asinh

→Tensor

asinh(x: Tensor)

Inverse hyperbolic sine.

Short-name alias of arcsinh. Defined for all real inputs.

xTensor

Input tensor. Domain is all of

\mathbb{R}

Tensor

Element-wise inverse hyperbolic sine.

Mathematical definition:

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

The function is odd: $\operatorname{asinh}(-x) = -\operatorname{asinh}(x)$ . Derivative is $1 / \sqrt{x^{2} + 1}$ .

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