e3x.nn.functions.mappings.reciprocal_mapping
- e3x.nn.functions.mappings.reciprocal_mapping(x, kind='shifted')[source]
Reciprocal mapping function.
Computes the function (when
kind = 'shifted')\[\mathrm{reciprocal\_mapping}(x) = \frac{1}{x+1}\]which is \(1\) for \(x = 0\) and \(0\) for \(x \to \infty\), or (when
kind = 'damped')\[\mathrm{reciprocal\_mapping}(x) = \frac{1-e^{-x}}{x}\]which is \(1\) for \(x = 0\) and \(\sim \frac{1}{x}\) for \(x \gg 1\), or (when
kind = 'cuspless')\[\mathrm{reciprocal\_mapping}(x) = \frac{1}{x+e^{-x}}\]which is similar to
kind = 'damped', but has no cusp at \(x = 0\).
- Parameters:
x (
<class 'Float[Array, '...']'>) – Input array.kind ({
'shifted','damped','cuspless'}, default:'shifted') – Which kind of mapping is used.
- Return type:
- Returns:
The function value.