Source code for neurokit2.complexity.entropy_power

import numpy as np
import pandas as pd
import scipy.integrate

from ..stats import density

[docs] def entropy_power(signal, **kwargs): """**Entropy Power (PowEn)** The Shannon Entropy Power (PowEn or SEP) is a measure of the effective variance of a random vector. It is based on the estimation of the density of the variable, thus relying on :func:`density`. .. warning:: We are not sure at all about the correct implementation of this function. Please consider helping us by double-checking the code against the formulas in the references. Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. **kwargs Other arguments to be passed to :func:`density_bandwidth`. Returns ------- powen : float The computed entropy power measure. info : dict A dictionary containing additional information regarding the parameters used. See Also -------- information_fisershannon Examples -------- .. ipython:: python import neurokit2 as nk import matplotlib.pyplot as plt signal = nk.signal_simulate(duration=10, frequency=[10, 12], noise=0.1) powen, info = nk.entropy_power(signal) powen # Visualize the distribution that the entropy power is based on @savefig entropy_power2.png scale=100% plt.plot(info["Values"], info["Density"]) @suppress plt.close() Change density bandwidth. .. ipython:: python powen, info = nk.entropy_power(signal, bandwidth=0.01) powen References ---------- * Guignard, F., Laib, M., Amato, F., & Kanevski, M. (2020). Advanced analysis of temporal data using Fisher-Shannon information: theoretical development and application in geosciences. Frontiers in Earth Science, 8, 255. * Vignat, C., & Bercher, J. F. (2003). Analysis of signals in the Fisher-Shannon information plane. Physics Letters A, 312(1-2), 27-33. * Dembo, A., Cover, T. M., & Thomas, J. A. (1991). Information theoretic inequalities. IEEE Transactions on Information theory, 37(6), 1501-1518. """ # Sanity checks if isinstance(signal, (np.ndarray, pd.DataFrame)) and signal.ndim > 1: raise ValueError( "Multidimensional inputs (e.g., matrices or multichannel data) are not supported yet." ) # we consider a random variable x whose probability density function is denoted as fx x_range, fx = density(signal, **kwargs) valid = np.where(fx > 0)[0] # In # The formula is somewhat different... # And on top of that it looks like it also differs between Dembo 1991 and Vignat 2003 # (The former divides by n) # Shannon Entropy ( H = fx[valid] * np.log(fx[valid]) H = -1 * scipy.integrate.simpson(H, x=x_range[valid]) # Entropy power powen = np.exp(2 * H / len(signal)) / (2 * np.pi * np.e) return powen, {"Density": fx[valid], "Values": x_range[valid]}