Common broadcasting patterns in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of broadcasting addition

What is the output of this code snippet using NumPy broadcasting?

NumPy

import numpy as np

arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([10, 20, 30])
result = arr1 + arr2
print(result)

A

[[11 22 33]
 [14 25 36]]

B

[[11 12 13]
 [14 15 16]]

C

[[10 20 30]
 [10 20 30]]

D

[[1 2 3 10 20 30]
 [4 5 6 10 20 30]]

💡 Hint

Remember how NumPy adds arrays with compatible shapes by stretching the smaller array.

The array arr2 with shape (3,) is broadcast across the rows of arr1 with shape (2,3). Each element in arr2 is added to the corresponding column in arr1.

❓ data_output

intermediate

Shape after broadcasting

Given these arrays, what is the shape of the result after broadcasting and multiplication?

NumPy

import numpy as np

arr1 = np.ones((4,1))
arr2 = np.array([1, 2, 3])
result = arr1 * arr2
print(result.shape)

A (4, 3)

B (4, 1)

C (3, 4)

D (1, 3)

💡 Hint

Check how the shapes (4,1) and (3,) align for broadcasting.

The array arr1 has shape (4,1) and arr2 has shape (3,). NumPy broadcasts arr2 to (1,3), then both arrays broadcast to (4,3).

🔧 Debug

advanced

Identify the broadcasting error

What error does this code raise when trying to add these arrays?

NumPy

import numpy as np

arr1 = np.array([[1, 2], [3, 4]])
arr2 = np.array([1, 2, 3])
result = arr1 + arr2

A TypeError: unsupported operand type(s) for +: 'int' and 'list'

B ValueError: operands could not be broadcast together with shapes (2,2) (3,)

C IndexError: index out of bounds

D No error, output is [[2 4] [4 6]]

💡 Hint

Check if the shapes of the arrays can be broadcast together.

The shapes (2,2) and (3,) are incompatible for broadcasting because the trailing dimensions do not match and neither is 1.

❓ visualization

advanced

Visualize broadcasting with reshaping

Which option correctly reshapes arr2 to broadcast with arr1 for element-wise multiplication?

NumPy

import numpy as np
import matplotlib.pyplot as plt

arr1 = np.arange(6).reshape(2,3)
arr2 = np.array([1, 2])

# Reshape arr2 here
arr2_reshaped = ???
result = arr1 * arr2_reshaped
plt.imshow(result)
plt.colorbar()
plt.show()

A arr2.reshape(3,1)

B arr2.reshape(1,2)

C arr2.reshape(2,1)

D arr2.reshape(3,2)

💡 Hint

arr1 shape is (2,3). To multiply, arr2 must broadcast to (2,3).

Reshaping arr2 to (2,1) allows it to broadcast across the 3 columns of arr1, resulting in shape (2,3).

🧠 Conceptual

expert

Broadcasting rules application

Given arrays with shapes (5,1,4) and (1,3,1), what is the shape of their broadcasted result?

A (5, 3, 1)

B (5, 1, 1)

C (1, 3, 4)

D (5, 3, 4)

💡 Hint

Compare dimensions from right to left, applying broadcasting rules.

Broadcasting compares dimensions from right to left: 4 and 1 broadcast to 4; 1 and 3 broadcast to 3; 5 and 1 broadcast to 5. Result shape is (5,3,4).