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

Concept Flow - np.unravel_index() for multi-dim positions

Start with flat index

↓

Input: flat index, shape

↓

Calculate multi-dim indices

↓

Return tuple of indices

↓

Use indices to access multi-dim array

np.unravel_index converts a flat index into a tuple of indices for a multi-dimensional array shape.

Execution Sample

NumPy

import numpy as np
flat_index = 7
shape = (3, 3)
multi_dim_pos = np.unravel_index(flat_index, shape)
print(multi_dim_pos)

This code converts the flat index 7 into a 2D position in a 3x3 array.

Execution Table

Step	Input flat_index	Input shape	Calculation	Output multi_dim_pos
1	7	(3, 3)	Calculate row = 7 // 3 = 2	(2, ?)
2	7	(3, 3)	Calculate col = 7 % 3 = 1	(2, 1)
3	7	(3, 3)	Return (2, 1)	(2, 1)
4	N/A	N/A	Print output	(2, 1)

💡 All calculations done, multi-dimensional index (2, 1) returned for flat index 7 in shape (3, 3).

Variable Tracker

Variable	Start	After Step 1	After Step 2	Final
flat_index	7	7	7	7
shape	(3, 3)	(3, 3)	(3, 3)	(3, 3)
row	N/A	2	2	2
col	N/A	N/A	1	1
multi_dim_pos	N/A	Partial (2, ?)	(2, 1)	(2, 1)

Key Moments - 3 Insights

Why does np.unravel_index return a tuple?

Because it converts a single flat index into multiple indices, one for each dimension, as shown in execution_table step 3.

How does np.unravel_index calculate each dimension's index?

It uses integer division and modulo operations step-by-step, as shown in execution_table steps 1 and 2.

What happens if the flat index is larger than the total size?

np.unravel_index will raise an error because the flat index must fit within the total number of elements in the shape.

Visual Quiz - 3 Questions

Look at the execution table, what is the row index calculated at step 1?

A 1

B 2

C 3

D 0

💡 Hint

Check the 'Calculation' column in execution_table row 1.

At which step is the column index calculated?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look for modulo operation in the 'Calculation' column.

If the shape was (4, 4) instead of (3, 3), what would be the multi_dim_pos for flat_index 7?

A (1, 3)

B (2, 1)

C (1, 2)

D (0, 7)

💡 Hint

Calculate row = 7 // 4 and col = 7 % 4 similar to execution_table steps.

Concept Snapshot

np.unravel_index(flat_index, shape) converts a flat index into a tuple of indices for a multi-dimensional array.
It uses integer division and modulo to find each dimension's index.
The output tuple matches the number of dimensions in shape.
Useful to find multi-dim positions from flat indices.
Example: np.unravel_index(7, (3,3)) returns (2,1).

Full Transcript

np.unravel_index takes a flat index and a shape tuple. It calculates each dimension's index by dividing and taking remainders. For example, with flat index 7 and shape (3,3), it divides 7 by 3 to get row 2, and remainder 1 for column. The result is (2,1). This tuple can be used to access elements in multi-dimensional arrays. If the flat index is too large, an error occurs. This function helps convert single indices into multi-dimensional 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