What is a tensor? A tensor is a generalization of vectors and matrices and is easily understood as a multidimensional array. A tensor can be a number, a vector, a matrix, or any n-dimensional array.
Examples
- 0-d tensor: scalar
- 1-d tensor: vector
- 2-d tensor: matrix
- 3-d tensor: cube
- n-d tensor: n-d array
Rank
The rank of a tensor is the number of dimensions present within the tensor. For example, the tensor [1, 2, 3] is a rank 1 tensor, while the tensor [[1, 2, 3], [4, 5, 6], [7, 8, 9]] is a rank 2 tensor.
Shape
The shape of a tensor is the number of elements in each dimension. For example, the tensor [[1, 2, 3], [4, 5, 6], [7, 8, 9]] has a shape of (3, 3).
PyTorch tensors
PyTorch tensors are similar to NumPy arrays, but can also be used on a GPU to accelerate computing.
Creating tensors
Directly from data
import torch
t = torch.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=torch.float32)
print(t)
print(f"shape: {t.shape}")
print(f"rank: {t.ndimension()}")
gives
tensor([[1., 2., 3.],
[4., 5., 6.],
[7., 8., 9.]])
shape: torch.Size([3, 3])
rank: 2
Random
import torch
t = torch.rand(3, 3)
print(t)
gives
tensor([[0.6242, 0.6879, 0.8598],
[0.7353, 0.8342, 0.7261],
[0.3044, 0.2123, 0.7667]])
Operations
import torch
t1 = torch.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=torch.float32)
t2 = torch.tensor([[9, 8, 7], [6, 5, 4], [3, 2, 1]], dtype=torch.float32)
print(t1 + t2)
print(t1 - t2)
print(t1 * t2)
print(t1 / t2)
print(t1 @ t2) # matrix multiplication (dot product)
gives
tensor([[10., 10., 10.],
[10., 10., 10.],
[10., 10., 10.]])
tensor([[-8., -6., -4.],
[-2., 0., 2.],
[ 4., 6., 8.]])
tensor([[ 9., 16., 21.],
[24., 25., 24.],
[21., 16., 9.]])
tensor([[0.1111, 0.2500, 0.4286],
[0.6667, 1.0000, 1.5000],
[2.3333, 4.0000, 9.0000]])
tensor([[ 30., 24., 18.],
[ 84., 69., 54.],
[138., 114., 90.]])
The Unconscious Hero 