Source code for dit.other.renyi_entropy

Renyi Entropy

from __future__ import division

import numpy as np

from ..helpers import normalize_rvs
from ..utils import flatten
from ..multivariate import entropy

__all__ = ('renyi_entropy',

[docs]def renyi_entropy(dist, order, rvs=None, rv_mode=None): """ Compute the Renyi entropy of order `order`. Parameters ---------- dist : Distribution The distribution to take the Renyi entropy of. order : float >= 0 The order of the Renyi entropy. rvs : list, None The indexes of the random variable used to calculate the Renyi entropy of. If None, then the Renyi entropy is calculated over all random variables. rv_mode : str, None Specifies how to interpret `rvs` and `crvs`. Valid options are: {'indices', 'names'}. If equal to 'indices', then the elements of `crvs` and `rvs` are interpreted as random variable indices. If equal to 'names', the the elements are interpreted as random variable names. If `None`, then the value of `dist._rv_mode` is consulted, which defaults to 'indices'. Returns ------- H_a : float The Renyi entropy. Raises ------ ditException Raised if `rvs` or `crvs` contain non-existant random variables. ValueError Raised if `order` is not a non-negative float. """ if order < 0: msg = "`order` must be a non-negative real number" raise ValueError(msg) if dist.is_joint and rvs is not None: rvs = list(flatten(normalize_rvs(dist, rvs, None, rv_mode)[0])) dist = dist.marginal(rvs, rv_mode) pmf = dist.pmf if order == 0: H_a = np.log2(pmf.size) elif order == 1: H_a = entropy(dist) elif order == np.inf: H_a = -np.log2(pmf.max()) else: H_a = 1/(1-order) * np.log2((pmf**order).sum()) return H_a