In [1]:
import numpy as np

In [2]:
a = np.arange(9).reshape(3, 3)
print(a.shape)
print(a)
b = np.arange(4, 4+9).reshape(3, 3)
print(b.shape)
print(b)

(3, 3)
[[0 1 2]
[3 4 5]
[6 7 8]]
(3, 3)
[[ 4  5  6]
[ 7  8  9]
[10 11 12]]

In [3]:
a+b

Out[3]:
array([[ 4,  6,  8],
[10, 12, 14],
[16, 18, 20]])

So this is easy and one-to-one.

What if the shapes do not match?

In [4]:
a = np.arange(9).reshape(3, 3)
print(a.shape)
print(a)
b = np.arange(3)
print(b.shape)
print(b)

(3, 3)
[[0 1 2]
[3 4 5]
[6 7 8]]
(3,)
[0 1 2]


What will this do?

In [5]:
a+b

Out[5]:
array([[ 0,  2,  4],
[ 3,  5,  7],
[ 6,  8, 10]])

It has broadcast along the last axis!

Can we broadcast along the first axis?

In [6]:
a+b.reshape(3, 1)

Out[6]:
array([[ 0,  1,  2],
[ 4,  5,  6],
[ 8,  9, 10]])

Rules:

• Shapes are matched axis-by-axis from last to first.
• A length-1 axis can be broadcast if necessary.