# Engineering Python 13D: NumPy Array Broadcasting Welcome to Engineering Python. This is a Python programming course for engineers. In this video, I’ll talk about NumPy array
broadcasting. Broadcasting describes how NumPy treats arrays
with different shapes during arithmetic operations. The smaller array is broadcast across the
larger array so the shapes match. I’ll demonstrate this using examples. First, we need to import numpy as np. Let’s create a 1D array with three elements. b is an integer number, 1. When we calculate a plus b, because their
shapes don’t match, we need to broadcast or stretch b horizontally so it has three elements
as well. That means, this number, 1, will be repeated
two more times. Now the shapes match, we will do the element-wise
addition. Another example, a is a 2 by 3 array. b is a 1 by 3 array. When we calculate a plus b, array b will be
stretched vertically to match the shape of a. Then we will do the element-wise addition. This is the result. The third example. a is still the 2 by 3 array. b is now a 2 by 1 array. When we calculate a plus b, array b will be
stretched horizontally to match the shape of a. Then we will do the element-wise addition. This is the result. If b is changed to just one integer number
like this, when we calculate a plus b, array b will be stretched both horizontally and
vertically to match the shape of a. Then we will do the element-wise addition. This is the result. If a is changed to a 2 by 1 array, and b is
a 1 by 3 array, when we calculate a plus b, array a will be stretched horizontally to
match the shape of b, and b will be stretched vertically to match the shape of a. Then we will do the element-wise addition. This is the result. If the dimensions mismatch, there will be
an error. For example, a is a 2 by 3 array, b is a 1
by 4 array. NumPy will not be able to broadcast b in any
direction to match the shape of a. So, this operation is not allowed in NumPy. Here is a more realistic application of array
broadcasting. We want to travel from Binghamton to New York
City. There are several cities on the route. We know that it’s 0 miles from Binghamton
to Binghamton, 43 miles from Binghamton to Hancock, 120 miles from Binghamton to Middletown,
153 miles from Binghamton to Sloatsburg, and 190 miles from Binghamton to New York City. Such information is stored in a NumPy array
named miles. We want to calculate the distances between
any two cities on the route. For example, what is the distance from Hancock
to New York City? Or from Hancock to Sloatsburg? To solve this problem, we only need to reshape
miles as a 5 by 1 array, and then subtract it from the original miles. The result is an array of the distances between
any two cities. For example, this 110 is the distance from
Hancock to Sloatsburg. This -147 is the distance from New York City
back to Hancock. Okay, that was about NumPy array broadcasting. The course materials are available on YouTube
and GitHub. You can watch the course videos in sequence. If you like this video, please subscribe and
share. I’m Yong Wang. Thanks for watching.

##### RELATED ARTICLES      Sam Dave Pollard says:

Nice one.
Many Thanks, Yong. Bashana Elikewela says:

Thanks Yong Wang says:

Hi Guys, please comment and let me know what you think about this Engineering Python open course. If you enjoy the video, please subscribe and share with your friends. Thanks! fupopanda says:

Clear and straight to the point TheMorganNSK says:

You are awesome, man! Thanks!