e3x.nn.functions.window.smooth_window

e3x.nn.functions.window.smooth_window(x, num, limit=1.0)

Smooth window basis functions.

Computes the basis functions (see smooth_switch)

\[\mathrm{smooth\_window}_k(x) = \mathrm{smooth\_switch}\left(\frac{K}{l}x - \frac{kl}{K}\right) - \mathrm{smooth\_switch}\left(1 -\frac{K}{l}x + \frac{kl}{K}\right)\]

where \(k=0 \dots K-1\) with \(K\) = num and \(l\) = limit. Plot for \(K = 5\) and \(l = 1\):

Parameters:

• x (<class 'Float[Array, '...']'>) – Input array.

• num (int) – Number of basis functions \(K\).

• limit (Union[Float[Array, ''], float], default: 1.0) – Basis functions are distributed between 0 and limit.

Return type:

<class 'Float[Array, '... num']'>

Returns:

Value of all basis functions for all values in x. The output shape follows the input, with an additional dimension of size num appended.