arccosh

→Tensor

arccosh(x: Tensor)

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Inverse hyperbolic cosine.

Verbose alias of acosh. Computes the principal branch $\operatorname{arccosh}(x) = \log\!\bigl(x + \sqrt{x^{2} - 1}\bigr)$ , defined for real $x \geq 1$ .

Parameters

xTensor

Input tensor; element-wise values must satisfy

x \geq 1

for a real result.

Returns

Tensor

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

Notes

Mathematical definition:

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

Inputs with $x < 1$ produce NaN through the real sqrt branch. The derivative is $1 / \sqrt{x^{2} - 1}$ , singular at $x = 1$ . Both arccosh and acosh refer to the same composite; either spelling may be used for parity with NumPy or reference-framework code.

Examples

>>> import lucid
>>> x = lucid.tensor([1.0, 2.0, 10.0])
>>> lucid.arccosh(x)
tensor([0., 1.317, 2.993])