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When you operate on two NumPy arrays with different shapes, broadcasting determines what happens. The rule: align shapes right-to-left; a dimension is compatible if it is equal or one of them is 1. Size-1 dimensions are stretched to match the other without copying memory. A `(3, 1)` column vector and a `(1, 4)` row vector broadcast to `(3, 4)`. This is not a loop: it is a zero-copy view processed with SIMD instructions.
import numpy as np
# I demonstrate broadcasting without any explicit loops
col = np.array([[1], [2], [3]]) # shape (3, 1)
row = np.array([[10, 20, 30, 40]]) # shape (1, 4)
result = col + row
# shape (3, 4): col stretched across 4 columns, row across 3 rows
# [[11, 21, 31, 41],
# [12, 22, 32, 42],
# [13, 23, 33, 43]]
# Broadcasting a scalar: simplest case
arr = np.arange(12).reshape(3, 4)
normalised = arr / arr.max() # scalar broadcasts to (3, 4)Broadcasting avoids explicit loops and achieves C-level SIMD performance
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NumPy: Broadcasting
The official guide with visual diagrams of how shapes are aligned and stretched.
https://numpy.org/doc/stable/user/basics.broadcasting.html