Scalar and array broadcasting in NumPy

Introduction

Broadcasting lets you do math between arrays of different sizes easily. It saves time and code by automatically expanding smaller arrays.

Adding a single number to every element in a list of numbers.

Multiplying each row of a table by a different number.

Subtracting the average value from each element in a dataset.

Scaling all values in an array by a constant factor.

Applying a formula to each element without writing loops.

Syntax

NumPy

import numpy as np

# Example: Add scalar to array
array = np.array([1, 2, 3])
scalar = 5
result = array + scalar

# Example: Add arrays with broadcasting
array1 = np.array([[1, 2, 3], [4, 5, 6]])
array2 = np.array([10, 20, 30])
result = array1 + array2

Broadcasting happens automatically when shapes are compatible.

A scalar is treated like an array with shape ().

Examples

Adds 10 to each element of the array.

NumPy

import numpy as np

# Scalar added to array
array = np.array([1, 2, 3])
scalar = 10
result = array + scalar
print(result)

Broadcasts 1D array across rows of 2D array.

NumPy

import numpy as np

# Adding 1D array to 2D array
array_2d = np.array([[1, 2, 3], [4, 5, 6]])
array_1d = np.array([10, 20, 30])
result = array_2d + array_1d
print(result)

Adding scalar to empty array returns empty array.

NumPy

import numpy as np

# Edge case: empty array
empty_array = np.array([])
scalar = 5
result = empty_array + scalar
print(result)

Scalar multiplies the single element.

NumPy

import numpy as np

# Edge case: single element array
single_element_array = np.array([100])
scalar = 3
result = single_element_array * scalar
print(result)

Sample Program

This program shows how a 1D array is added to each row of a 2D array by broadcasting. It also shows adding a scalar to every element.

NumPy

import numpy as np

# Create a 2D array
array_2d = np.array([[1, 2, 3], [4, 5, 6]])
print("Original 2D array:")
print(array_2d)

# Create a 1D array to broadcast
array_1d = np.array([10, 20, 30])
print("\n1D array to broadcast:")
print(array_1d)

# Add 1D array to 2D array using broadcasting
result_add = array_2d + array_1d
print("\nResult of adding 1D array to 2D array:")
print(result_add)

# Add scalar to 2D array
scalar_value = 5
result_scalar = array_2d + scalar_value
print("\nResult of adding scalar to 2D array:")
print(result_scalar)

Important Notes

Time complexity is O(n) where n is number of elements in the largest array.

Space complexity depends on the output array size, usually same as the largest input array.

Common mistake: shapes must be compatible for broadcasting, otherwise error occurs.

Use broadcasting to avoid writing loops and make code faster and cleaner.

Summary

Broadcasting lets you do math between arrays of different shapes easily.

Scalars act like arrays with no dimensions and can be combined with any array.

Always check array shapes to ensure broadcasting will work without errors.

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