e3x.nn.functions.cutoff.smooth_cutoff

e3x.nn.functions.cutoff.smooth_cutoff(x, cutoff=1.0)

Smooth cutoff function.

Computes the function

\[\begin{split}\mathrm{smooth\_cutoff}(x) = \begin{cases} \exp\left(1-\frac{1}{1-\left(\frac{x}{c}\right)^2}\right), & x < c\\ 0, & x \ge c \end{cases}\end{split}\]

which is zero beyond \(c\) = cutoff and is infinitely differentiable.

Parameters:

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

• cutoff (Union[Float[Array, ''], float], default: 1.0) – Cutoff value (must be larger than 0).

Return type:

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

Returns:

The function value.

Raises:

ValueError – If cutoff is smaller or equal to 0.