elephant.kernels.LaplacianKernel

class elephant.kernels.LaplacianKernel(sigma, invert=False)[source]

Class for laplacian kernels.

\[K(t) = \frac{1}{2 \tau} \exp\left(-\left|\frac{t}{\tau}\right|\right)\]

with \(\tau = \sigma / \sqrt{2}\).

The parameter invert has no effect on symmetric kernels.

Examples

from elephant import kernels
import quantities as pq
import numpy as np
import matplotlib.pyplot as plt

time_array = np.linspace(-3, 3, num=1000) * pq.s
kernel = kernels.LaplacianKernel(sigma=1*pq.s)
kernel_time = kernel(time_array)
plt.plot(time_array, kernel_time)
plt.title("LaplacianKernel with sigma=1s")
plt.xlabel("time, s")
plt.ylabel("kernel, 1/s")
plt.show()

(Source code, png, hires.png, pdf)

../../../_images/elephant-kernels-LaplacianKernel-1.png
__init__(sigma, invert=False)

Methods

__init__(sigma[, invert])

boundary_enclosing_area_fraction(fraction)

Calculates the boundary \(b\) so that the integral from \(-b\) to \(b\) encloses a certain fraction of the integral over the complete kernel.

cdf(time)

Cumulative Distribution Function, CDF.

icdf(fraction)

Inverse Cumulative Distribution Function, ICDF, also known as a quantile.

is_symmetric()

True for symmetric kernels and False otherwise (asymmetric kernels).

median_index(times)

Estimates the index of the Median of the kernel.

Attributes

min_cutoff

Half width of the kernel.