lucid.arcsin¶
The arcsin function computes the element-wise inverse sine of each element in the input tensor.
Function Signature¶
def arcsin(a: Tensor) -> Tensor
Parameters¶
a (Tensor): The input tensor for which the inverse sine is computed. Values should be in the range \([-1, 1]\).
Returns¶
- Tensor:
A new tensor containing the element-wise inverse sine of the input tensor. If a requires gradients, the resulting tensor will also require gradients.
Forward Calculation¶
\[\mathbf{out}_i = \arcsin(\mathbf{a}_i)\]
Backward Gradient Calculation¶
\[\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} = \frac{1}{\sqrt{1 - \mathbf{a}_i^2}}\]
Example¶
>>> import lucid
>>> a = Tensor([0, 0.5, 1], requires_grad=True)
>>> out = lucid.arcsin(a)
>>> print(out)
Tensor([0. 0.52359878 1.57079633], grad=None)