In [1]: 
import numpy as np
In [3]: 
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 [4]: 
a+b
Out[4]:
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 [5]: 
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 [6]: 
a+b
Out[6]:
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 [8]: 
a+b[:, np.newaxis]
Out[8]:
array([[ 0,  1,  2],
       [ 4,  5,  6],
       [ 8,  9, 10]])

What's the shape of the newaxis thing?

In [9]: 
b[:, np.newaxis].shape
Out[9]:
(3, 1)

Rules:

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