Source code for neurokit2.complexity.entropy_tsallis

import numpy as np

from .entropy_shannon import _entropy_freq

[docs] def entropy_tsallis(signal=None, q=1, symbolize=None, show=False, freq=None, **kwargs): """**Tsallis entropy (TSEn)** Tsallis Entropy is an extension of :func:`Shannon entropy <entropy_shannon>` to the case where entropy is nonextensive. It is similarly computed from a vector of probabilities of different states. Because it works on discrete inputs (e.g., [A, B, B, A, B]), it requires to transform the continuous signal into a discrete one. .. math:: TSEn = \\frac{1}{q - 1} \\left( 1 - \\sum_{x \\in \\mathcal{X}} p(x)^q \\right) Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. q : float Tsallis's *q* parameter, sometimes referred to as the entropic-index (default to 1). symbolize : str Method to convert a continuous signal input into a symbolic (discrete) signal. ``None`` by default, which skips the process (and assumes the input is already discrete). See :func:`complexity_symbolize` for details. show : bool If ``True``, will show the discrete the signal. freq : np.array Instead of a signal, a vector of probabilities can be provided. **kwargs Optional arguments. Not used for now. Returns -------- tsen : float The Tsallis entropy of the signal. info : dict A dictionary containing additional information regarding the parameters used. See Also -------- entropy_shannon, fractal_petrosian, entropy_renyi Examples ---------- .. ipython:: python import neurokit2 as nk signal = [1, 3, 3, 2, 6, 6, 6, 1, 0] tsen, _ = nk.entropy_tsallis(signal, q=1) tsen shanen, _ = nk.entropy_shannon(signal, base=np.e) shanen References ----------- * Tsallis, C. (2009). Introduction to nonextensive statistical mechanics: approaching a complex world. Springer, 1(1), 2-1. """ if freq is None: _, freq = _entropy_freq(signal, symbolize=symbolize, show=show) freq = freq / np.sum(freq) if np.isclose(q, 1): lnq_1_over_p = np.log(1 / freq) else: lnq_1_over_p = ((1 / freq) ** (1 - q) - 1) / (1 - q) tsens = freq * lnq_1_over_p return np.sum(tsens), {"Symbolization": symbolize, "Values": tsens}