Broadcasting with higher dimensions in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of broadcasting addition with 3D and 2D arrays

What is the output of the following code snippet?

NumPy

import numpy as np

A = np.ones((2,3,4))
B = np.arange(4)
result = A + B
print(result)

A

[[[1. 2. 3. 4.]
  [2. 3. 4. 5.]
  [3. 4. 5. 6.]]

 [[1. 2. 3. 4.]
  [2. 3. 4. 5.]
  [3. 4. 5. 6.]]]

B

[[[1. 1. 1. 1.]
  [2. 3. 4. 5.]
  [3. 4. 5. 6.]]

 [[1. 1. 1. 1.]
  [2. 3. 4. 5.]
  [3. 4. 5. 6.]]]

C

[[[1. 2. 3. 4.]
  [1. 2. 3. 4.]
  [1. 2. 3. 4.]]

 [[2. 3. 4. 5.]
  [2. 3. 4. 5.]
  [2. 3. 4. 5.]]]

D

[[[1. 2. 3. 4.]
  [1. 2. 3. 4.]
  [1. 2. 3. 4.]]

 [[1. 2. 3. 4.]
  [1. 2. 3. 4.]
  [1. 2. 3. 4.]]]

💡 Hint

Remember how numpy broadcasts arrays with different shapes by matching dimensions from the right.

Array A has shape (2,3,4) filled with ones. Array B has shape (4,). When adding, B is broadcasted to (1,1,4) and then to (2,3,4). So each element in the last dimension of A is added to the corresponding element in B. The result is a (2,3,4) array where each 4-element vector is [1+0, 1+1, 1+2, 1+3] = [1,2,3,4].

❓ data_output

intermediate

Shape after broadcasting multiplication

Given the arrays below, what is the shape of the result after multiplication?

NumPy

import numpy as np

X = np.ones((4,1,3))
Y = np.arange(3)
result = X * Y
print(result.shape)

A (4, 1, 3)

B (4, 3, 3)

C (4, 3)

D (3, 4, 3)

💡 Hint

Check how numpy aligns dimensions from the right and broadcasts accordingly.

X has shape (4,1,3), Y has shape (3,). Y is broadcasted to (1,1,3) to match X. Multiplication results in shape (4,1,3).

🔧 Debug

advanced

Identify the error in broadcasting with incompatible shapes

What error will the following code raise?

NumPy

import numpy as np

A = np.ones((2,3,4))
B = np.arange(5)
result = A + B

A IndexError: index 4 is out of bounds for axis 0 with size 4

B TypeError: unsupported operand type(s) for +: 'int' and 'numpy.ndarray'

C ValueError: operands could not be broadcast together with shapes (2,3,4) (5,)

D No error, outputs a (2,3,5) array

💡 Hint

Check if the shapes can be broadcasted according to numpy rules.

Array A has shape (2,3,4), B has shape (5,). The last dimensions 4 and 5 do not match and neither is 1, so broadcasting fails with a ValueError.

🚀 Application

advanced

Using broadcasting to normalize a 3D array

You have a 3D array representing 2 samples, each with 3 features and 4 observations. You want to subtract the mean of each feature across observations from the array. Which code correctly does this using broadcasting?

NumPy

import numpy as np

arr = np.array([[[1,2,3,4],[5,6,7,8],[9,10,11,12]],
                [[13,14,15,16],[17,18,19,20],[21,22,23,24]]])

# Compute mean and subtract

A

mean = arr.mean(axis=2, keepdims=True)
result = arr - mean

B

mean = arr.mean(axis=1, keepdims=True)
result = arr - mean

C

mean = arr.mean(axis=0, keepdims=True)
result = arr - mean

D

mean = arr.mean(axis=2)
result = arr - mean

💡 Hint

Think about which axis corresponds to observations and how to keep dimensions for broadcasting.

Observations are along axis 2. Taking mean along axis 2 with keepdims=True keeps shape compatible for broadcasting subtraction.

🧠 Conceptual

expert

Understanding broadcasting rules with higher dimensions

Given arrays A with shape (3,1,5,1) and B with shape (1,4,1,6), what is the shape of the result when computing A + B?

A (3, 4, 1, 6)

B (3, 4, 5, 6)

C (3, 1, 5, 6)

D Broadcasting error due to incompatible shapes

💡 Hint

Align shapes from the right and apply broadcasting rules dimension-wise.

Aligning shapes: A: (3,1,5,1) B: (1,4,1,6) Dimension-wise: 3 vs 1 -> 3 1 vs 4 -> 4 5 vs 1 -> 5 1 vs 6 -> 6 Result shape is (3,4,5,6).