Permutation Entropy Small

Problem

Compute normalized permutation entropy. For every window of order points spaced by delay, record the rank order pattern (ties broken by index) and build its empirical distribution; return the Shannon entropy of those patterns divided by log(order!).

Return 0.0 if order < 2, delay < 1, or the series has fewer than (order - 1) * delay + 1 points.

Hint

Monotone series produce a single ordinal pattern, so entropy is zero.

Test cases

case 1

in: [[1,2,3,4,5],2,1]

expected: 0

case 2

in: [[1,2,1,2,1,2],2,1]

expected: 0.9709505944546688

case 3

in: [[3,3,3,3],2,1]

expected: 0

case 4

in: [[5,4,3,2,1],3,1]

expected: 0

Starter codePython

import math
def permutation_entropy(series, order, delay):
    # Your code here
    pass

4 test cases · run your code against them in the editor