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Fancy Indexing with Integer Arrays0%
Fancy Indexing with Integer Arrays
Beginner12 min read•Updated: Jul 11, 2026
Fancy Indexing with Integer Arrays
In NumPy terminology, Fancy Indexing refers to indexing an array using arrays or sequences of integer indices rather than basic integer scalars or slice objects (start:stop:step).
While basic slicing allows you to extract regularly spaced sub-grids, fancy indexing provides complete freedom to access, reorder, or duplicate arbitrary elements across any dimension.
Click to Zoom1. 1D Fancy Indexing
To select elements at non-contiguous positions, pass a Python list or NumPy array of integers representing the desired target indices:
import numpy as np
data = np.array([100, 200, 300, 400, 500, 600, 700, 800])
# Select elements at index 1, 4, and 6
indices = [1, 4, 6]
subset = data[indices]
print("Selected elements:", subset)
# You can reorder, repeat, or reverse indices freely:
repeated = data[[0, 0, 7, 2, 7]]
print("Repeated selection:", repeated)
# Negative integers count backward from the end:
tail_elements = data[[-1, -3]]
print("Negative indices:", tail_elements)
Output:
Selected elements: [200 500 700]
Repeated selection: [100 100 800 300 800]
Negative indices: [800 600]
2. Multi-Dimensional Fancy Indexing
When working with 2D or N-dimensional matrices, fancy indexing allows row selection, column selection, or simultaneous point-coordinate extraction.
Selecting Specific Rows:
matrix = np.arange(1, 26).reshape(5, 5)
print("Original 5x5 Matrix:
", matrix)
# Extract row 0, row 2, and row 4
rows = matrix[[0, 2, 4]]
print("
Selected Rows (0, 2, 4):
", rows)
Coordinate-Based Indexing vs Rectangular Sub-grids:
When you pass two integer arrays matrix[rows, cols], NumPy pairs the indices element-by-element like coordinates (r0, c0), (r1, c1), (r2, c2), rather than taking a cross-product matrix:
# Extract matrix[0, 1], matrix[2, 3], and matrix[4, 0]
r = [0, 2, 4]
c = [1, 3, 0]
points = matrix[r, c]
print("
Extracted points at coordinates:", points)
Output:
Extracted points at coordinates: [ 2 14 21]
If you instead want a rectangular sub-grid (the cross-product of those rows and columns), combine integer slicing with np.ix_():
# Sub-matrix of rows [0, 2] and columns [1, 3]
subgrid = matrix[np.ix_([0, 2], [1, 3])]
print("
Rectangular sub-grid using np.ix_:
", subgrid)
3. Critical Difference: View vs Copy
This is one of the most vital architectural rules in NumPy:
| Indexing Technique | Memory Behavior | Modification Effect |
|---|---|---|
Basic Slicing (arr[1:4]) | Returns a VIEW (shared memory buffer) | Modifying view mutates original array |
Fancy Indexing (arr[[1, 4]]) | Returns a COPY (new memory allocation) | Modifying copy has NO effect on original |
Boolean Masking (arr[arr > 0]) | Returns a COPY (new memory allocation) | Modifying copy has NO effect on original |
arr = np.array([10, 20, 30, 40, 50])
# Fancy indexing creates an independent copy
copy_subset = arr[[1, 2]]
copy_subset[0] = 999
print("Original arr:", arr) # Unchanged: [10, 20, 30, 40, 50]
print("Copy subset:", copy_subset) # [999, 30]
4. In-Place Mutation with Fancy Indexing
Even though reading with fancy indexing yields a copy, assigning to fancy-indexed positions modifies the original array in-place:
board = np.zeros((4, 4), dtype=int)
# Set specific coordinates to 1
target_rows = [0, 1, 2, 3]
target_cols = [3, 2, 1, 0]
board[target_rows, target_cols] = 1
print("Board with anti-diagonal 1s:
", board)
Caution: Repeated Index Assignment Pitfall
If an index appears multiple times during in-place assignment, the assignment happens sequentially, but with operators like +=, repeated increments might only execute once unless you use np.add.at():
counter = np.zeros(5, dtype=int)
indices = [1, 1, 1, 3]
# Direct addition does NOT add 3 times!
counter[indices] += 1
print("Direct += assignment:", counter) # [0 1 0 1 0] -> incremented only once!
# Correct way for repeated index accumulation:
counter = np.zeros(5, dtype=int)
np.add.at(counter, indices, 1)
print("np.add.at() result:", counter) # [0 3 0 1 0] -> incremented 3 times!
Interactive Quiz
Multiple Choice Questions
Question 1
What does fancy indexing in NumPy return when selecting elements from an array?
Question 2
Given
matrix = np.arange(16).reshape(4, 4), what is the output of matrix[[0, 1], [2, 3]]?Question 3
Which NumPy function constructs an open mesh to extract a rectangular sub-grid using fancy indexing?
Question 4
If
arr = np.array([10, 20, 30]) and you execute idx = [0, 1]; sub = arr[idx]; sub[0] = 99, what is the value of arr[0]?Question 5
Why does
counter[[0, 0, 0]] += 1 fail to increment counter[0] by 3?Next Lesson
Conditional Selectors: np.where(), np.select() & np.extract()
Continue learning with hands-on practice, examples, and exercises in the upcoming topic.
Related Lessons
| Previous Lesson | Next Lesson |
|---|---|
| Boolean Masking & Conditional Filtering | Conditional Selectors: np.where(), np.select() & np.extract() |
Practice Quiz
Test your understanding of this lesson with 5 questions. Each question has one correct answer.