Hellinger distance for discrete probability distributions in Python

hellinger.py

"""
Three ways of computing the Hellinger distance between two discrete
probability distributions using NumPy and SciPy.
"""

import numpy as np
from scipy.linalg import norm
from scipy.spatial.distance import euclidean


_SQRT2 = np.sqrt(2)     # sqrt(2) with default precision np.float64


def hellinger1(p, q):
    return norm(np.sqrt(p) - np.sqrt(q)) / _SQRT2


def hellinger2(p, q):
    return euclidean(np.sqrt(p), np.sqrt(q)) / _SQRT2


def hellinger3(p, q):
    return np.sqrt(np.sum((np.sqrt(p) - np.sqrt(q)) ** 2)) / _SQRT2