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:

1. 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]])

1. 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.]])

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When do we actually use broadcasting? We often need to use broadcasting when we are preprocessing our data, and especially during normalization routines.

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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.]])