scaled_modified_bessel_k0

→Tensor

scaled_modified_bessel_k0(x: Tensor)

source

Exponentially scaled modified Bessel $K_0$ : $e^x K_0(x)$ .

Computes $e^{x} K_0(x)$ , the bounded counterpart of modified_bessel_k0. Because $K_0$ decays exponentially as $e^{-x}/\sqrt{x}$ , the scaled form is the natural quantity to manipulate in log-density expressions where direct evaluation of $K_0$ would underflow.

Parameters

xTensor

Input tensor; only

x > 0

is in the domain.

Returns

Tensor

$e^x K_0(x)$ element-wise, same shape and dtype as x.

Notes

Asymptotic: $e^x K_0(x) \sim \sqrt{\pi/(2x)}$ as $x \to \infty$ .

Examples

>>> import lucid
>>> from lucid.special import scaled_modified_bessel_k0
>>> scaled_modified_bessel_k0(lucid.tensor([1.0, 5.0, 20.0]))
Tensor([1.1445, 0.5478, 0.2745])