NumPy — Thinking in Arrays

From list to array

import numpy as np

prices = np.array([10, 25, 40, 8, 100])
print(prices)          # [ 10  25  40   8 100]
print(prices.mean())   # 36.6
print(prices.sum())    # 183
print(prices.max())    # 100

Looks like a list, behaves like a spreadsheet column. The summary methods (.mean(), .sum(), .std(), .min(), .max()) are built in and run in fast compiled code under the hood.

Vectorised maths — the whole point

Here's the shift. To add 15% tax to every price, you do not write a loop. You operate on the array directly:

with_tax = prices * 1.15
# [ 11.5  28.75  46.   9.2  115. ]

discounted = prices - 5          # subtract 5 from every element
totals     = prices * quantities # element-wise across two arrays

One expression touches every element. This isn't just shorter than a loop — for big data it's dramatically faster, because NumPy pushes the work down into optimised C instead of stepping through Python one item at a time. "Don't write the loop; express the operation" is the core data-science instinct, and NumPy is where you learn it.

🐘 PHP: There's no real PHP equivalent. In PHP you'd foreach over the array applying tax to each element, or reach for array_map. NumPy makes prices * 1.15 mean "every price, taxed" — the loop is implied and runs at machine speed. This is a genuinely new way of thinking, and it's the foundation of everything that follows.

Boolean masks — filtering by condition

Compare an array to a value and you get back an array of True/False — a "mask." Feed that mask back in as an index and you get only the matching elements. This is the ancestor of pandas filtering, so it's worth a careful look.

prices = np.array([10, 25, 40, 8, 100])

mask = prices >= 40          # [False False  True False  True]
big  = prices[mask]          # [ 40 100]

# usually written in one line:
big = prices[prices >= 40]   # [ 40 100]

# combine conditions with & and | (wrap each in parentheses!)
mid = prices[(prices >= 10) & (prices < 100)]   # [10 25 40]

Read prices[prices >= 40] as "the prices where price is at least 40." Note the operators are & and | (not and/or) for array masks, and each condition must be parenthesised — forgetting those parentheses is the classic NumPy/pandas gotcha you'll hit exactly once.

2-D arrays and axes

Real data is a grid — rows and columns — so arrays go 2-D. The new idea is the axis: axis=0 runs down columns, axis=1 runs across rows.

grid = np.array([
    [1200, 1800, 1500],   # North: Jan, Feb, Mar
    [ 900, 1100, 1300],   # South
])

grid.sum()              # 7800  -> everything
grid.sum(axis=0)        # [2100 2900 2800]  -> total per month (down columns)
grid.sum(axis=1)        # [4500 3300]       -> total per region (across rows)
grid[0]                 # first row  -> North's three months
grid[:, 1]              # all rows, column 1  -> every region's Feb

That axis concept carries straight into pandas, where axis=0 means "down the rows" and axis=1 means "across the columns." Getting comfortable with it now pays off immediately.