Source code for neurokit2.complexity.entropy_range

from .entropy_approximate import entropy_approximate
from .entropy_sample import entropy_sample

[docs] def entropy_range(signal, dimension=3, delay=1, tolerance="sd", approximate=False, **kwargs): """**Range Entropy (RangEn)** Introduced by Omidvarnia et al. (2018), Range Entropy (RangEn or RangeEn) refers to a modified form of SampEn (or ApEn). Both ApEn and SampEn compute the logarithmic likelihood that runs of patterns that are close remain close on the next incremental comparisons, of which this closeness is estimated by the Chebyshev distance. Range Entropy uses instead a normalized "range distance", resulting in modified forms of ApEn and SampEn, **RangEn (A)** (*mApEn*) and **RangEn (B)** (*mSampEn*). However, the RangEn (A), based on ApEn, often yields undefined entropies (i.e., *NaN* or *Inf*). As such, using RangEn (B) is recommended instead. RangEn is described as more robust to nonstationary signal changes, and has a more linear relationship with the Hurst exponent (compared to ApEn and SampEn), and has no need for signal amplitude correction. Note that the :func:`corrected <entropy_approximate>` version of ApEn (cApEn) can be computed by setting ``corrected=True``. Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. delay : int Time delay (often denoted *Tau* :math:`\\tau`, sometimes referred to as *lag*) in samples. See :func:`complexity_delay` to estimate the optimal value for this parameter. dimension : int Embedding Dimension (*m*, sometimes referred to as *d* or *order*). See :func:`complexity_dimension` to estimate the optimal value for this parameter. tolerance : float Tolerance (often denoted as *r*), distance to consider two data points as similar. If ``"sd"`` (default), will be set to :math:`0.2 * SD_{signal}`. See :func:`complexity_tolerance` to estimate the optimal value for this parameter. approximate : bool The entropy algorithm to use. If ``False`` (default), will use sample entropy and return *mSampEn* (**RangEn B**). If ``True``, will use approximate entropy and return *mApEn* (**RangEn A**). **kwargs Other arguments. See Also -------- entropy_approximate, entropy_sample Returns ------- RangEn : float Range Entropy. If undefined conditional probabilities are detected (logarithm of sum of conditional probabilities is ``ln(0)``), ``np.inf`` will be returned, meaning it fails to retrieve 'accurate' regularity information. This tends to happen for short data segments, increasing tolerance levels might help avoid this. info : dict A dictionary containing additional information regarding the parameters used. Examples ---------- .. ipython:: python import neurokit2 as nk signal = nk.signal_simulate(duration=2, sampling_rate=100, frequency=[5, 6]) # Range Entropy B (mSampEn) RangEnB, info = nk.entropy_range(signal, approximate=False) RangEnB # Range Entropy A (mApEn) RangEnA, info = nk.entropy_range(signal, approximate=True) RangEnA # Range Entropy A (corrected) RangEnAc, info = nk.entropy_range(signal, approximate=True, corrected=True) RangEnAc References ---------- * Omidvarnia, A., Mesbah, M., Pedersen, M., & Jackson, G. (2018). Range entropy: A bridge between signal complexity and self-similarity. Entropy, 20(12), 962. """ if approximate is False: # mSampEn - RangeEn (B) out = entropy_sample( signal, delay=delay, dimension=dimension, tolerance=tolerance, distance="range", **kwargs, ) else: # mApEn - RangeEn (A) out = entropy_approximate( signal, delay=delay, dimension=dimension, tolerance=tolerance, distance="range", **kwargs, ) return out