"""
Renyi Entropy.
"""
import numpy as np
from ..helpers import normalize_rvs
from ..multivariate import entropy
from ..utils import flatten
__all__ = ("renyi_entropy",)
[docs]
def renyi_entropy(dist, order, rvs=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.
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)[0]))
dist = dist.marginal(rvs)
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