NumPy in Ten Minutes

Every model you will ever train is, deep down, just arithmetic on big grids of numbers. NumPy is the tool for those grids. It is so central that nearly every machine learning library is built on top of it. Learn a handful of ideas now, and the rest of this course will feel far easier.

• Models are arithmetic on grids
• NumPy is the foundation
• A few ideas go a long way

Your first array

Here is an array of incomes. It looks like a list, but it is far more powerful. We can ask for the mean, or the maximum, directly. Now look at the next line. We multiply the whole array by ten thousand, with no loop at all, and every value changes. And the last line is a mask. We ask for only the values above four, and NumPy filters them for us. No loops. That idea is called vectorisation.

import numpy as np

incomes = np.array([3.2, 5.1, 8.3, 2.7, 6.4])

print("Mean:", incomes.mean())
print("Max: ", incomes.max())
print("In dollars:", incomes * 10000)
print("Above 4:", incomes[incomes > 4])

Mean: 5.140000000000001
Max:  8.3
In dollars: [32000. 51000. 83000. 27000. 64000.]
Above 4: [5.1 8.3 6.4]

Why it matters: speed

Why not just use Python lists? Let's race them. We add up the squares of five million numbers using a normal Python loop, and time it. Then we do the same with a NumPy array. Run it, and look at the difference. NumPy is many times faster, because the heavy work happens in compiled code. When your data has millions of rows, this difference decides whether your model trains in seconds, or in hours.

import numpy as np
import time

numbers = [float(n) for n in range(5_000_000)]
start = time.time()
total = sum(n * n for n in numbers)
print(f"Python loop: {time.time() - start:.4f} s")

array = np.array(numbers)
start = time.time()
total = (array * array).sum()
print(f"NumPy array: {time.time() - start:.4f} s")

Python loop: 0.2380 s
NumPy array: 0.0167 s

Rows and columns

Machine learning data is usually a two dimensional array. Each row is an example, and each column is a feature. Here are three districts, with income and house age. Shape says three rows, and two columns. Square brackets get a single row. The colon means every row, so colon comma one gets the second column. And axis zero means work down the columns, so we get the mean of each feature. This one is worth pausing on, because you will see it everywhere.

import numpy as np

X = np.array([[3.2, 41],
              [8.3, 21],
              [5.6, 52]])

print("Shape:", X.shape)
print("First row:", X[0])
print("Second column:", X[:, 1])
print("Mean of each column:", X.mean(axis=0))

Shape: (3, 2)
First row: [ 3.2 41. ]
Second column: [41. 21. 52.]
Mean of each column: [ 5.7 38. ]

Summary