How do I compute the approximate entropy of a bit string?

Question

Is there a standard way to do this?

Googling -- \"approximate entropy\" bits -- uncovers multiple academic papers but I\'d like to just find a chunk of pseudocode de

Answer 1

Here's an implementation in Python (I also added it to the Wiki page):

import numpy as np

def ApEn(U, m, r):

    def _maxdist(x_i, x_j):
        return max([abs(ua - va) for ua, va in zip(x_i, x_j)])

    def _phi(m):
        x = [[U[j] for j in range(i, i + m - 1 + 1)] for i in range(N - m + 1)]
        C = [len([1 for x_j in x if _maxdist(x_i, x_j) <= r]) / (N - m + 1.0) for x_i in x]
        return -(N - m + 1.0)**(-1) * sum(np.log(C))

    N = len(U)

    return _phi(m) - _phi(m + 1)

Example:

>>> U = np.array([85, 80, 89] * 17)
>>> ApEn(U, 2, 3)
-1.0996541105257052e-05

The above example is consistent with the example given on Wikipedia.