Calculate the local variation (Lv) as proposed in Shinomot et al. 2009. The Lv should be more robust than the coefficient of variation (Cv).

coefficient_of_variation.py

import numpy as np

def cv(spike_train: np.ndarray) -> float:
        """Calculate coefficient of variation (Cv) of the interspike intervals.
    
        $$\displaystyle{Cv = \frac{\sigma_{ISI}}{\mu_{ISI}}}$$

        Args:
            spike_train (np.ndarray): Spike train.

        Returns:
            float: Coefficient of variation.
        """

        _isi = np.diff(spike_train)
        return np.std(_isi) / np.mean(_isi)

local_variation.py

import numpy as np

def lv(spike_train: np.ndarray) -> float:
        """Calculate local variation (Lv) of ISI after Shinomoto et al. 2009.

        $$\displaystyle{Lv = \frac{3}{n-1} \sum_{i=1}^{n-1} 
        {\left(1\frac{I_i - I_{i+1}}{I_{i} + I_{i+1}}\right)}^2}$$

        Args:
            spike_train (np.ndarray): Spike train.

        Returns:
            float: Local variation.

        References:
            
            Shinomoto S, Kim H, Shimokawa T, Matsuno N, Funahashi S, et al.
              (2009) Relating Neuronal Firing Patterns to Functional
              Differentiation of Cerebral Cortex. PLOS Computational Biology
              5(7): e1000433. https://doi.org/10.1371/journal.pcbi.1000433
        """
        _isi = np.diff(spike_train)
        s_ = 3 / (len(_isi) - 1)
        lv_us = np.sum((np.diff(_isi) / (_isi[:-1] + _isi[1:]))**2)
        return s_ * lv_us

local_variation_refractory.py

import numpy as np

def lvR(spike_train: np.ndarray, r: float) -> float:
        """Local variation revised (LVr) of ISI after Shinomoto et al. 2009.

        This variant compensates for the refractory period by subtracting it.

        Note: 
            To get useful results, the spike train and the refractory period
            must be in the same unit (seconds or time steps).

        $$\displaystyle{LvR = \frac{3}{n-1} \sum_{i=1}^{n-1} 
        \left(1 - \frac{4 I_i I_{i+1}}{(I_{i} + I_{i+1})^2}\right) 
        \left( 1 + \frac{4R}{I_i + I_{i+1}}\right)}$$

        Args:
            spike_train (np.ndarray): Spike train. In seconds or time steps.
            r (float): Refractory period in seconds or time steps.

        Returns:
            float: Local variation revised.

        References:

            Shinomoto S, Kim H, Shimokawa T, Matsuno N, Funahashi S, et al.
              (2009) Relating Neuronal Firing Patterns to Functional
              Differentiation of Cerebral Cortex. PLOS Computational Biology
              5(7): e1000433. https://doi.org/10.1371/journal.pcbi.1000433
        """
        isi = np.diff(spike_train)
        s_ = 3 / (len(isi) - 1)
        si_ = isi[:-1] + isi[1:]
        ft_ = 1 - ((4 * (isi[:-1] * isi[1:])) / si_**2)
        st_ = 1 + ((4 * r) / si_)
        return s_ * np.sum(ft_ * st_)