Vectorised maths

Whole-array arithmetic

Every arithmetic operator works element by element, and two arrays of the same shape combine position by position:

a = np.array([1, 2, 3])
b = np.array([10, 20, 30])

a + b        # array([11, 22, 33])
b / a        # array([10., 10., 10.])
a ** 2       # array([1, 4, 9])

Mixing an array with a single number applies that number to everything — this is called broadcasting:

a * 100      # array([100, 200, 300])
a - 1        # array([0, 1, 2])

NumPy also ships the mathematical functions, and they too work on whole arrays: np.sqrt, np.round, np.abs, np.exp, np.log.

Your turn: convert an array of Celsius temperatures to Fahrenheit (F = C * 9/5 + 32), and round the result to one decimal place.

Comparing whole arrays

A comparison also applies element by element, and produces an array of booleans:

a = np.array([1, 5, 3, 8])
a > 3          # array([False, True, False, True])

That boolean array is the foundation of the next lesson, but it is already useful on its own, because True counts as 1:

(a > 3).sum()     # 2  — how many are above 3
(a > 3).any()     # True
(a > 3).all()     # False

Your turn: given daily rainfall, work out how many days were dry (exactly zero), and whether any day exceeded 20mm.