Broadcasting in NumPy

Broadcasting

Broadcasting allows NumPy to perform arithmetic operations on arrays of different shapes by implicitly expanding the smaller array.

Simple broadcast example

import numpy as np

A = np.arange(6).reshape(2,3)
B = np.array([10, 20, 30])   # shape (3,)
C = A + B   # B is broadcast across rows
print(C)

Rules of broadcasting

1. Align dimensions from the right.
2. If dimensions are equal, they are compatible.
3. If one dimension is 1, the array behaves as if it were copied.
4. Otherwise, broadcasting fails.

Higher‑dimensional broadcast

A = np.ones((2,1,3))
B = np.arange(3)   # shape (3,)
C = A * B   # result shape (2,1,3)
print(C.shape)

When broadcasting fails

np.arange(4) + np.arange(3)   # ValueError

Practical tip

Use np.broadcast_to to explicitly broadcast an array:

B = np.arange(3)
B_broadcast = np.broadcast_to(B, (2,3))
print(B_broadcast)