torchcurves.functional.rational

torchcurves.functional.rational(x, scale=1, out_min=-1, out_max=1)

Normalize values using the “Legendre Rational Functions” [1] normalization method.

The normalization is performed with the formula

\[x_{\mathrm{norm}} = \frac{x}{\sqrt{\mathrm{scale}^2 + x^2}},\]

where scale is a scaling factor.

Parameters:

• x (Union[Tensor, Sequence[Union[int, float]]]) – Input tensor to be normalized.

• scale (float) – Scale factor for normalization. (default=1)

• out_min (float) – Lower bound of the output interval (default=-1)

• out_max (float) – Upper bound of the output interval (default=1)

Return type:

Tensor

Returns:

Normalized tensor.

References

[1] Wang, Z.Q. and Guo, B.Y., 2004. Modified Legendre rational spectral method for the whole line. Journal of Computational Mathematics, pp.457-474.