braintools.analysis.spike.cv2

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braintools.analysis.spike.cv2#

braintools.analysis.spike.cv2(trains)#

Compute the local coefficient of variation CV2 of Holt et al. (1996).

\[\mathrm{CV2} = \frac{1}{n-1} \sum_{k=1}^{n-1} \frac{2 |I_{k+1} - I_k|}{I_{k+1} + I_k},\]

for the \(n\) intervals \(I_k\) of a neuron [1]. Comparing only neighbouring intervals makes CV2 insensitive to slow rate changes.

Parameters:

trains (SpikeTrains) – Spike trains with N neurons.

Returns:

CV2 of every neuron, shape (N,). nan for a neuron with fewer than 2 intervals, or with two consecutive zero intervals.

Return type:

Array

Raises:

TypeError – If trains is not a SpikeTrains.

See also

isi, cv, lv

Notes

Matches elephant.statistics.cv2(isi, with_nan=True). CV2 is about 1 for a Poisson process and 0 for a regular train. Works under jax.jit and jax.vmap, and is differentiable with respect to the spike times (except where two neighbouring intervals are equal, where |x| has a kink).

References

Examples

>>> import jax.numpy as jnp
>>> from braintools.spike import SpikeTrains
>>> from braintools.analysis.spike import cv2
>>> raster = jnp.zeros((10, 2)).at[jnp.array([0, 1, 3]), 0].set(1).at[0, 1].set(1)
>>> st = SpikeTrains.from_dense(raster, dt=1.)
>>> cv2(st)
Array([0.6666667,       nan], dtype=float32)
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