Boolean indexing for filtering in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Boolean indexing in numpy?

Boolean indexing is a way to select elements from a numpy array using a condition that returns True or False for each element. Only elements where the condition is True are selected.

beginner

How do you create a Boolean mask to filter values greater than 5 in a numpy array named arr?

You write mask = arr > 5. This creates an array of True/False values where True means the element is greater than 5.

beginner

What happens when you use a Boolean mask to index a numpy array?

The array returns only the elements where the mask is True, effectively filtering the array based on the condition.

beginner

Example: Given arr = np.array([1, 4, 6, 8]), what does arr[arr > 5] return?

It returns array([6, 8]) because only 6 and 8 are greater than 5.

intermediate

Can Boolean indexing be used with multi-dimensional numpy arrays?

Yes, Boolean indexing works with multi-dimensional arrays. The mask must have the same shape as the array, and it filters elements accordingly.

What does Boolean indexing return when applied to a numpy array?

A Only elements where the condition is False

B Only elements where the condition is True

C All elements regardless of condition

D The original array unchanged

Boolean indexing filters the array and returns only elements where the condition evaluates to True.

How do you create a Boolean mask for elements equal to 10 in a numpy array arr?

A mask = arr < 10

B mask = arr = 10

C mask = arr != 10

D mask = arr == 10

The correct syntax for equality comparison is arr == 10, which creates a Boolean mask.

If arr = np.array([2, 5, 7]), what is the result of arr[arr < 5]?

A array([2])

B array([5, 7])

C array([2, 5])

D array([7])

Only 2 is less than 5, so the filtered array contains just 2.

Can Boolean indexing be combined with multiple conditions in numpy?

A No, only one condition is allowed

B Yes, but only with or operator

C Yes, using & and | operators with parentheses

D No, Boolean indexing does not support conditions

Multiple conditions can be combined using & (and) and | (or) with parentheses to group conditions.

What shape must a Boolean mask have to filter a numpy array?

A The same shape as the array

B Any shape smaller than the array

C Only 1D shape

D Shape does not matter

The Boolean mask must have the same shape as the array to correctly filter elements.

Explain how Boolean indexing works in numpy and give a simple example.

Think about how True/False values select elements.

Describe how to filter a numpy array with multiple conditions using Boolean indexing.

Remember to use parentheses around each condition.

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