pyhgf.math.smoothed_rectangular

pyhgf.math.smoothed_rectangular(x, theta_l, phi_l=8.0, theta_r=0.0, phi_r=1.0)

Compute the smoothed rectangular weighting function \(b\).

The function is the product of a rising and a falling parametrised_sigmoid(), producing a smooth rectangular window.

Parameters:

• x (Array | ndarray | bool | number | bool | int | float | complex) – The point(s) at which the function is evaluated.

• theta_l (Array | ndarray | bool | number | bool | int | float | complex) – The location \(\theta\) of the rising (left) sigmoid.

• phi_l (Array | ndarray | bool | number | bool | int | float | complex) – The slope \(\phi\) of the rising (left) sigmoid.

• theta_r (Array | ndarray | bool | number | bool | int | float | complex) – The location \(\theta\) of the falling (right) sigmoid.

• phi_r (Array | ndarray | bool | number | bool | int | float | complex) – The slope \(\phi\) of the falling (right) sigmoid.

Returns:

The smoothed rectangular weighting evaluated at x.

Return type:

value