Multi-dimensional fancy indexing in NumPy - Step-by-Step Execution

Concept Flow - Multi-dimensional fancy indexing

Create 2D array

↓

Define index arrays for rows and columns

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Use fancy indexing: array[rows, cols

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Extract elements at specified positions

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Result: 1D array of selected elements

We start with a 2D array, then pick specific rows and columns using arrays of indices, and finally extract elements at those positions into a new array.

Execution Sample

NumPy

import numpy as np
arr = np.array([[10,20,30],[40,50,60],[70,80,90]])
rows = np.array([0,1,2])
cols = np.array([2,1,0])
result = arr[rows, cols]
print(result)

This code selects elements from a 2D array at positions (0,2), (1,1), and (2,0) using fancy indexing.

Execution Table

Step	Action	rows array	cols array	Indexed Elements	Result
1	Create 2D array	-	-	-	[[10 20 30] [40 50 60] [70 80 90]]
2	Define rows indices	[0,1,2]	-	-	-
3	Define cols indices	-	[2,1,0]	-	-
4	Apply fancy indexing arr[rows, cols]	[0,1,2]	[2,1,0]	[arr[0,2], arr[1,1], arr[2,0]]	[30 50 70]
5	Print result	-	-	-	[30 50 70]
6	End	-	-	-	Execution complete

💡 All specified indices processed, fancy indexing returns selected elements as 1D array.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
arr	-	[[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]]	[[10 20 30] [40 50 60] [70 80 90]]
rows	-	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]
cols	-	-	[2,1,0]	[2,1,0]	[2,1,0]
result	-	-	-	-	[30 50 70]

Key Moments - 3 Insights

Why does the result have length 3 instead of being a 2D array?

Because fancy indexing with arrays of indices selects elements pairwise from each (row, col) index, returning a 1D array of those elements as shown in execution_table step 4.

What happens if rows and cols arrays have different lengths?

Numpy raises an error because fancy indexing requires the row and column index arrays to have the same shape to pair elements correctly, as implied in step 4.

Why do we use arrays for rows and cols instead of lists?

Numpy fancy indexing works best with numpy arrays for efficient element-wise pairing and broadcasting, as shown in variable_tracker steps 2 and 3.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what element does arr[1,1] correspond to?

A 20

B 50

C 70

D 30

💡 Hint

Check the 'Indexed Elements' column at step 4 in execution_table.

At which step do we get the final result array [30, 50, 70]?

A Step 2

B Step 5

C Step 4

D Step 3

💡 Hint

Look at the 'Result' column in execution_table rows for step 4.

If we change cols to [0,0,0], what will be the result array?

A [10, 40, 70]

B [30, 50, 70]

C [10, 50, 90]

D [30, 40, 70]

💡 Hint

Refer to variable_tracker for cols array and how indexing pairs rows and cols.

Concept Snapshot

Multi-dimensional fancy indexing lets you pick elements from a numpy array using arrays of row and column indices.
Syntax: arr[rows_array, cols_array]
Rows and cols arrays must be same shape.
Result is a 1D array of elements at paired indices.
Useful for selecting scattered elements efficiently.

Full Transcript

We start with a 2D numpy array and two arrays of indices for rows and columns. Using fancy indexing, we select elements at positions defined by pairing each row index with the corresponding column index. This returns a 1D array of those elements. The process requires the row and column index arrays to have the same shape. This method is useful to extract specific elements scattered across the array efficiently.