Multi-dimensional fancy indexing in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of multi-dimensional fancy indexing with arrays

What is the output of the following code snippet using NumPy fancy indexing?

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)

A [30 50 70]

B [10 50 90]

C [30 40 90]

D [10 20 30]

💡 Hint

Remember that arr[rows, cols] selects elements at positions (rows[i], cols[i]) for each i.

The code selects elements at positions (0,2), (1,1), and (2,0) from the array, which are 30, 50, and 70 respectively.

❓ data_output

intermediate

Shape of result from multi-dimensional fancy indexing

Given the code below, what is the shape of the resulting array 'result'?

NumPy

import numpy as np
arr = np.arange(27).reshape(3,3,3)
rows = np.array([0, 1])
cols = np.array([1, 2])
result = arr[rows, cols]
print(result.shape)

A (2, 2)

B (2, 3)

C (3, 3)

D (3, 2)

💡 Hint

Check how fancy indexing with two arrays affects the shape when indexing a 3D array.

The indexing arr[rows, cols] selects elements at (0,1) and (1,2), each is a 1D array of length 3, so the result shape is (2,3).

🔧 Debug

advanced

Identify the error in multi-dimensional fancy indexing

What error does the following code raise when executed?

NumPy

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

A No error, outputs [2 3 4]

B ValueError: shape mismatch between rows and cols

C TypeError: unsupported operand type(s) for indexing

D IndexError: index 2 is out of bounds for axis 0 with size 2

💡 Hint

Check the size of the array and the indices used for rows.

The array has shape (2,2), so index 2 for rows is out of bounds causing IndexError.

🚀 Application

advanced

Extract diagonal elements using multi-dimensional fancy indexing

Which option correctly extracts the diagonal elements from a 2D NumPy array 'arr' using fancy indexing?

NumPy

import numpy as np
arr = np.array([[5, 6, 7], [8, 9, 10], [11, 12, 13]])

A arr[np.arange(3), np.arange(3)]

B arr[[0,1,2], [2,1,0]]

C arr[:, np.arange(3)]

D arr[np.arange(3), 0]

💡 Hint

Diagonal elements have the same row and column indices.

Using arr[np.arange(3), np.arange(3)] selects elements where row and column indices are equal, which are the diagonal elements.

🧠 Conceptual

expert

Effect of broadcasting in multi-dimensional fancy indexing

Given the code below, what is the shape of 'result' and why?

NumPy

import numpy as np
arr = np.arange(24).reshape(4,6)
rows = np.array([[0], [1], [2]])
cols = np.array([1, 3, 5])
result = arr[rows, cols]
print(result.shape)

A (1, 3) because rows is 2D and cols is 1D, resulting in minimal broadcast

B (4, 6) because fancy indexing returns the original array shape

C (3, 3) because rows and cols broadcast to shape (3,3) and select elements accordingly

D (3,) because rows and cols are flattened before indexing

💡 Hint

Consider how NumPy broadcasts arrays of shapes (3,1) and (3,) for indexing.

rows has shape (3,1) and cols has shape (3,), which broadcast to (3,3). The result shape matches this broadcasted shape.

Practice

1. What does multi-dimensional fancy indexing in NumPy allow you to do?

easy

A. Change the shape of the array without copying data.

B. Sort the array elements in ascending order.

C. Calculate the sum of all elements in the array.

D. Select specific elements from an array using lists of row and column indices.

Solution

1. Step 1: Understand the concept of fancy indexing

   Fancy indexing uses arrays or lists of indices to select elements from an array.

2. Step 2: Apply to multi-dimensional arrays

   In multi-dimensional fancy indexing, you provide lists of row and column indices to pick specific elements scattered in the array.

3. Final Answer:

   Select specific elements from an array using lists of row and column indices. -> Option D

4. Quick Check:

   Fancy indexing = element selection by index lists [OK]

Hint: Fancy indexing picks elements by matching row and column lists [OK]

Common Mistakes:

• Confusing fancy indexing with sorting
• Thinking it reshapes arrays
• Assuming it sums elements

2. Which of the following is the correct syntax for multi-dimensional fancy indexing in NumPy to select elements at rows [0, 2] and columns [1, 3] from array arr?

easy

A. arr[[0, 2], [1, 3]]

B. arr[0, 2, 1, 3]

C. arr[0:2, 1:3]

D. arr[[0, 1], [2, 3]]

Solution

1. Step 1: Recall fancy indexing syntax

   Multi-dimensional fancy indexing uses two lists inside square brackets: one for rows, one for columns.

2. Step 2: Match given indices

   To select elements at rows 0 and 2, columns 1 and 3, syntax is arr[[0, 2], [1, 3]].

3. Final Answer:

   arr[[0, 2], [1, 3]] -> Option A

4. Quick Check:

   Two index lists inside brackets = correct fancy indexing [OK]

Hint: Use two lists inside brackets for rows and columns [OK]

Common Mistakes:

• Using slicing instead of lists
• Mixing row and column indices in one list
• Using incorrect bracket placement

3. Given the array arr = np.array([[10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120]]), what is the output of arr[[0, 2], [1, 3]]?

medium

A. [20 120]

B. [20 40]

C. [10 120]

D. [50 110]

Solution

1. Step 1: Identify indices from fancy indexing

   Rows are [0, 2], columns are [1, 3]. So elements are arr[0,1] and arr[2,3].

2. Step 2: Find elements at these positions

   arr[0,1] = 20, arr[2,3] = 120, so output is [20 120].

3. Final Answer:

   [20 120] -> Option A

4. Quick Check:

   Elements at (0,1) and (2,3) = [20 120] [OK]

Hint: Match row and column indices element-wise [OK]

Common Mistakes:

• Selecting entire rows or columns instead of elements
• Mixing up row and column indices
• Expecting a 2D array output

4. What error will occur when running the code below?

import numpy as np
arr = np.array([[1,2,3],[4,5,6]])
rows = [0,1]
cols = [1]
print(arr[rows, cols])

medium

A. ValueError because arr is 2D

B. SyntaxError because of wrong brackets

C. IndexError due to mismatched index array shapes

D. No error, prints [2 5]

Solution

1. Step 1: Check shapes of index arrays

   rows has length 2, cols has length 1; shapes differ.

2. Step 2: Understand fancy indexing requirements

   Fancy indexing requires index arrays to have the same shape for element-wise selection.

3. Final Answer:

   IndexError due to mismatched index array shapes -> Option C

4. Quick Check:

   Index arrays must match shape [OK]

Hint: Index arrays must be same shape for fancy indexing [OK]

Common Mistakes:

• Assuming different length index lists work
• Confusing syntax error with runtime error
• Expecting partial output without error

5. You have a 3x4 array data representing sales for 3 stores (rows) over 4 months (columns). You want to select sales for store 0 in month 1, store 2 in month 3, and store 1 in month 0 using multi-dimensional fancy indexing. Which code correctly extracts these values?

hard

A. data[[0, 1, 2], [1, 3, 0]]

B. data[[0, 2, 1], [1, 3, 0]]

C. data[[1, 3, 0], [0, 2, 1]]

D. data[[0, 2, 1]][[1, 3, 0]]

Solution

1. Step 1: Match stores and months as row and column indices

   Stores: 0, 2, 1 correspond to rows; months: 1, 3, 0 correspond to columns.

2. Step 2: Use multi-dimensional fancy indexing syntax

   Use data[[0, 2, 1], [1, 3, 0]] to select elements at these positions element-wise.

3. Final Answer:

   data[[0, 2, 1], [1, 3, 0]] -> Option B

4. Quick Check:

   Row and column lists match stores and months [OK]

Hint: Pair store and month indices in two lists for fancy indexing [OK]

Common Mistakes:

• Swapping row and column lists
• Using chained indexing instead of fancy indexing
• Mismatching lengths of index lists