Broadcasting with higher dimensions in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a 3D array of zeros with shape (2, 3, 4).

NumPy

import numpy as np
arr = np.zeros([1])
print(arr.shape)

Drag options to blanks, or click blank then click option'

A(2, 3, 4)

B2, 3, 4

C[2, 3, 4]

D3, 4, 2

Attempts:

3 left

💡 Hint

Common Mistakes

Using a list instead of a tuple for the shape.

Passing separate numbers without parentheses.

The np.zeros function requires a tuple to specify the shape. So (2, 3, 4) is correct.

2fill in blank

medium

Complete the code to add a 1D array to a 3D array using broadcasting.

NumPy

import numpy as np
arr3d = np.ones((2, 3, 4))
arr1d = np.array([1, 2, 3, 4])
result = arr3d + [1]
print(result.shape)

Drag options to blanks, or click blank then click option'

Aarr1d.reshape(1, 4)

Barr1d.reshape(4, 1)

Carr1d.reshape(1, 1, 4)

Darr1d

Attempts:

3 left

💡 Hint

Common Mistakes

Using the original 1D array without reshaping.

Reshaping to incompatible shapes like (4, 1) or (1, 4).

To broadcast a 1D array over the last dimension of a 3D array, reshape it to (1, 1, 4).

3fill in blank

hard

Fix the error in the code to multiply a (3, 1) array with a (1, 4) array using broadcasting.

NumPy

import numpy as np
arr1 = np.array([[1], [2], [3]])
arr2 = np.array([[4, 5, 6, 7]])
result = arr1 [1] arr2
print(result.shape)

Drag options to blanks, or click blank then click option'

A/

B+

C-

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of multiplication.

Using division which would also broadcast but is not the intended operation.

Multiplying arrays with shapes (3,1) and (1,4) broadcasts to (3,4). The operator * is correct.

4fill in blank

hard

Fill both blanks to create a 3D array by broadcasting a (3, 1) array and a (1, 4) array.

NumPy

import numpy as np
arr1 = np.array([[1], [2], [3]])
arr2 = np.array([[4, 5, 6, 7]])
result = arr1 [1] arr2
print(result.shape == ([2]))

Drag options to blanks, or click blank then click option'

A*

B+

C(3, 4)

D(4, 3)

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication.

Confusing the shape order as (4, 3) instead of (3, 4).

Multiplying arr1 and arr2 broadcasts to shape (3, 4).

5fill in blank

hard

Fill all three blanks to multiply two arrays using broadcasting and verify the resulting shape.

NumPy

import numpy as np
a = np.ones((3,1))
b = np.arange(4).reshape(1,4)
result = a [1] b
print(result.shape == ([2], [3]))

Drag options to blanks, or click blank then click option'

A*

B3

C4

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using matrix multiplication @ instead of element-wise *.

Reversing the shape dimensions to (4,3).

The arrays with shapes (3,1) and (1,4) broadcast to (3,4) when using the element-wise multiplication operator *.

Practice

1. What does broadcasting in NumPy allow you to do when working with arrays of different shapes?

easy

A. Copy data from smaller arrays to larger arrays explicitly

B. Perform element-wise operations by stretching smaller arrays to match larger ones

C. Only work with arrays of the exact same shape

D. Convert arrays into lists automatically

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting lets NumPy perform operations on arrays with different shapes by stretching the smaller array without copying data.

2. Step 2: Compare options with concept

   Only Perform element-wise operations by stretching smaller arrays to match larger ones correctly describes this behavior. Options B, C, and D are incorrect because broadcasting does not copy data explicitly, does not require same shape, and does not convert arrays to lists.

3. Final Answer:

   Perform element-wise operations by stretching smaller arrays to match larger ones -> Option B

4. Quick Check:

   Broadcasting = Stretch smaller arrays [OK]

Hint: Broadcasting stretches smaller arrays to match bigger ones [OK]

Common Mistakes:

• Thinking broadcasting copies data
• Believing arrays must have same shape
• Confusing broadcasting with data type conversion

2. Which of the following NumPy array shapes can be broadcast together for element-wise addition?

easy

A. (4, 5) and (4, 5, 1)

B. (2, 3) and (3, 2)

C. (3, 1, 5) and (1, 4, 5)

D. (3, 3) and (2, 3)

Solution

1. Step 1: Check broadcasting rules for each dimension

   Shapes (3,1,5) and (1,4,5) can broadcast because dimensions are compatible: 3 vs 1, 1 vs 4, 5 vs 5.

2. Step 2: Verify other options

   Options A, B, and D have incompatible dimensions that cannot be broadcast for element-wise addition.

3. Final Answer:

   (3, 1, 5) and (1, 4, 5) -> Option C

4. Quick Check:

   Broadcast compatible shapes = (3,1,5) & (1,4,5) [OK]

Hint: Match dimensions from right, 1 or equal size broadcasts [OK]

Common Mistakes:

• Ignoring dimension order when checking compatibility
• Assuming all different shapes can broadcast
• Confusing shape sizes in different axes

3. What is the output of this code?

import numpy as np
A = np.ones((2, 3, 1))
B = np.arange(4).reshape(1, 1, 4)
C = A + B
print(C.shape)

medium

A. ValueError due to shape mismatch

B. (2, 3, 1)

C. (1, 1, 4)

D. (2, 3, 4)

Solution

1. Step 1: Analyze shapes of A and B

   A has shape (2, 3, 1), B has shape (1, 1, 4). Broadcasting rules allow these to combine because 1 can stretch to 2 and 3, and 1 can stretch to 4.

2. Step 2: Determine resulting shape

   The result shape is the maximum along each dimension: max(2,1)=2, max(3,1)=3, max(1,4)=4, so (2, 3, 4).

3. Final Answer:

   (2, 3, 4) -> Option D

4. Quick Check:

   Broadcast result shape = (2,3,4) [OK]

Hint: Result shape = max dimension sizes per axis [OK]

Common Mistakes:

• Confusing which dimension broadcasts to which
• Expecting error instead of broadcasting
• Mixing up shape order

4. Identify the error in this code snippet:

import numpy as np
X = np.ones((3, 1, 2))
Y = np.ones((2, 3))
Z = X + Y

medium

A. Shapes (3,1,2) and (2,3) cannot be broadcast together

B. Y should be reshaped to (1, 2, 3) before addition

C. X and Y have incompatible data types

D. No error, code runs fine

Solution

1. Step 1: Compare shapes for broadcasting

   X shape is (3,1,2), Y shape is (2,3). Aligning from right: 2 vs 3 (mismatch), 1 vs 2 (mismatch), 3 vs missing dimension.

2. Step 2: Conclude broadcasting compatibility

   Dimensions do not match or equal 1, so broadcasting fails and raises an error.

3. Final Answer:

   Shapes (3,1,2) and (2,3) cannot be broadcast together -> Option A

4. Quick Check:

   Broadcast error due to incompatible shapes [OK]

Hint: Check shapes right to left; mismatch means error [OK]

Common Mistakes:

• Assuming automatic reshaping without explicit code
• Ignoring dimension order in broadcasting
• Thinking data types cause this error

5. You have a 3D array data with shape (10, 1, 5) representing 10 samples, 1 channel, and 5 features. You want to add a bias vector of shape (5,) to each sample and channel. Which code correctly applies broadcasting to add the bias to data?

hard

A. bias = np.array([1,2,3,4,5])
data + bias

B. bias = np.array([[1,2,3,4,5]])
data + bias

C. bias = np.array([1,2,3,4,5]).reshape((5,1))
data + bias

D. bias = np.array([[[1,2,3,4,5]]])
data + bias

Solution

1. Step 1: Understand required bias shape and broadcasting

   data shape (10,1,5). Bias vector shape (5,) pads with 1s on left to (1,1,5) and broadcasts correctly across samples and channels.

2. Step 2: Evaluate each option

   A: bias shape (5,), correct. B: shape (1,5) also broadcasts correctly, but is redundant. C: shape (5,1) incompatible. D: shape (1,1,5) also broadcasts correctly, but is more verbose.

3. Final Answer:

   bias = np.array([1,2,3,4,5])
   data + bias -> Option A

4. Quick Check:

   (10,1,5) + (5,) -> broadcasts OK

Hint: Bias shape must match trailing dims with extra dims as 1 [OK]

Common Mistakes:

• Using 1D bias without extra dimensions
• Wrong reshape causing shape mismatch
• Assuming automatic dimension expansion without reshape