arcsinh

→Tensor

arcsinh(x: Tensor)

source

Inverse hyperbolic sine.

Verbose alias of asinh. Computes $\operatorname{arcsinh}(x) = \log\!\bigl(x + \sqrt{x^{2} + 1}\bigr)$ , defined for all real x.

Parameters

xTensor

Input tensor; domain is all of

\mathbb{R}

Returns

Tensor

Element-wise inverse hyperbolic sine, same shape as x.

Notes

Mathematical definition:

\operatorname{arcsinh}(x) = \log\!\bigl(x + \sqrt{x^{2} + 1}\bigr).

Odd function: $\operatorname{arcsinh}(-x) = -\operatorname{arcsinh}(x)$ . Derivative is $1 / \sqrt{x^{2} + 1}$ . Both arcsinh and asinh refer to the same composite.

Examples

>>> import lucid
>>> x = lucid.tensor([-1.0, 0.0, 1.0])
>>> lucid.arcsinh(x)
Tensor([-0.8814,  0.    ,  0.8814])