Broadcasting

Code

import numpy as np

# Add scalar to every element
a = np.array([1, 2, 3])
print(a + 10)

# Add row vector to every row of a matrix
matrix = np.ones((3, 4))
row = np.array([1, 2, 3, 4])
print(matrix + row)

# Normalize columns: subtract mean, divide by std
data = np.random.rand(5, 3)
mean = data.mean(axis=0)
std = data.std(axis=0)
normalized = (data - mean) / std

# Outer product via broadcasting
outer = np.arange(3).reshape(3, 1) * np.arange(4).reshape(1, 4)

Explanation

Broadcasting stretches smaller arrays to match a larger one without copying data, so arithmetic just works when trailing dimensions align or are 1. A scalar broadcasts against any array, and a row vector broadcasts against every row of a matrix. This pattern keeps normalization and outer-product code both short and fast.

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