Lucid3.0
fn

arcsin

→Tensor
arcsin(input: Tensor)
source

Element-wise inverse sine in radians.

Computes arcsin⁡(x)\arcsin(x) for entries in [−1,1][-1, 1]; out-of-domain values yield NaN.

Parameters

inputTensor
Input tensor.

Returns

Tensor

Element-wise result with the same shape as input.

Notes

Mathematical definition:

outi=arcsin⁡(inputi),inputi∈[−1,1]\text{out}_i = \arcsin(\text{input}_i), \quad \text{input}_i \in [-1, 1]

Result lies in [−π/2,π/2][-\pi/2, \pi/2]. Gradient: 1/1−x21 / \sqrt{1 - x^{2}}.

Examples

>>> import lucid
>>> x = lucid.tensor([1.0, 2.0, 3.0])
>>> lucid.arcsin(x)
Tensor([...])