload date  Hashes View 
Filename, size auto_diff0.4.0.tar.gz (15.4 kB)  File type Source  Python version None  Upload date  Hashes View 
Hashes for auto_diff0.4.0py3noneany.whl
Algorithm  Hash digest  

SHA256  a7006dcfc79cb5f39acf3c2331ec838a90c681bf1393354e4ae98b4c129ae3e9 

MD5  81732c71cd6769b4e95f909c6051f1dd 

BLAKE2256  4d608eadffc59b9bffee1e38fa83285fe82cf93edc7bef7bf26e08e0da82b42e 