NumPy Broadcasting Fundamentals

Introduction

This tutorial will introduce the concept of broadcasting in NumPy library. Broadcasting is a method of performing mathematical operations on arrays of various dimensions.

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Adding Two 1D Arrays of the Same Shape

import numpy as np

a = np.array([1,2,3,4])
b = np.array([2,7,8,9])
c = a+b;
print(c)

The output will be: [ 3 9 11 13]

Attempting to Add Two 1D Arrays with Different Shapes

import numpy as np

a = np.array([4,5,6,7])
b = np.array([1,3,5,7,9,11,14])
c = a+b;

This will produce an error because you cannot perform operations on arrays with different shapes.

Using Broadcasting to Add Two 1D Arrays with Different Shapes

import numpy as np

a = np.array([4,5,6,7])
b = np.array([10])
c = a+b;

print(c)

This will output [14 15 16 17] since array b is being broadcast across array a.

Broadcasting a 1D Array into a 2D Array

import numpy as np

a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([10, 20, 30])

print(a + b)

The output will be:

[[11 22 33]
 [14 25 36]]

The 1D array is broadcast across the second axis of the 2D array and added to each column.

Multiplying Arrays of Different Dimensions

import numpy as np

a = np.array([1, 2, 3])
b = np.array([[4, 5, 6], [7, 8, 9]])

print(a * b)

The output will be:

[[ 4 10 18]
 [ 7 16 27]]

The 1D array is broadcast across the first axis of the 2D array and multiplied to each row.

Summary

In this tutorial, we covered the concept of broadcasting in the NumPy library. Broadcasting is a method of performing mathematical operations on arrays of various dimensions. We also demonstrated how broadcasting works via adding and multiplying arrays. It is important to note that broadcasting can only be done if arrays satisfy certain conditions. Broadcasting only occurs if it doesn’t lead to a loss of information.