acosh

→Tensor

acosh(x: Tensor)

Inverse hyperbolic cosine.

Short-name alias of arccosh. Computes the principal branch of $\operatorname{arccosh}(x)$ for real inputs.

xTensor

Input tensor with values in the domain

x \geq 1

Tensor

Element-wise inverse hyperbolic cosine.

Mathematical definition:

\operatorname{acosh}(x) = \log\!\bigl(x + \sqrt{x^{2} - 1}\bigr), \qquad x \geq 1.

Inputs with $x < 1$ produce NaN. The derivative is $1 / \sqrt{x^{2} - 1}$ , which is singular at $x = 1$ .

>>> import lucid
>>> x = lucid.tensor([1.0, 2.0, 10.0])
>>> lucid.acosh(x)
Tensor([0.    , 1.3170, 2.9932])