lucid.div¶

lucid.div(a: Tensor, b: Tensor, /) → Tensor¶

The div function performs element-wise division between two Tensor objects. It returns a new Tensor representing the quotient, with gradient support for backpropagation.

Function Signature¶

def div(a: Tensor, b: Tensor) -> Tensor

Parameters¶

a (Tensor): The numerator tensor in the division operation.
b (Tensor): The denominator tensor in the division operation.

Returns¶

Tensor:
A new Tensor representing the element-wise quotient of a divided by b. If either a or b requires gradients, the resulting tensor will also require gradients.

Forward Calculation¶

The forward calculation for the division operation is:

\[\text{out} = \frac{a}{b}\]

where \(a\) and \(b\) are the data contained in the tensors a and b, respectively.

Backward Gradient Calculation¶

For each tensor a and b involved in the division, the gradient with respect to the output (out) is computed as follows:

\[\frac{\partial \text{out}}{\partial a} = \frac{1}{b}, \quad \frac{\partial \text{out}}{\partial b} = -\frac{a}{b^2}\]

Examples¶

Using div to divide two tensors:

>>> import lucid
>>> a = Tensor([6.0, 8.0, 10.0], requires_grad=True)
>>> b = Tensor([2.0, 4.0, 5.0], requires_grad=True)
>>> out = lucid.div(a, b)
>>> print(out)
Tensor([3.0, 2.0, 2.0], grad=None)

After calling backward() on out, gradients for a and b will be accumulated based on the backpropagation rules:

>>> out.backward()
>>> print(a.grad)
[0.5, 0.25, 0.2]
>>> print(b.grad)
[-1.5, -0.5, -0.4]