Scalar and array broadcasting in NumPy - Mini Project: Build & Apply

Scalar and Array Broadcasting with NumPy

📖 Scenario: Imagine you run a small bakery. You have a list of prices for different types of bread. You want to calculate the total cost if a customer buys multiple quantities of each bread type. Instead of writing a loop, you can use NumPy broadcasting to multiply the prices by the quantities easily.

🎯 Goal: Learn how to use scalar and array broadcasting in NumPy to multiply arrays and scalars efficiently.

📋 What You'll Learn

Create a NumPy array with exact bread prices

Create a scalar quantity to multiply with prices

Use broadcasting to multiply the scalar with the array

Print the resulting array showing total costs

💡 Why This Matters

🌍 Real World

Broadcasting helps quickly calculate costs, measurements, or any repeated operation without writing loops, saving time and reducing errors.

💼 Career

Data scientists and analysts use broadcasting to efficiently manipulate and analyze large datasets with fewer lines of code.

1

Create a NumPy array of bread prices

Import NumPy as np and create a NumPy array called prices with these exact values: 2.5, 3.0, 4.0, 5.5.

NumPy

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

Hint

Use np.array([...]) to create the array.

2

Create a scalar quantity for number of breads

Create a scalar variable called quantity and set it to the integer 3.

NumPy

import numpy as np
prices = np.array([2.5, 3.0, 4.0, 5.5])
# Create the quantity scalar
# Your code here

Hint

Just assign the number 3 to quantity.

3

Multiply prices by quantity using broadcasting

Create a new variable called total_costs that multiplies the prices array by the scalar quantity using broadcasting.

NumPy

import numpy as np
prices = np.array([2.5, 3.0, 4.0, 5.5])
quantity = 3
# Multiply prices by quantity using broadcasting
# Your code here

Hint

Use the * operator to multiply the array by the scalar.

4

Print the total costs array

Print the variable total_costs to display the total cost for each bread type.

NumPy

import numpy as np
prices = np.array([2.5, 3.0, 4.0, 5.5])
quantity = 3
total_costs = prices * quantity
# Print the total_costs array
# Your code here

Hint

Use print(total_costs) to show the result.

Practice

1. What happens when you add a scalar to a NumPy array using broadcasting?

easy

A. The scalar is added to each element of the array.

B. The scalar is ignored and the array remains unchanged.

C. An error occurs because shapes do not match.

D. The scalar replaces all elements in the array.

Solution

1. Step 1: Understand scalar and array addition

   A scalar is treated as an array with no dimensions and can be added to each element of the array.

2. Step 2: Apply broadcasting rules

   Broadcasting repeats the scalar value to match the shape of the array, adding it element-wise.

3. Final Answer:

   The scalar is added to each element of the array. -> Option A

4. Quick Check:

   Scalar + array = element-wise addition [OK]

Hint: Scalar acts like a single value added to all elements [OK]

Common Mistakes:

• Thinking scalar is ignored
• Expecting shape mismatch error
• Assuming scalar replaces array

2. Which of the following is the correct syntax to add scalar 5 to a NumPy array arr?

easy

A. arr.add(5)

B. arr + 5

C. add(arr, 5)

D. arr + [5]

Solution

1. Step 1: Recall NumPy scalar addition syntax

   Adding a scalar to an array is done simply by using the plus operator: arr + scalar.

2. Step 2: Evaluate options

   arr + 5 uses arr + 5, which is correct. arr.add(5) is invalid syntax. add(arr, 5) is not a NumPy function. arr + [5] tries to add a list, which changes behavior.

3. Final Answer:

   arr + 5 -> Option B

4. Quick Check:

   Use arr + scalar for scalar addition [OK]

Hint: Use plus operator directly for scalar addition [OK]

Common Mistakes:

• Using method .add() which doesn't exist
• Passing scalar inside a list
• Using non-existent add() function

3. What is the output of the following code?

import numpy as np
arr = np.array([1, 2, 3])
result = arr * 3
print(result)

medium

A. [3 3 3]

B. [1 2 3 3 6 9]

C. Error due to shape mismatch

D. [3 6 9]

Solution

1. Step 1: Understand scalar multiplication with array

   Multiplying an array by a scalar multiplies each element by that scalar.

2. Step 2: Calculate element-wise multiplication

   Each element in [1, 2, 3] is multiplied by 3, resulting in [3, 6, 9].

3. Final Answer:

   [3 6 9] -> Option D

4. Quick Check:

   Array * scalar = element-wise multiplication [OK]

Hint: Multiply each element by scalar directly [OK]

Common Mistakes:

• Expecting concatenation instead of multiplication
• Thinking output is repeated elements
• Assuming error due to shape mismatch

4. Identify the error in this code snippet:

import numpy as np
arr = np.array([1, 2, 3])
scalar = np.array([5])
result = arr + scalar
print(result)

medium

A. Output is [1 2 3 5]

B. Error because scalar is an array, not a number

C. No error; output is [6 7 8]

D. Error due to shape mismatch

Solution

1. Step 1: Check shapes of arrays

   arr shape is (3,), scalar shape is (1,). Broadcasting allows (1,) to expand to (3,).

2. Step 2: Apply broadcasting addition

   Each element of arr is added to 5, resulting in [6, 7, 8].

3. Final Answer:

   No error; output is [6 7 8] -> Option C

4. Quick Check:

   Broadcasting works with (3,) + (1,) arrays [OK]

Hint: Arrays with shape (n,) and (1,) broadcast correctly [OK]

Common Mistakes:

• Assuming scalar must be a plain number
• Thinking shape mismatch causes error
• Expecting concatenation instead of addition

5. Given a 2D array arr = np.array([[1, 2, 3], [4, 5, 6]]), what is the result of arr + np.array([10, 20, 30])?

hard

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

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

C. Error due to shape mismatch

D. [[10 20 30]
[10 20 30]]

Solution

1. Step 1: Analyze shapes for broadcasting

   arr shape is (2,3), and np.array([10, 20, 30]) shape is (3,). The second array broadcasts across rows.

2. Step 2: Perform element-wise addition row-wise

   Each row of arr adds the vector [10, 20, 30] element-wise, resulting in [[11, 22, 33], [14, 25, 36]].

3. Final Answer:

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

4. Quick Check:

   Broadcast vector added to each row [OK]

Hint: Vector added to each row in 2D array [OK]

Common Mistakes:

• Expecting error due to different shapes
• Adding vector only to first row
• Confusing addition with concatenation