Combining fancy and slice indexing in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is fancy indexing in numpy?

Fancy indexing means selecting elements from an array using another array of indices. It allows picking specific elements in any order.

beginner

How does slice indexing differ from fancy indexing?

Slice indexing selects a continuous range of elements using start:stop:step syntax, while fancy indexing selects elements at specific positions given by an array of indices.

intermediate

What happens when you combine fancy and slice indexing in numpy?

You can select specific rows or columns using fancy indexing and then select a slice of elements within those rows or columns. This lets you pick complex subsets of data.

beginner

Example: Given a 2D array, how to select rows 1 and 3, and columns 2 to 4?

Use arr[[1, 3], 2:5] to select rows 1 and 3 with columns from 2 up to 4 (5 is exclusive).

intermediate

Why is the order of fancy and slice indexing important in numpy?

The order matters because numpy first applies fancy indexing to select specific rows or columns, then applies slicing on the result. Changing order can change the output shape and values.

What does arr[[0, 2], 1:3] select from a 2D numpy array arr?

A Rows 1 and 3, columns 0 and 2

B Columns 0 and 2, rows 1 and 3

C Rows 0 and 2, columns 1 and 2

D Rows 0 to 2, columns 1 to 3

Fancy indexing selects rows 0 and 2, then slice 1:3 selects columns 1 and 2.

Which indexing method allows selecting elements at arbitrary positions in numpy?

A Fancy indexing

B None of the above

C Boolean indexing

D Slice indexing

Fancy indexing uses arrays of indices to select arbitrary elements.

What is the result shape of arr[[1, 2], 0:2] if arr has shape (4, 5)?

A (4, 2)

B (2, 2)

C (2, 5)

D (4, 5)

Selecting 2 rows (1 and 2) and slicing 2 columns results in shape (2, 2).

Can you combine fancy indexing on rows with slice indexing on columns in numpy?

A Yes, like arr[[0, 3], 1:4]

B No, numpy does not allow mixing

C Only if array is 1D

D Only if array is 3D

Numpy supports combining fancy and slice indexing on different axes.

What happens if you reverse the order: arr[1:3, [0, 2]] instead of arr[[1, 3], 0:2]?

A Selects all rows and columns

B Selects rows 1 and 3, columns 0 and 1

C Raises an error

D Selects rows 1 and 2, columns 0 and 2

Slice selects rows 1 and 2, fancy indexing selects columns 0 and 2.

Explain how to combine fancy and slice indexing to select specific rows and a range of columns from a 2D numpy array.

Think about selecting rows first, then columns.

Describe the difference between fancy indexing and slice indexing and how they can be used together in numpy.

Compare how each indexing method selects elements.

Practice

1. What does combining fancy indexing and slice indexing in NumPy allow you to do?
arr[[0, 2], 1:4] selects:

easy

A. Rows 0 to 2, columns 1 and 4

B. Rows 1 to 4, columns 0 and 2

C. Rows 0 and 2, columns 1 to 3

D. Rows 1 and 4, columns 0 to 2

Solution

1. Step 1: Understand fancy indexing for rows

   The fancy index [0, 2] selects rows 0 and 2 specifically.

2. Step 2: Understand slice indexing for columns

   The slice 1:4 selects columns starting at 1 up to but not including 4, so columns 1, 2, and 3.

3. Final Answer:

   Rows 0 and 2, columns 1 to 3 -> Option C

4. Quick Check:

   Fancy rows + slice columns = selected subarray [OK]

Hint: Fancy picks rows, slice picks continuous columns [OK]

Common Mistakes:

• Confusing rows and columns in indexing
• Forgetting slice end is exclusive
• Mixing up fancy and slice roles

2. Which of the following is the correct syntax to select rows 1 and 3 and columns 2 to 4 from a NumPy array arr?

easy

A. arr[[1, 3], 2:5]

B. arr[1:3, 2:5]

C. arr[1, 3, 2:5]

D. arr[[1, 3], [2:5]]

Solution

1. Step 1: Identify fancy indexing for rows

   To select rows 1 and 3, use fancy indexing with a list: [1, 3].

2. Step 2: Use slice for columns

   To select columns 2 to 4, use slice 2:5 (end exclusive).

3. Final Answer:

   arr[[1, 3], 2:5] -> Option A

4. Quick Check:

   Fancy rows + slice columns syntax correct [OK]

Hint: Fancy indexing uses lists, slice uses colon syntax [OK]

Common Mistakes:

• Using commas inside fancy index list
• Using slice inside list brackets
• Incorrect slice end index

3. Given the array:

import numpy as np
arr = np.array([[10, 20, 30, 40],
                [50, 60, 70, 80],
                [90, 100, 110, 120],
                [130, 140, 150, 160]])
print(arr[[1, 3], 1:3])

What is the output?

medium

A. [[ 70 80]
[150 160]]

B. [[ 60 70]
[140 150]]

C. [[ 50 60]
[130 140]]

D. [[ 60 70 80]
[140 150 160]]

Solution

1. Step 1: Select rows using fancy indexing

   Rows 1 and 3 are:
   [50, 60, 70, 80]
   [130, 140, 150, 160]

2. Step 2: Select columns 1 to 2 (slice 1:3)

   Columns 1 and 2 for these rows are:
   Row 1: 60, 70
   Row 3: 140, 150

3. Final Answer:

   [[ 60 70] [140 150]] -> Option B

4. Quick Check:

   Fancy rows + slice columns output matches [OK]

Hint: Pick rows first, then slice columns [OK]

Common Mistakes:

• Selecting wrong rows or columns
• Including column 3 by mistake
• Confusing row and column indices

4. What is wrong with this code snippet?

import numpy as np
arr = np.arange(16).reshape(4,4)
result = arr[1:3, [0, 2]]
print(result)

medium

A. It prints rows 1 and 2 with columns 0 and 2 correctly

B. It raises an error because slice and fancy indexing cannot be combined

C. It prints rows 0 and 2 with columns 1 and 3 incorrectly

D. It raises an error because the fancy index list is invalid

Solution

1. Step 1: Understand slice and fancy indexing combination

   Slice 1:3 selects rows 1 and 2. Fancy index [0, 2] selects columns 0 and 2.

2. Step 2: Check if code runs and output

   This combination is valid in NumPy and prints the selected subarray without error.

3. Final Answer:

   It prints rows 1 and 2 with columns 0 and 2 correctly -> Option A

4. Quick Check:

   Slice rows + fancy columns works fine [OK]

Hint: Slice and fancy indexing can combine on different axes [OK]

Common Mistakes:

• Thinking slice and fancy indexing cannot mix
• Confusing which axis uses slice or fancy
• Expecting an error when code is valid

5. You have a 5x5 NumPy array arr. You want to select rows 0, 2, and 3, but only columns 1 to 3 inclusive. Which code correctly does this?

hard

A. arr[1:4, [0, 2, 4]]

B. arr[0:5:2, 1:4]

C. arr[[0, 2, 4], [1, 2, 3]]

D. arr[[0, 2, 3], 1:4]

Solution

1. Step 1: Identify fancy indexing for rows

   Rows 0, 2, and 3 are selected using fancy indexing: [0, 2, 3].

2. Step 2: Use slice for columns 1 to 3 inclusive

   Slice 1:4 selects columns 1, 2, and 3 (end index exclusive).

3. Final Answer:

   arr[[0, 2, 3], 1:4] -> Option D

4. Quick Check:

   Fancy rows + slice columns selects correct subarray [OK]

Hint: Fancy list for rows, slice for continuous columns [OK]

Common Mistakes:

• Using slice for rows instead of fancy list
• Using fancy list for columns incorrectly
• Off-by-one error in slice end index