Boolean indexing for filtering in NumPy

Introduction

Boolean indexing helps you pick only the data you want from a big list or table. It makes finding and using specific data easy and fast.

You want to find all temperatures above 30 degrees in a weather dataset.

You need to select only the students who passed an exam from a list of scores.

You want to filter out all negative numbers from a list of measurements.

You want to get all sales records where the amount is greater than 1000.

You want to find all rows in a table where a condition is true, like customers from a certain city.

Syntax

NumPy

filtered_array = array[condition]

The condition is a Boolean array or expression that is the same shape as array.

Only elements where condition is True are kept in filtered_array.

Examples

This keeps only numbers greater than 25 from the array.

NumPy

import numpy as np
arr = np.array([10, 20, 30, 40, 50])
filtered = arr[arr > 25]

This keeps numbers between 15 and 35 inclusive.

NumPy

arr = np.array([5, 15, 25, 35, 45])
filtered = arr[(arr >= 15) & (arr <= 35)]

This keeps only even numbers from the array.

NumPy

arr = np.array([1, 2, 3, 4, 5])
filtered = arr[arr % 2 == 0]

Sample Program

This program creates a list of ages and then uses Boolean indexing to select only those 18 or older. It prints both the full list and the filtered list.

NumPy

import numpy as np

# Create an array of ages
ages = np.array([12, 17, 24, 35, 42, 15, 19])

# Filter ages to get only adults (18 and older)
adults = ages[ages >= 18]

print("All ages:", ages)
print("Adults only:", adults)

Important Notes

Boolean indexing works with arrays of any shape, not just 1D.

Make sure the condition array matches the shape of the original array.

You can combine multiple conditions using & (and), | (or), but use parentheses around each condition.

Summary

Boolean indexing lets you pick data by True/False conditions.

It is a fast and simple way to filter arrays in numpy.

Use logical operators to combine multiple conditions.

Practice

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

easy

A. Select elements from an array based on True/False conditions

B. Sort an array in ascending order

C. Change the data type of an array

D. Calculate the sum of all elements in an array

Solution

1. Step 1: Understand boolean indexing concept

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

2. Step 2: Compare with other options

   Sorting, changing data type, and summing are different numpy operations, not boolean indexing.

3. Final Answer:

   Select elements from an array based on True/False conditions -> Option A

4. Quick Check:

   Boolean indexing = filtering by True/False [OK]

Hint: Boolean indexing picks elements where condition is True [OK]

Common Mistakes:

• Confusing boolean indexing with sorting
• Thinking it changes data types
• Assuming it calculates sums

2. Which of the following is the correct syntax to filter array arr for values greater than 5 using boolean indexing?

easy

A. arr > 5[arr]

B. arr[arr > 5]

C. arr.filter(arr > 5)

D. arr[arr < 5]

Solution

1. Step 1: Identify correct boolean indexing syntax

   In numpy, filtering uses arr[condition] where condition is a boolean array.

2. Step 2: Check each option

   arr[arr > 5] uses correct syntax. arr > 5[arr] is invalid syntax. arr.filter(arr > 5) is not a numpy method. arr[arr < 5] filters for less than 5, not greater.

3. Final Answer:

   arr[arr > 5] -> Option B

4. Quick Check:

   Correct syntax is arr[condition] [OK]

Hint: Use arr[condition] to filter arrays in numpy [OK]

Common Mistakes:

• Placing condition outside brackets
• Using non-existent filter method
• Mixing up greater than and less than

3. What is the output of the following code?

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

medium

A. [7 4 9]

B. [2 4]

C. [7 9 1]

D. [2 7 4 9 1]

Solution

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

   This condition selects odd numbers because odd numbers have remainder 1 when divided by 2.

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 C

4. Quick Check:

   Filter odd numbers = [7 9 1] [OK]

Hint: Use modulo (%) to filter odd/even numbers [OK]

Common Mistakes:

• Selecting even numbers instead of odd
• Including all elements without filtering
• Misunderstanding modulo operator

4. The following code throws an error. What is the mistake?

import numpy as np
arr = np.array([10, 15, 20, 25])
filtered = arr[arr > 15 and arr < 25]

medium

A. Using 'and' instead of '&' for element-wise condition

B. Missing parentheses around conditions

C. Using 'or' instead of 'and'

D. Array is not defined properly

Solution

1. Step 1: Identify boolean operator error

   In numpy, element-wise logical operations require '&' instead of Python's 'and'.

2. Step 2: Understand why 'and' causes error

   'and' expects single boolean, but arr > 15 and arr < 25 returns arrays, causing TypeError.

3. Final Answer:

   Using 'and' instead of '&' for element-wise condition -> Option A

4. Quick Check:

   Use '&' for element-wise logical AND [OK]

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

Common Mistakes:

• Using 'and' instead of '&' in numpy conditions
• Forgetting parentheses around each condition
• Assuming 'or' works like '|'

5. Given a numpy array data = np.array([3, 6, 9, 12, 15, 18]), how would you filter values that are divisible by 3 but not by 6 using boolean indexing?

hard

A. data[(data % 3 == 0) & (data % 6 == 0)]

B. data[(data % 3 == 0) | (data % 6 != 0)]

C. data[(data % 3 != 0) & (data % 6 == 0)]

D. data[(data % 3 == 0) & (data % 6 != 0)]

Solution

1. Step 1: Define conditions for filtering

   We want numbers divisible by 3 (data % 3 == 0) but not divisible by 6 (data % 6 != 0).

2. Step 2: Combine conditions with element-wise AND

   Use '&' to combine both conditions inside parentheses for correct boolean indexing.

3. Step 3: Apply combined condition to data array

   data[(data % 3 == 0) & (data % 6 != 0)] correctly applies both conditions with '&'. Others use wrong operators or conditions.

4. Final Answer:

   data[(data % 3 == 0) & (data % 6 != 0)] -> Option D

5. Quick Check:

   Use & and parentheses for combined conditions [OK]

Hint: Combine conditions with & and parentheses for filtering [OK]

Common Mistakes:

• Using | instead of & for AND condition
• Mixing up divisibility conditions
• Forgetting parentheses around each condition