np.unravel_index() for multi-dim positions in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.unravel_index() do in NumPy?

It converts a flat (1D) index into a tuple of coordinate indices for a given shape of a multi-dimensional array.

beginner

How do you use np.unravel_index() to find the 2D position of the flat index 5 in a shape (3, 4)?

Use np.unravel_index(5, (3, 4)). It returns (1, 1), meaning row 1, column 1 in the 3x4 array.

intermediate

What is the output of np.unravel_index([3, 7], (3, 3))?

It returns two arrays: (array([1, 2]), array([0, 1])) which correspond to the row and column indices for flat indices 3 and 7 in a 3x3 array.

beginner

Why is np.unravel_index() useful in real life?

It helps find the position in multi-dimensional data when you only have a single flat index, like finding a seat in a theater when you know the seat number but not the row and column.

intermediate

What happens if you provide a flat index that is out of bounds for the given shape in np.unravel_index()?

NumPy raises an error because the flat index does not fit inside the array shape. The index must be less than the total number of elements.

What does np.unravel_index(8, (3, 3)) return?

A (2, 2)

B (1, 2)

C (0, 8)

D Error

The flat index 8 corresponds to row 2, column 2 in a 3x3 array.

If you have a flat index array [0, 4, 7] and shape (3, 3), what does np.unravel_index() return?

A ([0, 1, 2], [0, 2, 1])

B ([0, 1, 2], [0, 0, 1])

C Error

D ([0, 1, 2], [0, 1, 1])

Flat indices 0, 4, 7 correspond to positions (0,0), (1,1), and (2,1) respectively.

What is the required input for np.unravel_index()?

A Only array shape

B Multi-dimensional index and array shape

C Flat index and array shape

D Only flat index

You need a flat index (or indices) and the shape of the array to convert to multi-dimensional indices.

What happens if you pass a flat index equal to the total number of elements in the array to np.unravel_index()?

A Returns (0, 0, ...)

B Raises an error

C Returns last element's position

D Returns None

Flat indices must be less than the total number of elements; otherwise, an error is raised.

Which of these is a valid use case for np.unravel_index()?

A Finding multi-dimensional coordinates from a flat index

B Flattening a multi-dimensional array

C Sorting array elements

D Calculating mean of array

np.unravel_index() converts flat indices to multi-dimensional coordinates.

Explain how np.unravel_index() helps convert a flat index into multi-dimensional coordinates. Give a simple example.

Think about how a single number can point to a position in a grid.

Describe what happens if you provide an out-of-range flat index to np.unravel_index(). Why is this important?

Consider what happens if you try to find a seat number that doesn't exist.

Practice

1. What does np.unravel_index() do in NumPy?

easy

A. It returns the total number of elements in an array.

B. It converts a flat index into a tuple of coordinate indices for a given shape.

C. It reshapes an array into a new shape without changing data.

D. It flattens a multi-dimensional array into a one-dimensional array.

Solution

1. Step 1: Understand the function purpose

   np.unravel_index() takes a flat index and a shape to find the multi-dimensional coordinates.

2. Step 2: Compare options with function behavior

   Only It converts a flat index into a tuple of coordinate indices for a given shape. describes converting a flat index to multi-dimensional indices, which matches the function's purpose.

3. Final Answer:

   It converts a flat index into a tuple of coordinate indices for a given shape. -> Option B

4. Quick Check:

   Function purpose = convert flat index to coordinates [OK]

Hint: Remember: unravel means 'find coordinates' from flat index [OK]

Common Mistakes:

• Confusing unravel_index with flatten or reshape functions
• Thinking it returns the total number of elements
• Assuming it changes the array data

2. Which of the following is the correct syntax to use np.unravel_index() for a flat index 5 in a shape (3, 3)?

easy

A. np.unravel_index((3, 3), 5)

B. np.unravel_index(5, 3, 3)

C. np.unravel_index(5, (3, 3))

D. np.unravel_index([5], (3, 3))

Solution

1. Step 1: Recall the function signature

   The correct syntax is np.unravel_index(indices, shape), where indices is an integer or array and shape is a tuple.

2. Step 2: Match options to syntax

   np.unravel_index(5, (3, 3)) matches the correct syntax with index 5 and shape (3, 3). np.unravel_index([5], (3, 3)) uses a list for index which is allowed but less common for single index.

3. Final Answer:

   np.unravel_index(5, (3, 3)) -> Option C

4. Quick Check:

   Syntax = np.unravel_index(index, shape) [OK]

Hint: Use np.unravel_index(index, shape) with shape as a tuple [OK]

Common Mistakes:

• Swapping the order of arguments
• Passing shape as separate numbers instead of a tuple
• Using list instead of integer for single index without need

3. What is the output of the following code?

import numpy as np
index = 7
shape = (3, 3)
result = np.unravel_index(index, shape)
print(result)

medium

A. (1, 1)

B. (1, 2)

C. (2, 0)

D. (2, 1)

Solution

1. Step 1: Understand the shape and flat index

   The shape is (3, 3), so the array has 3 rows and 3 columns. Flat indices go row-wise: 0 to 8.

2. Step 2: Calculate multi-dimensional indices for flat index 7

   Index 7 corresponds to row = 7 // 3 = 2, column = 7 % 3 = 1, so position is (2, 1).

3. Final Answer:

   (2, 1) -> Option D

4. Quick Check:

   Row = 7//3=2, Col = 7%3=1 [OK]

Hint: Divide index by shape dims to find row, mod for column [OK]

Common Mistakes:

• Mixing row and column order
• Using zero-based index incorrectly
• Confusing division and modulo operations

4. The code below raises an error. What is the cause?

import numpy as np
index = 10
shape = (3, 3)
result = np.unravel_index(index, shape)
print(result)

medium

A. Index 10 is out of bounds for shape (3, 3).

B. Shape must be a list, not a tuple.

C. np.unravel_index requires a 1D array, not a scalar index.

D. Missing import statement for numpy.

Solution

1. Step 1: Check the shape size

   Shape (3, 3) means total elements = 3*3 = 9, so valid flat indices are 0 to 8.

2. Step 2: Analyze the index value

   Index 10 is greater than 8, so it is out of bounds and causes an error.

3. Final Answer:

   Index 10 is out of bounds for shape (3, 3). -> Option A

4. Quick Check:

   Max index = 8, given index = 10 [OK]

Hint: Check if index < product of shape dims to avoid errors [OK]

Common Mistakes:

• Assuming tuple shape is invalid
• Thinking np.unravel_index needs array input only
• Ignoring index bounds for given shape

5. You have a 3D array with shape (4, 3, 2). You want to find the multi-dimensional indices for flat indices [5, 10, 15]. Which code correctly returns these positions?

hard

A. np.unravel_index([5, 10, 15], (4, 3, 2))

B. np.unravel_index(5, 10, 15, (4, 3, 2))

C. np.unravel_index((5, 10, 15), (4, 3, 2))

D. np.unravel_index([5, 10, 15], 4, 3, 2)

Solution

1. Step 1: Understand input for multiple indices

   To convert multiple flat indices, pass a list or array of indices as first argument and shape tuple as second.

2. Step 2: Match options to correct syntax

   np.unravel_index([5, 10, 15], (4, 3, 2)) correctly passes a list of indices and the shape tuple. np.unravel_index((5, 10, 15), (4, 3, 2)) passes a tuple instead of list, which also works but less common. np.unravel_index(5, 10, 15, (4, 3, 2)) and D have wrong argument formats.

3. Final Answer:

   np.unravel_index([5, 10, 15], (4, 3, 2)) -> Option A

4. Quick Check:

   Multiple indices = list + shape tuple [OK]

Hint: Use list of indices and shape tuple for multiple positions [OK]

Common Mistakes:

• Passing multiple indices as separate arguments
• Using tuple instead of list for indices (less common but works)
• Passing shape as separate numbers instead of tuple