lucid.sinh¶
The sinh function computes the element-wise hyperbolic sine of each element in the input tensor.
Function Signature¶
def sinh(a: Tensor) -> Tensor
Parameters¶
a (Tensor): The input tensor for which the hyperbolic sine is computed.
Returns¶
- Tensor:
A new tensor containing the element-wise hyperbolic sine of the input tensor. If a requires gradients, the resulting tensor will also require gradients.
Forward Calculation¶
\[\mathbf{out}_i = \sinh(\mathbf{a}_i) = \frac{e^{\mathbf{a}_i} - e^{-\mathbf{a}_i}}{2}\]
Backward Gradient Calculation¶
\[\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} = \cosh(\mathbf{a}_i)\]
Example¶
>>> import lucid
>>> a = Tensor([0, 1, 2], requires_grad=True)
>>> out = lucid.sinh(a)
>>> print(out)
Tensor([0. 1.17520119 3.62686041], grad=None)