NumPy: Boolean and Fancy Indexing
Last updated: 2026-08-26
1. What You'll Learn
- ❶ Boolean masks — using conditional expressions to generate True/False arrays for filtering
- ❷
np.where— ternary conditional selection and element replacement - ❸ Fancy indexing — selecting elements in arbitrary order with integer arrays
- ❹ Combined indexing — mixing basic and advanced indexing
- ❺ Advanced indexing returns copies — the key difference from views
2. Story
Alice has 100,000 temperature readings and needs to find all readings above 40°C. She writes temps[temps > 40] and gets the result instantly. Bob is amazed: "A Python loop with if statements would take at least 5 lines — NumPy does it in one line, nearly 100x faster!" This is the power of NumPy advanced indexing — complex data filtering with concise expressions.
3. Boolean Masks
(1) What Is a Boolean Mask
A boolean mask is a True/False array with the same shape as the original. NumPy comparison operators work element-wise and return boolean arrays.
PYTHON
import numpy as np
arr = np.array([3, -1, 4, -2, 5])
mask = arr > 0
print(mask) # [ True False True False True]
print(arr[mask]) # [3 4 5]
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
(2) Comparison Operators
| Operator | Meaning | Equivalent Function |
|---|---|---|
> |
Greater than | np.greater |
>= |
Greater or equal | np.greater_equal |
< |
Less than | np.less |
<= |
Less or equal | np.less_equal |
== |
Equal | np.equal |
!= |
Not equal | np.not_equal |
(3) Logical Combinations
Combine multiple conditions with logical operators — use & (and), | (or), ~ (not), not Python's and/or/not. Each condition must be wrapped in parentheses.
PYTHON
arr = np.array([1, 5, 8, 3, 9, 2])
mask = (arr > 3) & (arr < 8) # 3 < arr < 8
print(arr[mask]) # [5]
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
| Logical Op | Meaning | Equivalent Function |
|---|---|---|
& |
Logical AND | np.logical_and |
| |
Logical OR | np.logical_or |
~ |
Logical NOT | np.logical_not |
4. np.where and Conditional Selection
(1) Three-argument form: np.where(condition, x, y)
Returns elements from x where condition is True, from y where False.
PYTHON
import numpy as np
arr = np.array([-3, 5, -1, 8, -2, 7])
result = np.where(arr > 0, arr, 0)
print(result) # [0 5 0 8 0 7]
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
(2) One-argument form: np.where(condition)
Returns the indices where the condition is True.
PYTHON
indices = np.where(arr > 0)
print(indices) # (array([1, 3, 5]),)
print(arr[indices]) # [5 8 7]
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
5. Fancy Indexing
Fancy indexing uses integer arrays to select elements in any order.
PYTHON
import numpy as np
a = np.arange(10) # [0 1 2 3 4 5 6 7 8 9]
# Select specific indices
print(a[[0, 3, 7]]) # [0 3 7]
# Select in any order, with repeats
print(a[[5, 5, 1, 9]]) # [5 5 1 9]
# 2D fancy indexing
b = np.arange(12).reshape(3, 4)
print(b[[0, 2]]) # rows 0 and 2
print(b[:, [0, 2, 3]]) # columns 0, 2, 3 for all rows
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
⚠️ Note: The code below needs to run in a local Python environment.
▶ Example
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
: Boolean mask filtering (Difficulty ⭐)
PYTHON
import numpy as np
scores = np.array([55, 82, 91, 47, 73, 100, 68])
passing = scores[scores >= 60]
print("Passing:", passing) # [82 91 73 100 68]
excellent = scores[scores >= 90]
print("Excellent:", excellent) # [91 100]
# Multiple conditions
mid = scores[(scores >= 60) & (scores < 90)]
print("Mid-range:", mid) # [82 73 68]
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
⚠️ Note: The code below needs to run in a local Python environment.
▶ Example
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
: np.where for conditional replacement (Difficulty ⭐⭐)
PYTHON
import numpy as np
# Clip to range: replace values outside [0, 100]
data = np.array([-5, 120, 30, -20, 80, 200])
clipped = np.where(data < 0, 0, np.where(data > 100, 100, data))
print("Clipped:", clipped) # [ 0 100 30 0 80 100]
# Categorize
grades = np.array([45, 72, 88, 55, 91])
letter = np.where(grades >= 85, 'A',
np.where(grades >= 70, 'B',
np.where(grades >= 60, 'C', 'D')))
print("Grades:", letter) # ['D' 'B' 'A' 'D' 'A']
TEXT
📖 Display only
> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.
⚠️ Note: The code below needs to run in a local Python environment.
6. Comparison Tables
(1) Indexing Methods
| Method | Syntax | Returns | Copies? | Use Case |
|---|---|---|---|---|
| Basic slice | a[1:3] |
View | No | Sub-array, contiguous range |
| Integer index | a[2] |
Scalar | N/A | Single element |
| Boolean mask | a[mask] |
1D array | Yes | Conditional filtering |
| Fancy indexing | a[[1,3,5]] |
Array | Yes | Arbitrary order selection |
| np.where | np.where(cond, x, y) |
Array | Yes | Ternary selection |
(2) Boolean vs Fancy
| Feature | Boolean Mask | Fancy Indexing |
|---|---|---|
| Syntax | arr[arr > 0] |
arr[[1, 3, 5]] |
| Selection logic | Condition-based | Position-based |
| Result shape | 1D (flattened) | Same shape as index array |
| Speed | Fast for large masks | Fast for sparse selection |
▶ Example: 2D fancy indexing with np.ix_ (Difficulty ⭐⭐)
PYTHON
import numpy as np
arr = np.arange(20).reshape(4, 5)
print("Original:\n", arr)
# Select specific rows and columns
rows = [0, 2, 3]
cols = [1, 3]
result = arr[np.ix_(rows, cols)]
print("Rows [0,2,3], Cols [1,3]:\n", result)
# Modify selected elements
arr[np.ix_([0, 1], [0, 4])] = -1
print("After modification:\n", arr)
Output:
TEXT 📖 Display onlyOriginal: [[ 0 1 2 3 4] [ 5 6 7 8 9] [10 11 12 13 14] [15 16 17 18 19]] Rows [0,2,3], Cols [1,3]: [[ 1 3] [11 13] [16 18]] After modification: [[-1 1 2 3 -1] [-1 6 7 8 -1] [10 11 12 13 14] [15 16 17 18 19]]
❓ FAQ
Q Can I use a boolean mask to modify values?
A Yes!
arr[arr > 0] = 0 sets all positive values to 0. This is an in-place modification. np.where(arr > 0, 0, arr) returns a new array instead.Q What's the difference between arr[mask] and np.where(mask)?
A
arr[mask] returns the values where mask is True. np.where(mask) returns the indices where mask is True. Use arr[mask] for the values, np.where(mask) when you need positions.Q Can I use fancy indexing with 2D arrays?
A Yes.
arr[[0,2], [1,3]] selects elements at (0,1) and (2,3). For independent row/column selection, use arr[np.ix_([0,2], [1,3])].Q Do boolean masks always return 1D arrays?
A For 2D+ arrays, yes — the mask flattens the result to 1D. Use
np.where(mask) to get the original shape indices.📖 Summary
- Boolean masks:
arr[arr > 0]— filter by condition, returns a copy - Logical combinations: use
&,|,~with parentheses around each condition np.where(cond, x, y): ternary selection — returns x where True, y where Falsenp.where(cond): returns indices where condition is True- Fancy indexing:
arr[[i1, i2, ...]]— select by arbitrary integer indices - Advanced indexing (boolean + fancy) always returns a copy, not a view
📝 Exercises
-
Beginner (Difficulty ⭐): Create an array of 20 random integers between -10 and 10. Use a boolean mask to extract all positive values. Use
np.whereto replace all negative values with 0. -
Intermediate (Difficulty ⭐⭐): Create a 5x5 array of random integers 0-100. Use boolean masks to: (a) count values above 50, (b) replace values below 20 with 20, (c) extract the row and column indices of all values > 80 using
np.where. -
Advanced (Difficulty ⭐⭐⭐): Create a 10x4 array of student scores (10 students, 4 subjects). Use fancy indexing to: (a) select students at positions [0,3,7] for all subjects, (b) select subjects at positions [1,3] for all students, (c) compute the average of the top 3 students by total score.
