Boolean indexing in NumPy - Step-by-Step Execution

Concept Flow - Boolean indexing

Start with array

↓

Create boolean mask

↓

Apply mask to array

↓

Get filtered array

↓

Use filtered array for analysis or output

Boolean indexing uses a mask of True/False values to select elements from an array.

Execution Sample

NumPy

import numpy as np
arr = np.array([10, 15, 20, 25, 30])
mask = arr > 20
filtered = arr[mask]
print(filtered)

This code selects elements from arr that are greater than 20 using boolean indexing.

Execution Table

Step	Action	Array 'arr'	Mask 'mask'	Filtered array 'filtered'
1	Create array	[10, 15, 20, 25, 30]	N/A	N/A
2	Create mask arr > 20	[10, 15, 20, 25, 30]	[False, False, False, True, True]	N/A
3	Apply mask to arr	[10, 15, 20, 25, 30]	[False, False, False, True, True]	[25, 30]
4	Print filtered	[10, 15, 20, 25, 30]	[False, False, False, True, True]	[25, 30]

💡 Finished filtering; mask selects elements > 20, resulting in [25, 30]

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
arr	N/A	[10, 15, 20, 25, 30]	[10, 15, 20, 25, 30]	[10, 15, 20, 25, 30]	[10, 15, 20, 25, 30]
mask	N/A	N/A	[False, False, False, True, True]	[False, False, False, True, True]	[False, False, False, True, True]
filtered	N/A	N/A	N/A	[25, 30]	[25, 30]

Key Moments - 3 Insights

Why does the mask have True only for some elements?

The mask is created by comparing each element to 20 (arr > 20). Only elements greater than 20 get True, as shown in step 2 of the execution_table.

What happens if we use the mask directly without applying it to arr?

The mask itself is just True/False values, not the filtered data. You must apply it to arr (arr[mask]) to get the selected elements, as in step 3.

Can the filtered array have fewer elements than the original?

Yes, because the mask selects only elements where the condition is True, so filtered array is smaller or equal in size, shown in step 3.

Visual Quiz - 3 Questions

Look at the execution_table at step 2, what is the value of mask?

A [False, False, False, True, True]

B [True, True, False, False, False]

C [False, True, True, False, True]

D [True, False, True, True, False]

💡 Hint

Check the 'Mask mask' column at step 2 in the execution_table.

At which step does the filtered array get its values?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look at the 'Filtered array filtered' column in the execution_table to see when it changes from N/A.

If we change the condition to arr >= 25, how would the mask change at step 2?

A [False, False, False, True, True]

B [False, False, False, False, True]

C [False, False, False, True, False]

D [True, True, True, True, True]

💡 Hint

Compare arr values to 25 and mark True where arr >= 25, then check mask pattern.

Concept Snapshot

Boolean indexing in numpy:
- Create a boolean mask by comparing array elements.
- Use mask to select elements: filtered = arr[mask]
- Mask is same shape as array, with True/False.
- Result is array of elements where mask is True.
- Useful for filtering data easily.

Full Transcript

Boolean indexing lets you pick elements from a numpy array using True/False values. First, you make a mask by checking a condition on each element. For example, arr > 20 creates a mask with True where elements are greater than 20. Then you use this mask to get only those elements from the array by writing arr[mask]. The filtered array contains only the selected elements. This method is simple and powerful for filtering data in numpy.

Practice

1. What does boolean indexing in numpy allow you to do?

easy

A. Create a new array filled with zeros

B. Change the data type of an array

C. Sort the array elements in ascending order

D. Select elements from an array using a True/False mask

Solution

1. Step 1: Understand boolean indexing concept

   Boolean indexing uses a True/False array to pick elements from another array.

2. Step 2: Identify the correct operation

   Only Select elements from an array using a True/False mask describes selecting elements based on True/False values.

3. Final Answer:

   Select elements from an array using a True/False mask -> Option D

4. Quick Check:

   Boolean indexing = Select elements [OK]

Hint: Boolean mask picks elements where True appears [OK]

Common Mistakes:

• Confusing boolean indexing with sorting
• Thinking it changes data types
• Assuming it creates new arrays with zeros

2. Which of the following is the correct syntax to select elements greater than 5 from a numpy array arr using boolean indexing?

easy

A. arr[arr < 5]

B. arr > 5[arr]

C. arr[arr > 5]

D. arr.select(arr > 5)

Solution

1. Step 1: Understand boolean indexing syntax

   The correct syntax is to use the array with a boolean mask inside square brackets: arr[condition].

2. Step 2: Check each option

   arr[arr > 5] uses arr[arr > 5], which is correct. Others have wrong order or invalid methods.

3. Final Answer:

   arr[arr > 5] -> Option C

4. Quick Check:

   Correct syntax = arr[condition] [OK]

Hint: Put condition inside brackets after array name [OK]

Common Mistakes:

• Placing condition before array name
• Using invalid methods like select()
• Using wrong comparison operators

3. What is the output of the following code?

import numpy as np
arr = np.array([2, 7, 4, 9, 1])
result = arr[arr % 2 == 1]

medium

A. [7 9 1]

B. [2 4]

C. [7 4 9]

D. [2 7 4 9 1]

Solution

1. Step 1: Understand the condition arr % 2 == 1

   This condition selects elements where the remainder when divided by 2 is 1, i.e., odd numbers.

2. Step 2: Apply condition to array elements

   Elements 7, 9, and 1 are odd, so they are selected.

3. Final Answer:

   [7 9 1] -> Option A

4. Quick Check:

   Odd elements = [7 9 1] [OK]

Hint: Filter with modulo to get odd numbers [OK]

Common Mistakes:

• Selecting even numbers instead
• Confusing modulo operator
• Returning full array instead of filtered

4. The following code has a problem. What is the problem?

import numpy as np
arr = np.array([1, 2, 3, 4])
mask = arr > 2
print(arr[mask == True])

medium

A. mask == True is unnecessary and redundant

B. arr should be converted to list first

C. Comparison operator > is invalid for numpy arrays

D. Square brackets cannot be used for indexing

Solution

1. Step 1: Analyze the boolean mask creation

   mask = arr > 2 creates a boolean array correctly.

2. Step 2: Check the indexing expression

   Using mask == True is redundant since mask is already boolean. It's unnecessary and bad practice.

3. Step 3: Correct usage

   Use arr[mask] directly without comparing mask to True.

4. Final Answer:

   mask == True is unnecessary and redundant -> Option A

5. Quick Check:

   Use boolean mask directly [OK]

Hint: Use mask directly, no need for '== True' [OK]

Common Mistakes:

• Adding '== True' to boolean mask
• Trying to convert numpy array to list for indexing
• Misunderstanding comparison operators

5. Given a numpy array data = np.array([10, 15, 20, 25, 30]), how can you select elements greater than 12 and less than 28 using boolean indexing?

hard

A. data[data > 12 and data < 28]

B. data[(data > 12) & (data < 28)]

C. data[data > 12 | data < 28]

D. data[(data > 12) or (data < 28)]

Solution

1. Step 1: Understand combining conditions with & and parentheses

   In numpy, use & for element-wise AND and wrap each condition in parentheses.

2. Step 2: Check each option

   data[(data > 12) & (data < 28)] correctly uses & (element-wise AND) with parentheses around each condition. Using Python keywords and/or cause errors because they don't work element-wise on arrays. Using | (bitwise OR) selects elements greater than 12 or less than 28, which is wrong here.

3. Final Answer:

   data[(data > 12) & (data < 28)] -> Option B

4. Quick Check:

   Use & with parentheses for AND conditions [OK]

Hint: Use & with parentheses for multiple conditions [OK]

Common Mistakes:

• Using 'and' or 'or' instead of & or |
• Not using parentheses around conditions
• Using | (OR) instead of & (AND) for filtering