1D and 2D broadcasting in NumPy - Mini Project: Build & Apply

1D and 2D broadcasting

📖 Scenario: You work in a small bakery that tracks daily sales of different types of bread. You want to analyze the sales data to understand how many breads were sold each day and how the prices affect total revenue.

🎯 Goal: Build a small program using numpy to apply 1D and 2D broadcasting. You will create arrays for daily sales and prices, then calculate total revenue using broadcasting.

📋 What You'll Learn

Create a 2D numpy array called sales representing the number of breads sold for 3 types over 4 days.

Create a 1D numpy array called prices representing the price of each bread type.

Use broadcasting to calculate the total revenue per day for each bread type.

Print the resulting revenue array.

💡 Why This Matters

🌍 Real World

Broadcasting helps quickly perform operations on sales and price data without writing loops, saving time and reducing errors.

💼 Career

Data analysts and scientists use broadcasting in numpy to efficiently handle and analyze multi-dimensional data like sales, prices, and revenues.

1

Create the sales data array

Create a 2D numpy array called sales with these exact values: [[10, 15, 7], [12, 18, 5], [9, 14, 8], [11, 16, 6]]. This array represents the number of breads sold for 3 types over 4 days.

NumPy

import numpy as np
# Create the 2D numpy array called sales with the given values
# Your code here

Hint

Use np.array() to create the 2D array with the exact values.

2

Create the prices array

Create a 1D numpy array called prices with these exact values: [2.5, 3.0, 4.0]. This array represents the price of each bread type.

NumPy

import numpy as np
sales = np.array([[10, 15, 7], [12, 18, 5], [9, 14, 8], [11, 16, 6]])
# Create the 1D numpy array called prices with the given values
# Your code here

Hint

Use np.array() to create the 1D array with the exact prices.

3

Calculate total revenue using broadcasting

Use broadcasting to multiply the sales array by the prices array and store the result in a new variable called revenue. This will calculate the total revenue per bread type for each day.

NumPy

import numpy as np
sales = np.array([[10, 15, 7], [12, 18, 5], [9, 14, 8], [11, 16, 6]])
prices = np.array([2.5, 3.0, 4.0])
# Multiply sales by prices using broadcasting and store in revenue
# Your code here

Hint

Simply multiply the 2D sales array by the 1D prices array to use broadcasting.

4

Print the revenue array

Print the revenue array to display the total revenue per bread type for each day.

NumPy

import numpy as np
sales = np.array([[10, 15, 7], [12, 18, 5], [9, 14, 8], [11, 16, 6]])
prices = np.array([2.5, 3.0, 4.0])
revenue = sales * prices
# Print the revenue array
# Your code here

Hint

Use print(revenue) to show the final result.

Practice

1. What does broadcasting in NumPy allow you to do with arrays of different shapes?

easy

A. Only add arrays if they have the exact same shape

B. Sort arrays in ascending order

C. Convert arrays into lists automatically

D. Perform element-wise operations without manually reshaping arrays

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting lets NumPy perform math on arrays with different shapes by stretching smaller arrays.

2. Step 2: Identify what broadcasting enables

   This means you can do element-wise operations without manually reshaping arrays to the same shape.

3. Final Answer:

   Perform element-wise operations without manually reshaping arrays -> Option D

4. Quick Check:

   Broadcasting = element-wise operations on different shapes [OK]

Hint: Broadcasting stretches smaller arrays to match bigger ones [OK]

Common Mistakes:

• Thinking arrays must have the same shape to operate
• Confusing broadcasting with sorting or reshaping
• Assuming broadcasting copies data

2. Which of the following is the correct way to add a 1D array b = np.array([1, 2, 3]) to each row of a 2D array a with shape (4, 3)?

easy

A. a + b

B. a + b.T

C. a + b.reshape(3, 1)

D. a + b.reshape(1, 4)

Solution

1. Step 1: Check shapes of arrays

   Array a has shape (4, 3), and b has shape (3,). Adding a + b broadcasts b across rows.

2. Step 2: Understand broadcasting rules

   Since b matches the number of columns, it adds to each row correctly without reshaping.

3. Final Answer:

   a + b -> Option A

4. Quick Check:

   1D array added across rows = a + b [OK]

Hint: Add 1D array directly if its length matches columns [OK]

Common Mistakes:

• Trying to transpose 1D array which has no effect
• Reshaping to wrong dimensions causing errors
• Confusing rows and columns in shapes

3. What is the output of the following code?

import numpy as np
a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([10, 20, 30])
result = a + b
print(result)

medium

A. [[11 22 33]
[14 25 36]]

B. [[11 12 13]
[14 15 16]]

C. [[10 20 30]
[10 20 30]]

D. Error due to shape mismatch

Solution

1. Step 1: Analyze shapes and operation

   a shape is (2,3), b shape is (3,). Adding broadcasts b across rows.

2. Step 2: Calculate element-wise addition

   Row 1: [1+10, 2+20, 3+30] = [11, 22, 33]
   Row 2: [4+10, 5+20, 6+30] = [14, 25, 36]

3. Final Answer:

   [[11 22 33] [14 25 36]] -> Option A

4. Quick Check:

   Broadcast add across rows = [[11 22 33], [14 25 36]] [OK]

Hint: Add 1D array to 2D rows matches columns [OK]

Common Mistakes:

• Expecting error due to different shapes
• Adding element-wise without broadcasting
• Confusing rows and columns in addition

4. Identify the error in this code snippet:

import numpy as np
a = np.array([[1, 2], [3, 4], [5, 6]])
b = np.array([10, 20, 30])
result = a + b
print(result)

medium

A. Using wrong operator for addition

B. Syntax error in array creation

C. Shapes of a and b are incompatible for broadcasting

D. No error, code runs fine

Solution

1. Step 1: Check shapes of arrays

   a shape is (3, 2), b shape is (3,). They differ in second dimension.

2. Step 2: Understand broadcasting rules

   Broadcasting requires trailing dimensions to match or be 1. Here, 2 != 3, so addition fails.

3. Final Answer:

   Shapes of a and b are incompatible for broadcasting -> Option C

4. Quick Check:

   Shape mismatch causes broadcasting error [OK]

Hint: Check trailing dimensions match or are 1 for broadcasting [OK]

Common Mistakes:

• Assuming any shapes can broadcast
• Ignoring dimension order in arrays
• Thinking 1D arrays always broadcast to 2D

5. You have a 2D array data of shape (5, 4) representing 5 samples with 4 features each. You want to subtract the mean of each feature (given as a 1D array mean_vals of length 4) from the corresponding feature column in data. Which code correctly applies broadcasting to do this?

hard

A. data - mean_vals.reshape(4, 1)

B. data - mean_vals

C. data - mean_vals.reshape(1, 5)

D. data - mean_vals.T

Solution

1. Step 1: Understand shapes and operation

   data shape is (5, 4), mean_vals shape is (4,). Subtracting mean_vals from data broadcasts mean_vals across rows.

2. Step 2: Confirm correct broadcasting

   Since mean_vals length matches columns, data - mean_vals subtracts feature-wise means correctly.

3. Final Answer:

   data - mean_vals -> Option B

4. Quick Check:

   Subtract 1D array from 2D rows = data - mean_vals [OK]

Hint: Subtract 1D array matching columns directly [OK]

Common Mistakes:

• Reshaping mean_vals incorrectly causing errors
• Transposing 1D array which has no effect
• Trying to subtract mean_vals across wrong axis