lucid.square¶
The square function computes the element-wise square of each element in the input tensor.
Function Signature¶
def square(a: Tensor) -> Tensor
Parameters¶
a (Tensor): The input tensor to be squared element-wise.
Returns¶
- Tensor:
A new tensor containing the squared values of the elements in the input tensor. If a requires gradients, the resulting tensor will also require gradients.
Forward Calculation¶
\[\mathbf{out}_i = (\mathbf{a}_i)^2\]
Backward Gradient Calculation¶
\[\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} = 2 \mathbf{a}_i\]
Example¶
>>> import lucid
>>> a = Tensor([1, 2, 3], requires_grad=True)
>>> out = lucid.square(a)
>>> print(out)
Tensor([1. 4. 9.], grad=None)