atanh

→Tensor

atanh(x: Tensor)

Inverse hyperbolic tangent.

Short-name alias of arctanh. Domain is the open interval $(-1, 1)$ ; values at the boundary diverge to $\pm\infty$ .

xTensor

Input tensor with values in

|x| < 1

Tensor

Element-wise inverse hyperbolic tangent.

Mathematical definition:

\operatorname{atanh}(x) = \tfrac{1}{2}\, \log\!\Bigl(\tfrac{1 + x}{1 - x}\Bigr), \qquad |x| < 1.

Values outside $(-1, 1)$ produce NaN; $x = \pm 1$ produces $\pm\infty$ . The derivative is $1 / (1 - x^{2})$ .

>>> import lucid
>>> x = lucid.tensor([-0.5, 0.0, 0.5])
>>> lucid.atanh(x)
Tensor([-0.5493,  0.    ,  0.5493])