Handling the Dimensions and Sizes of PyTorch Tensors

Definition

Let’s call $A$ a PyTorch tensor.

• The following pair $(a_{0}, a_{1}, \dots, a_{n-1})$ is called the size of $A$.

  $$ \text{A.size() = torch.Size}([a_{0}, a_{1}, \dots, a_{n-1} ]) $$

• Let’s refer to $\prod \limits_{i=0}^{n-1} a_{i} = a_{0} \times a_{1} \times \cdots a_{n-1}$ as the dimension of $A$.

• Call $A$ a $n$-dimensional tensor.

  $a_{i}$ are the sizes of the respective $i$th dimensions, which are integers greater than $1$. Since this is Python, note that it starts from the $0$th dimension.

>>> A = torch.ones(2,3,4)
tensor([[[1., 1., 1., 1.],
         [1., 1., 1., 1.],
         [1., 1., 1., 1.]],

        [[1., 1., 1., 1.],
         [1., 1., 1., 1.],
         [1., 1., 1., 1.]]])

For example, the dimension of such a tensor $A$ is $3$, its size is $24=2 \cdot 3 \cdot 4$, and its dimension is $(2,3,4)$.

.dim(), .ndim

Returns the dimension of the tensor.

>>> A.dim()
3

>>> A.ndim
3

.shape, .size()

Returns the size of the tensor.

>>> A.shape
torch.Size([2, 3, 4])
>>> A.shape[1]
3

>>> A.size()
torch.Size([2, 3, 4])
>>> A.size(2)
4

.view(), .reshape()

Changes the size of the tensor while keeping its dimension.

If you use $-1$ as an argument, the size is adjusted automatically. For instance, as in the following example, changing a tensor of size $(2,3,4)$ with .view(4,-1) changes its size to $(4,6)$.

>>> A.reshape(8,3)
tensor([[1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.]])

>>> A.view(3,-1)
tensor([[1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.]])

>>> A.view(-1,4)
tensor([[1., 1., 1., 1.],
        [1., 1., 1., 1.],
        [1., 1., 1., 1.],
        [1., 1., 1., 1.],
        [1., 1., 1., 1.],
        [1., 1., 1., 1.]])