# 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.

--------
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 https://github.com/fishinfo/FiShPy/blob/master/FiSh.py
# 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 (https://en.wikipedia.org/wiki/Entropy_power_inequality)
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]}

```