scaled_modified_bessel_k1

→Tensor

scaled_modified_bessel_k1(x: Tensor)

source

Exponentially scaled modified Bessel $K_1$ : $e^x K_1(x)$ .

Computes $e^x K_1(x)$ , the bounded scaled variant of modified_bessel_k1 suitable for stable evaluation of log-densities involving $K_1$ at large argument.

Parameters

xTensor

Input tensor; only

x > 0

is in the domain.

Returns

Tensor

$e^x K_1(x)$ element-wise, same shape and dtype as x.

Notes

Asymptotic: $e^x K_1(x) \sim \sqrt{\pi/(2x)}$ as $x \to \infty$ .

Examples

>>> import lucid
>>> from lucid.special import scaled_modified_bessel_k1
>>> scaled_modified_bessel_k1(lucid.tensor([1.0, 5.0, 20.0]))
Tensor([1.6362, 0.6001, 0.2820])