NumPy vectorization: think in arrays

The #1 rule of numerical Python: if you're writing a for-loop over numbers, you're doing it wrong.

What vectorization means

An ufunc (universal function) operates on whole arrays in C, not Python. a + b where both are arrays does the addition element-wise, in a single tight C loop.

The performance story

• Python loop: interpreter overhead per iteration, ~50 ns each.
• NumPy op: compiled C, ~1 ns per element + minimal setup.
• Typical speedup: 20–200× for pure numerical work.

Broadcasting: shapes that don't match, work anyway

NumPy virtually stretches smaller arrays across bigger ones:

• Scalar + array: scalar reaches every cell.
• Row (1×n) + column (m×1): produces m×n.
• Rules: shapes match right-to-left, dim of 1 stretches, missing dims prepended as 1.

Boolean masking

a[a > 2] returns only elements matching. The killer feature for filtering.

Cheat sheet

• np.zeros, np.ones, np.arange, np.linspace — construct.
• a.reshape(2, 3) — same data, new shape.
• a.sum(), .mean(), .std(), .max(), .argmax() — reductions.
• np.where(cond, if_true, if_false) — vectorized ternary.
• np.dot(a, b) / a @ b — matrix multiply.

Try it

1. Compute Euclidean distance between two random 100k vectors — with a loop, then vectorized. Time both.
2. Given a 2D array of grades, mark every value < 40 as 0 using np.where.