2D array indexing (row, col) in NumPy

Introduction

We use 2D array indexing to find or change values in a table-like structure by pointing to its row and column.

Looking up a specific value in a spreadsheet-like data.

Changing a pixel color in an image represented as a 2D array.

Extracting a row or column from a dataset for analysis.

Updating a cell in a game board like tic-tac-toe.

Accessing sensor data arranged by time and sensor number.

Syntax

NumPy

import numpy as np

# Create a 2D array
array_2d = np.array([[1, 2, 3],
                     [4, 5, 6],
                     [7, 8, 9]])

# Access element at row i, column j
value = array_2d[i, j]

# Change element at row i, column j
array_2d[i, j] = new_value

Rows and columns start counting from 0, so the first row is 0, the first column is 0.

Use comma inside the square brackets to separate row and column indices.

Examples

Accessing the top-left element (row 0, column 0).

NumPy

import numpy as np

array_2d = np.array([[10, 20, 30],
                     [40, 50, 60],
                     [70, 80, 90]])

# Access element at first row, first column
print(array_2d[0, 0])  # Output: 10

Edge case: array with only one element.

NumPy

import numpy as np

array_2d = np.array([[5]])

# Access the only element in a 1x1 array
print(array_2d[0, 0])  # Output: 5

Edge case: empty 2D array has no elements to access.

NumPy

import numpy as np

array_2d = np.array([]).reshape(0, 0)

# Trying to access element in empty array will cause error
# print(array_2d[0, 0])  # This will raise IndexError

Changing the bottom-right element (row 2, column 2) to 99.

NumPy

import numpy as np

array_2d = np.array([[1, 2, 3],
                     [4, 5, 6],
                     [7, 8, 9]])

# Change element at last row, last column
array_2d[2, 2] = 99
print(array_2d)

Sample Program

This program creates a 3x3 array, prints it, accesses one element, then changes another element and prints the updated array.

NumPy

import numpy as np

# Create a 3x3 2D array
array_2d = np.array([[1, 2, 3],
                     [4, 5, 6],
                     [7, 8, 9]])

print("Original array:")
print(array_2d)

# Access element at row 1, column 2
value = array_2d[1, 2]
print(f"Value at row 1, column 2: {value}")

# Change element at row 0, column 1
array_2d[0, 1] = 20
print("Array after changing element at row 0, column 1 to 20:")
print(array_2d)

Important Notes

Time complexity for accessing or changing one element is O(1) - very fast.

Space complexity depends on the array size, but indexing itself uses no extra space.

Common mistake: forgetting that indexing starts at 0, so row 1 is actually the second row.

Use 2D indexing when you want to work with specific cells; use slicing if you want whole rows or columns.

Summary

2D array indexing uses [row, column] to find or change values.

Rows and columns start at 0, so count carefully.

Accessing or changing one element is very fast and simple.

Practice

1. What does arr[2, 1] mean when arr is a 2D numpy array?

easy

A. Access the element in the 3rd row and 2nd column

B. Access the element in the 2nd row and 3rd column

C. Access the entire 2nd row

D. Access the entire 1st column

Solution

1. Step 1: Understand zero-based indexing

   In numpy, counting starts at 0, so index 2 means the 3rd row, and index 1 means the 2nd column.

2. Step 2: Interpret the indexing

   arr[2, 1] accesses the element at row 3, column 2.

3. Final Answer:

   Access the element in the 3rd row and 2nd column -> Option A

4. Quick Check:

   Row 2, Col 1 means 3rd row, 2nd column [OK]

Hint: Remember: rows and columns start counting at zero [OK]

Common Mistakes:

• Confusing row and column order
• Starting count from 1 instead of 0
• Thinking arr[2,1] returns a row or column

2. Which of the following is the correct syntax to access the element in the 1st row and 3rd column of a numpy 2D array arr?

easy

A. arr[1, 3]

B. arr[0, 2]

C. arr[3, 1]

D. arr[2, 0]

Solution

1. Step 1: Recall zero-based indexing

   The 1st row is index 0, and the 3rd column is index 2.

2. Step 2: Match indexes to syntax

   So, arr[0, 2] accesses the element in the 1st row and 3rd column.

3. Final Answer:

   arr[0, 2] -> Option B

4. Quick Check:

   Row 0, Col 2 = 1st row, 3rd column [OK]

Hint: Count rows and columns from zero for correct indexing [OK]

Common Mistakes:

• Using 1-based indexes like arr[1,3]
• Swapping row and column indexes
• Using parentheses instead of brackets

3. Given the numpy array:

import numpy as np
arr = np.array([[5, 10, 15], [20, 25, 30], [35, 40, 45]])
print(arr[1, 2])

What is the output?

medium

A. 30

B. 25

C. 20

D. 45

Solution

1. Step 1: Identify the element at row 1, column 2

   Row 1 is the second row: [20, 25, 30]. Column 2 is the third element in that row, which is 30.

2. Step 2: Confirm the printed value

   The code prints arr[1, 2], so the output is 30.

3. Final Answer:

   30 -> Option A

4. Quick Check:

   arr[1,2] = 30 [OK]

Hint: Remember row then column to find the element [OK]

Common Mistakes:

• Choosing element from wrong row or column
• Confusing zero-based indexing
• Reading the array incorrectly

4. What is wrong with this code snippet?

import numpy as np
arr = np.array([[1, 2], [3, 4]])
print(arr[2, 0])

medium

A. Prints 3 correctly

B. SyntaxError due to wrong brackets

C. IndexError because row 2 does not exist

D. Prints 1 correctly

Solution

1. Step 1: Check array shape and indexes

   The array has 2 rows (index 0 and 1). Index 2 for row is out of range.

2. Step 2: Understand error type

   Accessing arr[2, 0] causes an IndexError because row 2 does not exist.

3. Final Answer:

   IndexError because row 2 does not exist -> Option C

4. Quick Check:

   Row index 2 is invalid for 2-row array [OK]

Hint: Check array shape before indexing to avoid errors [OK]

Common Mistakes:

• Assuming indexing starts at 1
• Ignoring array shape
• Confusing error types

5. You have a 4x4 numpy array arr filled with numbers 1 to 16 in row-major order. Which code correctly changes the element in the last row and second column to 100?

hard

A. arr[3, -2] = 100

B. arr[4, 2] = 100

C. arr[-1, 2] = 100

D. arr[3, 1] = 100

Solution

1. Step 1: Identify last row and second column indexes

   For a 4x4 array, rows and columns are indexed 0 to 3. Last row is index 3, second column is index 1.

2. Step 2: Check each option

   arr[3, 1] = 100 uses arr[3, 1] which is correct. arr[4, 2] = 100 uses invalid index 4. arr[-1, 2] = 100 uses column index 2 (third column), not second. arr[3, -2] = 100 uses negative index -2 for column which is the third column, not second.

3. Final Answer:

   arr[3, 1] = 100 -> Option D

4. Quick Check:

   Last row = 3, second column = 1 [OK]

Hint: Use zero-based indexes: last row is size-1, second column is 1 [OK]

Common Mistakes:

• Using out-of-range indexes like 4
• Confusing negative indexes for columns
• Mixing row and column positions