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Tensor

Introduction

  • Tensors are the basic building block of all the machine learning and deep learning.
  • Their job is to represent data in a numerical way
  • For example, you could represent an #image as a tensor with shape [3, 224, 224] which would mean [colour_channels, height, width], as in the image has 3 colour channels (red, green, blue), a height of 224 pixels and a width of 224 pixels.

Language

tensor-speak

Creating tensors

First a scalar

  • A single number
  • A scalar is a single number, and in tensor-speak it's a zero dimension tensor. (Ref: 02_Math)
  • Usually used as variable a
Initialize a scalar

# Scalar
scalar = torch.tensor(7)
scalar
tensor(7)

  • That means, although scalar is a single number, it's of type torch.Tensor.
Checking dimensions of a tensor

scalar.ndim
0

from torch.Tensor to a Python integer

# Get the Python number within a tensor (only works with one-element tensors)
scalar.item()
7

Second a vector

  • A number with direction (e.g. wind speed with direction) but can also have many other numbers
  • A vector is a single dimension tensor but can contain many numbers. (Ref: 02_Math)
  • As in, you could have a vector [3, 2] to describe [bedrooms, bathrooms] in your house. Or you could have [3, 2, 2] to describe [bedrooms, bathrooms, car_parks] in your house.
  • The important trend here is that a vector is flexible in what it can represent (the same with tensors).
  • Usually used as variable y
Initialize a vector

# Vector
vector = torch.tensor([7, 7])
vector
tensor([7, 7])

Checking dimensions of a tensor

# Check the number of dimensions of vector
vector.ndim
1

Number of dimensions a tensor in PyTorch = Number of square brackets on the outside ([) and you only need to count one side.

Checking shape
  • The shape tells you how the elements inside them are arranged. 
    # Check shape of vector
vector.shape
    torch.Size([2])

Third the Matrix

  • A 2-dimensional array of numbers
  • Usually used as variable Q
Initialize a matrix

MATRIX = torch.tensor([[7, 8], [9, 10]])
print(MATRIX)
tensor([[ 7, 8], [ 9, 10]])

Dimension & Shape

print("Dimentions: ", MATRIX.ndim) # two dimensions

print("Shape: ", MATRIX.shape) #two elements deep and two elements wide
Dimentions: 2 Shape: torch.Size([2, 2])

Lets Tensor now
  • An n-dimensional array of numbers
  • Usually used as variable X

# Initialize a tensor

TENSOR = torch.tensor([[[1, 2, 3], [3, 6, 9],[2, 4, 5]]])
print(TENSOR)

# Check number of dimensions for TENSOR
print("Dimentions: ", TENSOR.ndim)

# Check number of size for TENSOR
print("Shape: ", TENSOR.shape) # The dimensions go outer to inner.
tensor([[[1, 2, 3], [3, 6, 9], [2, 4, 5]]]) Dimensions: 3 Shape: torch.Size([1, 3, 3])

  • when building machine learning models with PyTorch, it's rare you'll create tensors by hand (like what we've being doing).
  • Instead, a machine learning model often starts out with large random tensors of numbers and adjusts these random numbers as it works through data to better represent it.

  • In essence: Start with random numbers -> look at data -> update random numbers -> look at data -> update random numbers...

  • As a data scientist, you can define how the machine learning model starts (initialization), looks at data (representation) and updates (optimization) its random numbers.

Create a tensor of random numbers w/ torch.rand()

# Create a random tensor of size (3, 4)
random_tensor = torch.rand(size=(3, 4))
random_tensor, random_tensor.dtype
(tensor([[0.3554, 0.3453, 0.3330, 0.2967], [0.1251, 0.0410, 0.0230, 0.8989], [0.2398, 0.1786, 0.7962, 0.1559]]), torch.float32)

  • The flexibility of torch.rand() is that we can adjust the size to be whatever we want.
  • For example, say you wanted a random tensor in the common image shape of [224, 224, 3] ([height, width, color_channels]).

# Create a random tensor of size (224, 224, 3)
random_image_size_tensor = torch.rand(size=(224, 224, 3))
random_image_size_tensor.shape, random_image_size_tensor.ndim
(torch.Size([224, 224, 3]), 3)