Source code for dit.other.extropy

"""
The extropy
"""

from ..helpers import RV_MODES
from ..math.ops import get_ops

import numpy as np


[docs]def extropy(dist, rvs=None, rv_mode=None): """ Returns the extropy J[X] over the random variables in `rvs`. If the distribution represents linear probabilities, then the extropy is calculated with units of 'bits' (base-2). Parameters ---------- dist : Distribution or float The distribution from which the extropy is calculated. If a float, then we calculate the binary extropy. rvs : list, None The indexes of the random variable used to calculate the extropy. If None, then the extropy is calculated over all random variables. This should remain `None` for ScalarDistributions. rv_mode : str, None Specifies how to interpret the elements of `rvs`. Valid options are: {'indices', 'names'}. If equal to 'indices', then the elements of `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. Returns ------- J : float The extropy of the distribution. """ try: # Handle binary extropy. float(dist) except TypeError: pass else: # Assume linear probability for binary extropy. import dit dist = dit.ScalarDistribution([dist, 1-dist]) rvs = None rv_mode = RV_MODES.INDICES if dist.is_joint(): if rvs is None: # Set to entropy of entire distribution rvs = list(range(dist.outcome_length())) rv_mode = RV_MODES.INDICES d = dist.marginal(rvs, rv_mode=rv_mode) else: d = dist pmf = d.pmf if d.is_log(): base = d.get_base(numerical=True) npmf = d.ops.log(1-d.ops.exp(pmf)) terms = -base**npmf * npmf else: # Calculate entropy in bits. log = get_ops(2).log npmf = 1 - pmf terms = -npmf * log(npmf) J = np.nansum(terms) return J