elephant.kernels.AlphaKernel

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

Class for alpha kernels.

K(t) = \left\{\begin{array}{ll} (1 / \tau^2) \ t\ \exp{(-t / \tau)}, & t > 0 \\ 0, & t \leq 0 \end{array} \right.

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

For the alpha kernel an analytical expression for the boundary of the integral as a function of the area under the alpha kernel function cannot be given. Hence in this case the value of the boundary is determined by kernel-approximating numerical integration, inherited from the Kernel class.

Attributes:
min_cutofffloat

Half width of the kernel.
__call__(self, t)

Evaluates the kernel at all points in the array t.

Parameters:
tpq.Quantity

Vector with the interval on which the kernel is evaluated, not necessarily a time interval.
Returns:
pq.Quantity

Vector with the result of the kernel evaluations.
Raises:
TypeError

If t is not pq.Quantity.

If the dimensionality of t and sigma are different.
boundary_enclosing_area_fraction(self, fraction)

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

By definition the returned value is hence non-negative, even if the whole probability mass of the kernel is concentrated over negative support for inverted kernels.

Returns:
pq.Quantity

Boundary of the kernel containing area fraction under the kernel density.
Raises:
ValueError

If fraction was chosen too close to one, such that in combination with integral approximation errors the calculation of a boundary was not possible.
is_symmetric(self)

In the case of symmetric kernels, this method is overwritten in the class SymmetricKernel, where it returns True, hence leaving the here returned value False for the asymmetric kernels.

Returns:
bool

True in classes SymmetricKernel, RectangularKernel, TriangularKernel, EpanechnikovLikeKernel, GaussianKernel, and LaplacianKernel. False in classes Kernel, ExponentialKernel, and AlphaKernel.
property min_cutoff

Half width of the kernel.

Returns:
float

The returned value varies according to the kernel type.