np.unravel_index() for multi-dim positions in NumPy

Introduction

We use np.unravel_index() to find the row and column positions in a multi-dimensional array from a single flat index. It helps us understand where a value is located in a grid or table.

You have a flat index from a flattened array and want to find its position in the original 2D or 3D array.

You want to convert a single number index into coordinates for image pixels in height and width.

You need to locate the position of the maximum or minimum value in a multi-dimensional dataset.

You want to map linear indices back to multi-dimensional indices for data analysis or visualization.

Syntax

NumPy

np.unravel_index(indices, shape, order='C')

indices can be a single integer or an array of integers representing flat indices.

shape is the shape of the multi-dimensional array you want to map to.

Examples

Find the 2D position of flat index 5 in a 3x3 array.

NumPy

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

Find positions of flat indices 3 and 7 in a 3x3 array.

NumPy

np.unravel_index([3, 7], (3, 3))

Find the 3D position of flat index 10 in a 2x3x4 array.

NumPy

np.unravel_index(10, (2, 3, 4))

Sample Program

This code converts flat indices back to their row and column positions in a 3x4 array. It shows how to use np.unravel_index() for single and multiple indices.

NumPy

import numpy as np

# Suppose we have a 3x4 array
shape = (3, 4)

# Flat index to convert
flat_index = 7

# Get the multi-dimensional position
position = np.unravel_index(flat_index, shape)
print(f"Flat index {flat_index} corresponds to position {position} in shape {shape}.")

# For multiple indices
flat_indices = [5, 11]
positions = np.unravel_index(flat_indices, shape)
print(f"Flat indices {flat_indices} correspond to positions {positions} in shape {shape}.")

Important Notes

The output is a tuple of arrays, each array representing the indices along one dimension.

By default, order='C' means row-major order (like reading rows first).

You can use order='F' for column-major order if needed.

Summary

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

It works for any shape and can handle single or multiple indices.

This helps find exact locations in arrays from flat positions.

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