Common broadcasting patterns in NumPy - Mini Project: Build & Apply

Common broadcasting patterns

📖 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 sales compare to a daily target.

🎯 Goal: Build a small program using numpy arrays to apply common broadcasting patterns. You will create sales data, set a daily sales target, calculate total sales per day, and compare sales to the target using broadcasting.

📋 What You'll Learn

Use numpy arrays to store sales data

Create a daily sales target as a single number

Use broadcasting to sum sales per day

Use broadcasting to compare daily sales to the target

Print the final comparison result

💡 Why This Matters

🌍 Real World

Broadcasting is a powerful tool in data science to efficiently compare and combine data without writing loops. It helps analyze sales, sensor data, or any tabular data quickly.

💼 Career

Understanding broadcasting is essential for data analysts and scientists to write clean, fast, and readable code when working with arrays and matrices.

1

Create the sales data array

Import numpy as np and create a 2D numpy array called sales with these exact values: [[10, 15, 20], [12, 18, 25], [14, 20, 30]]. Each row is a day, and each column is a bread type.

NumPy

# Import numpy and create the sales array
# Your code here

Hint

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

2

Set the daily sales target

Create a variable called daily_target and set it to the integer 50. This is the sales goal for each day.

NumPy

import numpy as np
sales = np.array([[10, 15, 20], [12, 18, 25], [14, 20, 30]])
# Create the daily_target variable
# Your code here

Hint

Just assign the number 50 to the variable daily_target.

3

Calculate total sales per day using broadcasting

Create a variable called total_sales that sums the sales of all bread types for each day using np.sum on sales with axis=1.

NumPy

import numpy as np
sales = np.array([[10, 15, 20], [12, 18, 25], [14, 20, 30]])
daily_target = 50
# Calculate total sales per day
# Your code here

Hint

Use np.sum with axis=1 to sum rows (days).

4

Compare total sales to daily target and print result

Create a variable called target_met that compares total_sales to daily_target using the >= operator. Then print target_met.

NumPy

import numpy as np
sales = np.array([[10, 15, 20], [12, 18, 25], [14, 20, 30]])
daily_target = 50
total_sales = np.sum(sales, axis=1)
# Compare total_sales to daily_target and print
# Your code here

Hint

Use total_sales >= daily_target to get a boolean array, then print it.

Practice

1. What does broadcasting in NumPy allow you to do?

easy

A. Perform operations on arrays of different shapes without explicit loops

B. Only add arrays of the exact same shape

C. Convert arrays into lists automatically

D. Sort arrays in ascending order

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting lets NumPy perform element-wise operations on arrays with different shapes by automatically expanding the smaller array.

2. Step 2: Compare options

   Only Perform operations on arrays of different shapes without explicit loops correctly describes this feature. Options A, B, and C describe unrelated behaviors.

3. Final Answer:

   Perform operations on arrays of different shapes without explicit loops -> Option A

4. Quick Check:

   Broadcasting = operations on different shapes [OK]

Hint: Broadcasting means math on different shaped arrays without loops [OK]

Common Mistakes:

• Thinking broadcasting requires arrays to have the same shape
• Confusing broadcasting with sorting or type conversion
• Assuming broadcasting changes array data types

2. Which of the following is the correct way to add a 1D array to each row of a 2D array using broadcasting?

easy

A. result = matrix + vector.T where matrix.shape = (3,4) and vector.shape = (4,)

B. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (3,)

C. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,)

D. result = matrix + vector.reshape(3,1) where matrix.shape = (3,4) and vector.shape = (4,)

Solution

1. Step 1: Check shapes for broadcasting

   Adding a 1D array of shape (4,) to each row of a (3,4) matrix works because the vector matches the number of columns.

2. Step 2: Evaluate options

   result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,) matches this pattern. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (3,) tries to add a (3,) vector to (3,4) matrix which fails. result = matrix + vector.T where matrix.shape = (3,4) and vector.shape = (4,) uses transpose incorrectly. result = matrix + vector.reshape(3,1) where matrix.shape = (3,4) and vector.shape = (4,) reshapes vector wrongly.

3. Final Answer:

   result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,) -> Option C

4. Quick Check:

   Vector shape matches columns for row-wise addition [OK]

Hint: Add vector matching columns to matrix rows for broadcasting [OK]

Common Mistakes:

• Using vector shape matching rows instead of columns
• Trying to transpose 1D vector which has no effect
• Reshaping vector incorrectly before addition

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])
C = A + B
print(C)

medium

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

B. [[11 22 33]
[14 25 36]
[10 20 30]]

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

D. ValueError due to shape mismatch

Solution

1. Step 1: Understand shapes of A and B

   A has shape (2,3), B has shape (3,). B will broadcast across rows of A.

2. Step 2: Perform element-wise addition

   Each row of A adds B: [1+10, 2+20, 3+30] = [11, 22, 33], [4+10, 5+20, 6+30] = [14, 25, 36].

3. Final Answer:

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

4. Quick Check:

   Broadcast adds vector to each matrix row [OK]

Hint: Add vector to each matrix row when vector shape matches columns [OK]

Common Mistakes:

• Expecting an extra row in output
• Confusing broadcasting with stacking arrays
• Thinking shape mismatch causes error here

4. Identify the error in this code snippet:

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

medium

A. y should be reshaped to (3,1) before addition

B. No error, code runs fine

C. X and y must have the same number of columns

D. Shapes (3,2) and (3,) cannot broadcast together

Solution

1. Step 1: Check shapes of X and y

   X shape is (3,2), y shape is (3,). Broadcasting rules require trailing dimensions to match or be 1.

2. Step 2: Analyze broadcasting compatibility

   Here, last dims are 2 (X) and 1 (y) after broadcasting rules, so y broadcasts along columns. The addition works without error.

3. Final Answer:

   No error, code runs fine -> Option B

4. Quick Check:

   Broadcasting allows (3,2) + (3,) by treating (3,) as (3,1) [OK]

Hint: Trailing dimensions must match or be 1 for broadcasting [OK]

Common Mistakes:

• Assuming broadcasting works if first dims match
• Not checking trailing dimension compatibility
• Thinking reshaping y to (3,1) fixes addition here

5. Given a 2D array M of shape (4,3) and a 1D array v of shape (4,), how can you add v to each column of M using broadcasting?

hard

A. M + v.T

B. M + v

C. M + v.reshape(1,4)

D. M + v.reshape(4,1)

Solution

1. Step 1: Understand shapes and desired operation

   M is (4,3), v is (4,). To add v to each column, v must be reshaped to (4,1) to broadcast along columns.

2. Step 2: Check each option

   M + v.reshape(4,1) reshapes v to (4,1), allowing broadcasting with M (4,3). M + v tries to add (4,) to (4,3) which broadcasts incorrectly. M + v.reshape(1,4) reshapes v to (1,4), incompatible. M + v.T uses transpose on 1D array which has no effect.

3. Final Answer:

   M + v.reshape(4,1) -> Option D

4. Quick Check:

   Reshape vector to (rows,1) to add to columns [OK]

Hint: Reshape vector to (rows,1) to add to matrix columns [OK]

Common Mistakes:

• Adding vector without reshaping when shapes differ
• Using reshape(1, rows) instead of (rows,1)
• Assuming transpose changes 1D array shape