Negative indexing in NumPy

Introduction

Negative indexing helps you access elements from the end of a list or array easily. It saves time when you want to get last items without counting the total length.

You want the last element of a data array without knowing its length.

You need to slice the last few rows of a dataset quickly.

You want to access elements from the end in a loop or function.

You are working with time series data and want recent values.

You want to reverse access without creating a reversed copy.

Syntax

NumPy

array[-index]

Index -1 means the last element, -2 means second last, and so on.

This works the same way for 1D and multi-dimensional arrays.

Examples

Prints the last element of the array, which is 50.

NumPy

import numpy as np
arr = np.array([10, 20, 30, 40, 50])
print(arr[-1])

Prints the third last element, which is 30.

NumPy

print(arr[-3])

Accesses the last row and second last column, printing 8.

NumPy

matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print(matrix[-1, -2])

Sample Program

This program shows how to use negative indexing to get elements from the end of 1D and 2D numpy arrays.

NumPy

import numpy as np

# Create a 1D array
numbers = np.array([5, 10, 15, 20, 25])

# Access last element using negative index
last_element = numbers[-1]

# Access second last element
second_last = numbers[-2]

# Create a 2D array
matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Access element from last row, last column
element = matrix[-1, -1]

print(f"Last element in numbers: {last_element}")
print(f"Second last element in numbers: {second_last}")
print(f"Element from last row and last column in matrix: {element}")

Important Notes

Negative indexing is very handy for quick access but be careful not to use an index smaller than -length, or it will cause an error.

It works well with slicing too, like arr[-3:] to get last three elements.

Summary

Negative indexing lets you count from the end of arrays easily.

-1 is the last element, -2 is second last, and so on.

It works for both 1D and multi-dimensional numpy arrays.

Practice

1. What does negative indexing in a numpy array allow you to do?

easy

A. Sort the array in descending order

B. Access elements starting from the end of the array

C. Change the size of the array

D. Access elements only at the beginning of the array

Solution

1. Step 1: Understand negative indexing concept

   Negative indexing means counting elements from the end of the array, starting at -1 for the last element.

2. Step 2: Compare options with concept

   Only Access elements starting from the end of the array correctly describes accessing elements from the end using negative indexes.

3. Final Answer:

   Access elements starting from the end of the array -> Option B

4. Quick Check:

   Negative indexing = Access from end [OK]

Hint: Negative index -1 means last element [OK]

Common Mistakes:

• Thinking negative index changes array size
• Confusing negative indexing with sorting
• Assuming negative index accesses start only at beginning

2. Which of the following is the correct syntax to get the last element of a numpy array arr using negative indexing?

easy

A. arr[0]

B. arr[1]

C. arr[-0]

D. arr[-1]

Solution

1. Step 1: Recall negative index for last element

   In numpy, -1 is used to access the last element of an array.

2. Step 2: Check each option

   arr[-1] uses arr[-1] which correctly accesses the last element. Others do not.

3. Final Answer:

   arr[-1] -> Option D

4. Quick Check:

   Last element = arr[-1] [OK]

Hint: Use arr[-1] for last element [OK]

Common Mistakes:

• Using arr[-0] which is same as arr[0]
• Using positive index 1 which is second element
• Confusing zero index with negative zero

3. Given the numpy array arr = np.array([10, 20, 30, 40, 50]), what is the output of arr[-3]?

medium

A. 20

B. 40

C. 30

D. 50

Solution

1. Step 1: Understand negative index -3

   Negative index -3 means counting from the end: last is -1 (50), second last -2 (40), third last -3 (30).

2. Step 2: Identify element at index -3

   The element at arr[-3] is 30.

3. Final Answer:

   30 -> Option C

4. Quick Check:

   arr[-3] = 30 [OK]

Hint: Count backward: -1 last, -2 second last, -3 third last [OK]

Common Mistakes:

• Counting negative index from start instead of end
• Mixing up index -3 with positive index 3
• Off-by-one errors in counting

4. Consider the code snippet:

import numpy as np
arr = np.array([5, 10, 15, 20])
print(arr[-5])

What is the error in this code?

medium

A. IndexError: index -5 is out of bounds for axis 0 with size 4

B. SyntaxError due to negative index

C. Prints 5

D. Prints 20

Solution

1. Step 1: Check array size and index used

   Array has 4 elements, valid negative indexes are -1 to -4.

2. Step 2: Understand index -5 usage

   Index -5 is outside valid range, causing IndexError.

3. Final Answer:

   IndexError: index -5 is out of bounds for axis 0 with size 4 -> Option A

4. Quick Check:

   Negative index out of range = IndexError [OK]

Hint: Negative index must be >= -array length [OK]

Common Mistakes:

• Assuming negative index wraps around infinitely
• Thinking negative index causes syntax error
• Expecting last element instead of error

5. You have a 2D numpy array arr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]). What does arr[-1, -2] return?

hard

A. 8

B. 7

C. 6

D. 9

Solution

1. Step 1: Understand negative indexing in 2D arrays

   For rows, -1 means last row: [7, 8, 9]. For columns, -2 means second last column.

2. Step 2: Identify element at arr[-1, -2]

   Last row is [7, 8, 9], second last column is element 8.

3. Final Answer:

   8 -> Option A

4. Quick Check:

   arr[-1, -2] = 8 [OK]

Hint: Negative indexes count from end in each dimension [OK]

Common Mistakes:

• Mixing row and column indexes
• Using positive indexes instead of negative
• Confusing which axis negative index applies to