1D and 2D broadcasting in NumPy - Step-by-Step Execution

Concept Flow - 1D and 2D broadcasting

Start with arrays

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Check shapes

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Align dimensions

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Broadcast smaller array

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Perform element-wise operation

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Output result

Broadcasting matches array shapes by expanding smaller arrays to perform element-wise operations.

Execution Sample

NumPy

import numpy as np
A = np.array([[1,2,3],[4,5,6]])
B = np.array([10,20,30])
C = A + B
print(C)

Add a 2D array and a 1D array using broadcasting to get a 2D result.

Execution Table

Step	A shape	B shape	Broadcasted B shape	Operation	Result element example
1	(2,3)	(3,)	(2,3)	Broadcast B to match A	B becomes [[10,20,30],[10,20,30]]
2	(2,3)	(3,)	(2,3)	Add A and broadcasted B element-wise	C[0,0] = 1 + 10 = 11
3	(2,3)	(3,)	(2,3)	Add A and broadcasted B element-wise	C[1,2] = 6 + 30 = 36
4	(2,3)	(3,)	(2,3)	Final result C	[[11,22,33],[14,25,36]]

💡 Broadcasting completes when shapes align and operation finishes.

Variable Tracker

Variable	Start	After Broadcast	Final
A	[[1,2,3],[4,5,6]]	[[1,2,3],[4,5,6]]	[[1,2,3],[4,5,6]]
B	[10,20,30]	[[10,20,30],[10,20,30]]	[[10,20,30],[10,20,30]]
C	N/A	N/A	[[11,22,33],[14,25,36]]

Key Moments - 2 Insights

Why does B get repeated to match A's shape?

Because B has shape (3,) and A has (2,3), numpy repeats B along the missing dimension to (2,3) so element-wise addition works, as shown in execution_table step 1.

Can broadcasting happen if shapes are incompatible?

No, broadcasting requires dimensions to be equal or one of them to be 1. Here, B's shape (3,) is compatible with A's (2,3) because 3 matches and 2 can be broadcasted.

Visual Quiz - 3 Questions

Look at the execution_table, what is the shape of B after broadcasting at step 1?

A (2,3)

B (3,)

C (1,3)

D (3,2)

💡 Hint

Check the 'Broadcasted B shape' column at step 1 in execution_table.

At which step does the element-wise addition start in the execution_table?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look for the first step mentioning 'Add A and broadcasted B element-wise'.

If B was shape (2,1) instead of (3,), what would happen to broadcasting?

A B would broadcast to (3,2)

B Broadcasting would fail due to incompatible shapes

C B would broadcast to (2,3) by repeating the second dimension

D B would remain (2,1) and no operation possible

💡 Hint

Recall broadcasting rules: dimension 1 can be stretched to match 3.

Concept Snapshot

1D and 2D broadcasting in numpy:
- Smaller array expands to match larger array shape
- Dimensions must be equal or 1
- Enables element-wise operations without explicit loops
- Example: (2,3) + (3,) broadcasts (3,) to (2,3)
- Result shape matches the larger array

Full Transcript

This lesson shows how numpy broadcasting works between 1D and 2D arrays. We start with two arrays: A with shape (2,3) and B with shape (3,). Because B has fewer dimensions, numpy repeats it along the missing dimension to shape (2,3). Then element-wise addition happens between A and broadcasted B. The final result is a (2,3) array where each element is the sum of corresponding elements from A and B. Broadcasting requires dimensions to be equal or one of them to be 1. This allows simple, efficient operations without manual loops.