e3x.nn.functions.mappings.exponential_mapping

e3x.nn.functions.mappings.exponential_mapping(x, gamma=1.0, cuspless=False)

Exponential mapping function.

Computes the function (when cuspless = False)

\[\mathrm{exponential\_mapping}(x) = \exp\left(-\gamma x\right)\,,\]

or (when cuspless = True)

\[\mathrm{exponential\_mapping}(x) = \exp\left(-\gamma (x+e^{-x}-1)\right)\,,\]

where \(\gamma\) = gamma.

Plots for cuspless = False:

Plots for cuspless = True:

Parameters:

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

• gamma (Union[Float[Array, ''], float], default: 1.0) – Exponential decay constant.

• cuspless (bool, default: False) – If this is True, a cuspless exponential mapping is returned.

Return type:

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

Returns:

The function value.