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

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Input: flat index, shape

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Calculate multi-dim indices

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Return tuple of indices

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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.