arctanh

→Tensor

arctanh(x: Tensor)

source

Inverse hyperbolic tangent.

Verbose alias of atanh. Computes $\operatorname{arctanh}(x) = \tfrac{1}{2}\log\!\bigl((1+x)/(1-x)\bigr)$ , defined for $|x| < 1$ .

Parameters

xTensor

Input tensor; element-wise values must satisfy

|x| < 1

for a finite real result.

Returns

Tensor

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

Notes

Mathematical definition:

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

Boundary values $x = \pm 1$ produce $\pm\infty$ ; $|x| > 1$ produces NaN. Derivative is $1 / (1 - x^{2})$ . Both arctanh and atanh refer to the same composite.

Examples

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