2D array indexing (row, col) in NumPy - Step-by-Step Execution

Concept Flow - 2D array indexing (row, col)

Create 2D array

↓

Choose row index

↓

Choose column index

↓

Access element at (row, col)

↓

Return element value

We start with a 2D array, pick a row and column index, then access the element at that position.

Execution Sample

NumPy

import numpy as np
arr = np.array([[10,20,30],[40,50,60],[70,80,90]])
element = arr[1,2]
print(element)

This code creates a 3x3 array and accesses the element in the 2nd row, 3rd column.

Execution Table

Step	Action	Row Index	Column Index	Element Accessed	Output
1	Create 2D array	-	-	-	[[10 20 30] [40 50 60] [70 80 90]]
2	Select row index	1	-	-	-
3	Select column index	1	2	-	-
4	Access element at (1,2)	1	2	arr[1,2]	60
5	Print element	-	-	-	60

💡 Element at row 1, column 2 is accessed and printed; execution ends.

Variable Tracker

Variable	Start	After Step 1	After Step 4	Final
arr	undefined	[[10 20 30] [40 50 60] [70 80 90]]	[[10 20 30] [40 50 60] [70 80 90]]	[[10 20 30] [40 50 60] [70 80 90]]
element	undefined	undefined	60	60
row index	undefined	undefined	1	1
column index	undefined	undefined	2	2

Key Moments - 3 Insights

Why do we use arr[1,2] instead of arr[1][2]?

In numpy, arr[1,2] accesses the element at row 1, column 2 directly in one step, which is more efficient. arr[1][2] works but accesses row 1 first as a sub-array, then column 2, which is two steps.

What happens if the row or column index is out of range?

An IndexError occurs because numpy arrays have fixed sizes. For example, arr[3,0] is invalid since row 3 does not exist (rows are 0 to 2). See execution_table step 4 for valid indexing.

Are row and column indices zero-based or one-based?

Indices start at 0 in numpy. So row 1 means the second row, column 2 means the third column. This is shown in the execution_table where arr[1,2] accesses the second row, third column.

Visual Quiz - 3 Questions

Look at the execution table, what is the value of 'element' after step 4?

A 50

B 60

C 30

D 40

💡 Hint

Check the 'Element Accessed' and 'Output' columns in step 4 of the execution_table.

At which step is the 2D array 'arr' created?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look at the 'Action' column in the execution_table for when the array is first defined.

If we change the row index to 0 and column index to 1, what element will be accessed?

A 40

B 50

C 20

D 10

💡 Hint

Refer to the variable_tracker for arr values and remember indexing starts at 0.

Concept Snapshot

2D array indexing syntax: arr[row, col]
Indices start at 0 (zero-based).
Access element by specifying row then column.
Out-of-range indices cause errors.
arr[1,2] accesses 2nd row, 3rd column element.
Use arr[row, col] for efficient access.

Full Transcript

This visual trace shows how to access elements in a 2D numpy array using row and column indices. We create a 3x3 array, then pick row 1 and column 2 to get the element 60. Indices start at zero, so row 1 is the second row. The execution table tracks each step: array creation, index selection, element access, and printing. The variable tracker shows how 'arr' and 'element' change. Key moments clarify why numpy uses arr[row, col] syntax, zero-based indexing, and what happens if indices are out of range. The quiz tests understanding of element values and indexing steps.

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