If sizes equal or one is 1, dimension is compatible
↓
If all dimensions compatible
↓
Broadcast smaller array by repeating along size 1 dims
↓
Perform element-wise operation
↓
Output broadcasted result
Broadcasting compares array shapes from right to left, matching dimensions if equal or one is 1, then repeats smaller arrays to match larger ones for element-wise operations.
Execution Sample
Data Analysis Python
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 2x3 array to a 1x3 array using broadcasting to match shapes.
Execution Table
Step
Array Shapes
Dimension Check
Broadcast Action
Result Shape
Output Sample
1
A: (2,3), B: (3,)
Compare last dims: 3 vs 3 (compatible)
B shape treated as (1,3)
(2,3)
N/A
2
A: (2,3), B broadcasted to (2,3)
Compare first dims: 2 vs 1 (1 is broadcastable)
B repeated along first dim
(2,3)
N/A
3
Perform element-wise addition
N/A
Add each element
(2,3)
[[11, 22, 33], [14, 25, 36]]
4
End
N/A
N/A
(2,3)
Final broadcasted sum
💡 Broadcasting completes when all dimensions are compatible and arrays match shape for operation.
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 - 3 Insights
Why can B with shape (3,) be added to A with shape (2,3)?
Because broadcasting treats B's shape as (1,3), then repeats it along the first dimension to match A's 2 rows, as shown in execution_table step 2.
What happens if dimensions are not equal and neither is 1?
Broadcasting fails because dimensions are incompatible. The code would raise an error, which is why all dimension checks must pass as in execution_table step 1.
Does broadcasting change the original arrays?
No, broadcasting creates a temporary view or repeated version for the operation without modifying original arrays, as variable_tracker shows B is unchanged after broadcast.
Visual Quiz - 3 Questions
Test your understanding
Look at the execution_table at step 2, what is the shape of B after broadcasting?
A(1,3)
B(3,)
C(2,3)
D(2,1)
💡 Hint
Refer to execution_table row 2 under 'Result Shape' and 'Broadcast Action' columns.
At which step does the element-wise addition happen according to the execution_table?
AStep 3
BStep 1
CStep 2
DStep 4
💡 Hint
Check the 'Step' and 'Broadcast Action' columns for when addition occurs.
If B had shape (2,1) instead of (3,), how would broadcasting change?
AB would broadcast along first dimension to (1,3)
BB would broadcast along second dimension to (2,3)
CBroadcasting would fail due to incompatible shapes
DB would remain (2,1) without broadcasting
💡 Hint
Think about matching dimensions from right to left and repeating size 1 dims.
Concept Snapshot
Broadcasting rules:
- Compare shapes from right to left
- Dimensions match if equal or one is 1
- Smaller array repeats along size 1 dims
- Enables element-wise operations on different shaped arrays
- Original arrays stay unchanged
- Errors if dimensions incompatible
Full Transcript
Broadcasting lets us do math on arrays with different shapes by matching their dimensions from right to left. If dimensions are equal or one is 1, they are compatible. The smaller array is repeated along those size 1 dimensions to match the bigger array. Then element-wise operations like addition happen. For example, adding a 2x3 array to a 1x3 array works because the smaller array is treated as 1x3 and repeated twice. Broadcasting does not change the original arrays. If dimensions don't match and neither is 1, broadcasting fails with an error.