NumPy · Vectorisation

Vectorisation means expressing a computation as whole-array operations so that NumPy runs the loop in compiled C. ufuncs (np.sqrt, np.exp, +, *) apply element-wise. Reductions (sum, mean, max) collapse an axis:

• axis=0: down the rows, giving one result per column
• axis=1: across each row, giving one result per row

I timed the same computation (root-mean-square of a million numbers) both ways. The exact numbers depend on the machine, so the snippet only prints the speed-up factor, rounded.

import numpy as np, time, math, random

random.seed(0)
data = [random.random() for _ in range(1_000_000)]
arr = np.array(data)

t0 = time.perf_counter()
rms_loop = math.sqrt(sum(x * x for x in data) / len(data))
t1 = time.perf_counter()
rms_vec = np.sqrt(np.mean(arr ** 2))
t2 = time.perf_counter()

print(round(rms_loop, 6), round(float(rms_vec), 6))
print("vectorised is faster:", (t2 - t1) < (t1 - t0))
print("speed-up at least 10x:", (t1 - t0) / (t2 - t1) > 10)

M = np.arange(12).reshape(3, 4)
print(M.sum(axis=0), M.sum(axis=1), M.max())
print(np.exp(np.array([0.0, 1.0])).round(4))

Output:

0.577079 0.577079
vectorised is faster: True
speed-up at least 10x: True
[12 15 18 21] [ 6 22 38] 11
[1.     2.7183]