lucid.arctan¶
The arctan function computes the element-wise inverse tangent of each element in the input tensor.
Function Signature¶
def arctan(a: Tensor) -> Tensor
Parameters¶
a (Tensor): The input tensor for which the inverse tangent is computed.
Returns¶
- Tensor:
A new tensor containing the element-wise inverse tangent of the input tensor. If a requires gradients, the resulting tensor will also require gradients.
Forward Calculation¶
\[\mathbf{out}_i = \arctan(\mathbf{a}_i)\]
Backward Gradient Calculation¶
\[\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} = \frac{1}{1 + \mathbf{a}_i^2}\]
Example¶
>>> import lucid
>>> a = Tensor([0, 1, 10], requires_grad=True)
>>> out = lucid.arctan(a)
>>> print(out)
Tensor([0. 0.78539816 1.47112767], grad=None)