scipy.stats.entropy(pk, qk=None, base=None)

import numpy as np

def kl(p, q):
"""Kullback-Leibler divergence D(P || Q) for discrete distributions

Parameters
----------
p, q : array-like, dtype=float, shape=n
Discrete probability distributions.
"""
p = np.asarray(p, dtype=np.float)
q = np.asarray(q, dtype=np.float)

return np.sum(np.where(p != 0, p * np.log(p / q), 0))

from itertools import product
KL = [kl(hist_mat[:,i],hist_mat[:,j]) for i,j in product( range(0,K), range(0,K) )]

def kullback_leibler_divergence(X):

    """
    Finds the pairwise Kullback-Leibler divergence
    matrix between all rows in X.

    Parameters
    ----------
    X : array_like, shape (n_samples, n_features)
        Array of probability data. Each row must sum to 1.

    Returns
    -------
    D : ndarray, shape (n_samples, n_samples)
        The Kullback-Leibler divergence matrix. A pairwise matrix D such that D_{i, j}
        is the divergence between the ith and jth vectors of the given matrix X.

    Notes
    -----
    Based on code from Gordon J. Berman et al.
    (https://github.com/gordonberman/MotionMapper)

    References:
    -----------
    Berman, G. J., Choi, D. M., Bialek, W., & Shaevitz, J. W. (2014).
    Mapping the stereotyped behaviour of freely moving fruit flies.
    Journal of The Royal Society Interface, 11(99), 20140672.
    """

    X_log = np.log(X)
    X_log[np.isinf(X_log) | np.isnan(X_log)] = 0

    entropies = -np.sum(X * X_log, axis=1)

    D = np.matmul(-X, X_log.T)
    D = D - entropies
    D = D / np.log(2)
    D *= (1 - np.eye(D.shape[0]))

    return D