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Autograd can automatically differentiate native Python and Numpy code. It can handle a large subset of Python's features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives. It supports reverse-mode differentiation (a.k.a. backpropagation), which means it can efficiently take gradients of scalar-valued functions with respect to array-valued arguments, as well as forward-mode differentiation, and the two can be composed arbitrarily. The main intended application of Autograd is gradient-based optimization. For more information, check out the tutorial and the examples directory.

Example use:

>>> import autograd.numpy as np  # Thinly-wrapped numpy
>>> from autograd import grad    # The only autograd function you may ever need
>>>
>>> def tanh(x):                 # Define a function
...     return (1.0 - np.exp((-2 * x))) / (1.0 + np.exp(-(2 * x)))
...
>>> grad_tanh = grad(tanh)       # Obtain its gradient function
>>> grad_tanh(1.0)               # Evaluate the gradient at x = 1.0
np.float64(0.419974341614026)
>>> (tanh(1.0001) - tanh(0.9999)) / 0.0002  # Compare to finite differences
np.float64(0.41997434264973155)

We can continue to differentiate as many times as we like, and use