Element-wise operations
Element-wise operations
An element-wise operation operates on corresponding elements between tensors.
Two tensors must have the same shape in order to perform element-wise operations on them.
Suppose we have the following two tensors（Both of these tensors are rank-2 tensors with a shape of 2 \(\times\) 2）:
t1 = torch.tensor([
[1, 2],
[3, 4]
], dtype=torch.float32)
t2 = torch.tensor([
[9, 8],
[7, 6]
], dtype=torch.float32)
The elements of the first axis are arrays and the elements of the second axis are numbers.
# Example of the first axis
> print(t1[0])
tensor([1., 2.])
# Example of the second axis
> print(t1[0][0])
tensor(1.)
Addition is an element-wise operation.
> t1 + t2
tensor([[10., 10.],
[10., 10.]])
In fact, all the arithmetic operations, add, subtract, multiply, and divide are element-wise operations. There are two ways we can do this:
- Using these symbolic operations:
> t + 2
tensor([[3., 4.],
[5., 6.]])
> t - 2
tensor([[-1., 0.],
[1., 2.]])
> t * 2
tensor([[2., 4.],
[6., 8.]])
> t / 2
tensor([[0.5000, 1.0000],
[1.5000, 2.0000]])
- Or equivalently, these built-in tensor methods:
> t.add(2)
tensor([[3., 4.],
[5., 6.]])
> t.sub(2)
tensor([[-1., 0.],
[1., 2.]])
> t.mul(2)
tensor([[2., 4.],
[6., 8.]])
> t.div(2)
tensor([[0.5000, 1.0000],
[1.5000, 2.0000]])
Broadcasting tensors
Broadcasting is the concept whose implementation allows us to add scalars to higher dimensional tensors.
We can see what the broadcasted scalar value looks like using the broadcast_to()Numpy function:
> np.broadcast_to(2, t.shape)
array([[2, 2],
[2, 2]])
//This means the scalar value is transformed into a rank-2 tensor just like t, and //just like that, the shapes match and the element-wise rule of having the same //shape is back in play.
Trickier example of broadcasting
t1 = torch.tensor([
[1, 1],
[1, 1]
], dtype=torch.float32)
t2 = torch.tensor([2, 4], dtype=torch.float32)
Even through these two tensors have differing shapes, the element-wise operation is possible, and broadcasting is what makes the operation possible.
> np.broadcast_to(t2.numpy(), t1.shape)
array([[2., 4.],
[2., 4.]], dtype=float32)
>t1 + t2
tensor([[3., 5.],
[3., 5.]])
When do we actually use broadcasting? We often need to use broadcasting when we are preprocessing our data, and especially during normalization routines.
Comparison operations are element-wise. For a given comparison operation between tensors, a new tensor of the same shape is returned with each element containing either a 0 or a 1.
> t = torch.tensor([
[0, 5, 0],
[6, 0, 7],
[0, 8, 0]
], dtype=torch.float32)
Let's check out some of the comparison operations.
> t.eq(0)
tensor([[1, 0, 1],
[0, 1, 0],
[1, 0, 1]], dtype=torch.uint8)
> t.ge(0)
tensor([[1, 1, 1],
[1, 1, 1],
[1, 1, 1]], dtype=torch.uint8)
> t.gt(0)
tensor([[0, 1, 0],
[1, 0, 1],
[0, 1, 0]], dtype=torch.uint8)
> t.lt(0)
tensor([[0, 0, 0],
[0, 0, 0],
[0, 0, 0]], dtype=torch.uint8)
> t.le(7)
tensor([[1, 1, 1],
[1, 1, 1],
[1, 0, 1]], dtype=torch.uint8)
Element-wise operations using functions
Here are some examples:
> t.abs()
tensor([[0., 5., 0.],
[6., 0., 7.],
[0., 8., 0.]])
> t.sqrt()
tensor([[0.0000, 2.2361, 0.0000],
[2.4495, 0.0000, 2.6458],
[0.0000, 2.8284, 0.0000]])
> t.neg()
tensor([[-0., -5., -0.],
[-6., -0., -7.],
[-0., -8., -0.]])
> t.neg().abs()
tensor([[0., 5., 0.],
[6., 0., 7.],
[0., 8., 0.]])
