Broadcasting for distance matrices in NumPy - Mini Project: Build & Apply

Broadcasting for Distance Matrices

📖 Scenario: Imagine you have a few cities with their coordinates on a map. You want to find the distance between every pair of cities. This helps in planning trips or deliveries.

🎯 Goal: You will create a program that calculates the distance matrix between cities using numpy broadcasting. This means you will find all distances without writing loops, making the code fast and simple.

📋 What You'll Learn

Use numpy arrays to store city coordinates

Use broadcasting to calculate pairwise distances

Calculate Euclidean distance between points

Output the full distance matrix

💡 Why This Matters

🌍 Real World

Calculating distance matrices is useful in mapping, delivery route planning, and clustering locations based on proximity.

💼 Career

Data scientists and analysts often use broadcasting to efficiently compute distance matrices for machine learning, geographic analysis, and optimization problems.

1

Create city coordinates array

Create a numpy array called cities with these exact coordinates: [0, 0], [3, 4], and [6, 8]. Each coordinate is a list of two numbers representing x and y positions.

NumPy

# Create the numpy array called cities with the given coordinates
# Your code here

Need a hint?

Use np.array and pass a list of lists with the coordinates.

2

Prepare for broadcasting

Create two new variables: cities_expanded_1 by adding a new axis to cities at position 1 using np.newaxis, and cities_expanded_2 by adding a new axis to cities at position 0 using np.newaxis.

NumPy

import numpy as np

cities = np.array([[0, 0], [3, 4], [6, 8]])

# Add new axis at position 1 to cities and assign to cities_expanded_1
# Add new axis at position 0 to cities and assign to cities_expanded_2
# Your code here

Need a hint?

Use np.newaxis inside the square brackets to add a dimension.

3

Calculate the distance matrix using broadcasting

Create a variable called distances that calculates the Euclidean distance between each pair of cities using cities_expanded_1 and cities_expanded_2. Use the formula: square root of the sum of squared differences along the last axis.

NumPy

import numpy as np

cities = np.array([[0, 0], [3, 4], [6, 8]])
cities_expanded_1 = cities[:, np.newaxis, :]
cities_expanded_2 = cities[np.newaxis, :, :]

# Calculate the Euclidean distance matrix and assign it to distances
# Your code here

Need a hint?

Subtract the expanded arrays, square the result, sum over the last axis, then take the square root.

4

Print the distance matrix

Print the variable distances to display the full distance matrix between the cities.

NumPy

import numpy as np

cities = np.array([[0, 0], [3, 4], [6, 8]])
cities_expanded_1 = cities[:, np.newaxis, :]
cities_expanded_2 = cities[np.newaxis, :, :]

distances = np.sqrt(np.sum((cities_expanded_1 - cities_expanded_2) ** 2, axis=-1))

# Print the distances array
# Your code here

Need a hint?

Use print(distances) to show the matrix.