Multi-dimensional fancy indexing in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is multi-dimensional fancy indexing in NumPy?

It is a way to select elements from a NumPy array using arrays of indices for each dimension, allowing complex and flexible selection of elements.

beginner

How does multi-dimensional fancy indexing differ from simple slicing?

Simple slicing uses ranges and steps to select continuous blocks, while fancy indexing uses arrays of indices to select arbitrary elements, possibly non-contiguous and repeated.

intermediate

Given a 2D array, what happens if you use two index arrays of the same shape for fancy indexing?

NumPy selects elements at positions specified by pairs of indices from the two arrays, element-wise, producing an output array of the same shape as the index arrays.

intermediate

Why is multi-dimensional fancy indexing useful in data science?

It allows selecting and manipulating specific elements or patterns in data arrays efficiently, which is helpful for filtering, transforming, or extracting data subsets.

intermediate

What is the output shape when using multi-dimensional fancy indexing with index arrays of shape (3, 2)?

The output array will have the same shape (3, 2), with each element selected according to the corresponding indices in the index arrays.

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

A Change array data types

B Only slice arrays with start, stop, step

C Sort arrays in place

D Select elements using arrays of indices for each dimension

Multi-dimensional fancy indexing uses arrays of indices to select elements from each dimension.

If you have a 2D array and use two index arrays of shape (2, 3), what will be the shape of the output?

A (3, 2)

B (6,)

C (2, 3)

D (2,)

The output shape matches the shape of the index arrays used for fancy indexing.

Which of the following is NOT true about fancy indexing?

A It can select repeated elements

B It returns a view of the original array

C It can select elements in any order

D It uses arrays of indices

Fancy indexing returns a copy, not a view, of the selected elements.

What happens if index arrays used in multi-dimensional fancy indexing have different shapes?

A NumPy broadcasts them to a common shape

B An error is raised

C Only the first index array is used

D The output shape is the shape of the larger array

NumPy broadcasts index arrays to a common shape before selecting elements.

Why might you use multi-dimensional fancy indexing instead of loops?

A It is faster and uses vectorized operations

B It is slower but easier to read

C It uses less memory but is slower

D It only works for 1D arrays

Fancy indexing is vectorized and usually faster than explicit loops.

Explain how multi-dimensional fancy indexing works in NumPy with an example.

Think about how you pick elements by row and column indices stored in arrays.

Describe the difference between slicing and multi-dimensional fancy indexing.

Consider how you select elements in a list versus picking specific positions.

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