{"id":4496,"date":"2022-08-15T02:26:28","date_gmt":"2022-08-15T02:26:28","guid":{"rendered":"https:\/\/www.pythontutorial.net\/?page_id=4496"},"modified":"2022-08-15T15:35:15","modified_gmt":"2022-08-15T15:35:15","slug":"numpy-broadcasting","status":"publish","type":"page","link":"https:\/\/www.pythontutorial.net\/python-numpy\/numpy-broadcasting\/","title":{"rendered":"NumPy Broadcasting"},"content":{"rendered":"\n

Summary<\/strong>: in this tutorial, you’ll learn about NumPy broadcasting and understand how it works.<\/p>\n\n\n\n

Introduction to the NumPy broadcasting #<\/a><\/h2>\n\n\n\n

In previous tutorials, you learned how to perform arithmetic operations on equal-sized arrays using the add()<\/code><\/a><\/code>, subtract()<\/code><\/a><\/code>, multiply()<\/code><\/a><\/code>, and divide()<\/code><\/a><\/code> functions or as +<\/code>, -<\/code>, *<\/code>, and \/<\/code> operators.<\/p>\n\n\n\n

To perform arithmetic operations on arrays of different shapes, NumPy uses a technique called broadcasting.<\/p>\n\n\n\n

By definition, broadcasting is a set of rules for applying arithmetic operations on arrays of different shapes. We’ll cover these rules in detail shortly.<\/p>\n\n\n\n

Before that, let’s take some simple broadcasting examples. For instance, you can use the + operator to add a number to an array like this:<\/p>\n\n\n

import<\/span> numpy as<\/span> np\n\na = np.array([1<\/span>, 2<\/span>, 3<\/span>])\nb = a + 1<\/span>\nprint(b)<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
Output:<\/p>\n\n\n
[2<\/span> 3<\/span> 4<\/span>]<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
This example adds the number one to a 1D array using the operator +<\/code>. Internally, NumPy adds the number 1 to every element of the array. This technique is called broadcasting. <\/p>\n\n\n\n
In other words, NumPy broadcasts the number one across the first dimension to match the shape of the 1D array.<\/p>\n\n\n\n
Conceptually, you can think of the above broadcasting as equivalent to the following:<\/p>\n\n\n
import<\/span> numpy as<\/span> np\n\na = np.array([1<\/span>, 2<\/span>, 3<\/span>])\nb = a + np.array([1<\/span>, 1<\/span>, 1<\/span>])\nprint(b)<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
So adding the number one to a 1D array is like duplicating the number one into another 1D array [1, 1, 1] and adding that array to the array:<\/p>\n\n\n\n
\"NumPy<\/figure>\n\n\n\n
However, NumPy broadcasts number one without duplicating it. By doing this, NumPy can manage effciently and speeds up calculation in most cases.<\/p>\n\n\n\n
Similarly, you can add a 1D array to a 2D array using broadcasting like this:<\/p>\n\n\n
import<\/span> numpy as<\/span> np\n\na = np.array([\n    [1<\/span>, 2<\/span>, 3<\/span>],\n    [4<\/span>, 5<\/span>, 6<\/span>]\n])\nb = np.array([10<\/span>, 20<\/span>, 30<\/span>])\nc = a + b\nprint(c)<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
Output:<\/p>\n\n\n
[[11<\/span> 22<\/span> 33<\/span>]\n [14<\/span> 25<\/span> 36<\/span>]]<\/code><\/span>Code language:<\/span> Python<\/span> (<\/span>python<\/span>)<\/span><\/small><\/pre>\n\n\n
In this example, NumPy broadcasts the 1D array b<\/code> across the second dimension to match the shape of the array a.<\/p>\n\n\n\n
NumPy broadcasting rules #<\/a><\/h2>\n\n\n\n
NumPy defines a set of rules for broadcasting:<\/p>\n\n\n\n