Common broadcasting patterns in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is broadcasting in NumPy?

Broadcasting is a way NumPy allows arrays of different shapes to work together in arithmetic operations by automatically expanding the smaller array along the missing dimensions.

beginner

Explain the rule: When does broadcasting work between two arrays?

Broadcasting works when for each dimension, the sizes are equal or one of them is 1. NumPy stretches the dimension with size 1 to match the other.

beginner

What happens when you add a 1D array of shape (3,) to a 2D array of shape (2,3)?

The 1D array is broadcasted along the first dimension to match the 2D array shape (2,3), so each row adds the 1D array values.

beginner

How does broadcasting handle a scalar value with an array?

A scalar is treated as an array with shape (), so it broadcasts to the shape of the array, applying the scalar value to every element.

intermediate

What is the broadcasting pattern when multiplying a (3,1) array with a (1,4) array?

The (3,1) array is broadcasted along the second dimension and the (1,4) array along the first dimension, resulting in a (3,4) array where each element is the product of corresponding broadcasted values.

Which condition must be true for broadcasting to work between two arrays?

A Both arrays have the same number of elements

B Dimensions are equal or one is 1

C Arrays have the same data type

D Arrays have the same number of dimensions

Broadcasting requires that for each dimension, the sizes are equal or one of them is 1.

What is the shape of the result when adding arrays of shapes (4,1) and (1,5)?

A (1,5)

B (1,1)

C (4,1)

D (4,5)

The arrays broadcast to shape (4,5) by expanding the dimensions with size 1.

If you add a scalar to an array of shape (3,3), what is the shape of the result?

A (3,1)

B (1,3)

C (3,3)

D ()

The scalar broadcasts to the array shape, so the result has the same shape as the array.

What happens if you try to broadcast arrays with shapes (2,3) and (3,2)?

A Broadcasting fails due to incompatible shapes

B Broadcasting succeeds with shape (2,3,3,2)

C Broadcasting succeeds with shape (3,3)

D Broadcasting succeeds with shape (2,2)

Broadcasting fails because dimensions are not equal and neither is 1 in corresponding positions.

Which broadcasting pattern is used when multiplying arrays of shapes (3,1) and (1,4)?

A Result shape is (3,4) by expanding both arrays

B Result shape is (3,1)

C Result shape is (1,4)

D Multiplication is not possible

Both arrays broadcast to shape (3,4), multiplying each element accordingly.

Describe how NumPy broadcasting works with an example of adding a (2,3) array to a (3,) array.

Think about how the smaller array is stretched to match the larger array's shape.

Explain why broadcasting fails when trying to operate on arrays with shapes (2,3) and (3,2).

Check each dimension from the right and see if they are equal or one is 1.

Practice

1. What does broadcasting in NumPy allow you to do?

easy

A. Perform operations on arrays of different shapes without explicit loops

B. Only add arrays of the exact same shape

C. Convert arrays into lists automatically

D. Sort arrays in ascending order

Solution

1. Step 1: Understand broadcasting concept

   Broadcasting lets NumPy perform element-wise operations on arrays with different shapes by automatically expanding the smaller array.

2. Step 2: Compare options

   Only Perform operations on arrays of different shapes without explicit loops correctly describes this feature. Options A, B, and C describe unrelated behaviors.

3. Final Answer:

   Perform operations on arrays of different shapes without explicit loops -> Option A

4. Quick Check:

   Broadcasting = operations on different shapes [OK]

Hint: Broadcasting means math on different shaped arrays without loops [OK]

Common Mistakes:

• Thinking broadcasting requires arrays to have the same shape
• Confusing broadcasting with sorting or type conversion
• Assuming broadcasting changes array data types

2. Which of the following is the correct way to add a 1D array to each row of a 2D array using broadcasting?

easy

A. result = matrix + vector.T where matrix.shape = (3,4) and vector.shape = (4,)

B. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (3,)

C. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,)

D. result = matrix + vector.reshape(3,1) where matrix.shape = (3,4) and vector.shape = (4,)

Solution

1. Step 1: Check shapes for broadcasting

   Adding a 1D array of shape (4,) to each row of a (3,4) matrix works because the vector matches the number of columns.

2. Step 2: Evaluate options

   result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,) matches this pattern. result = matrix + vector where matrix.shape = (3,4) and vector.shape = (3,) tries to add a (3,) vector to (3,4) matrix which fails. result = matrix + vector.T where matrix.shape = (3,4) and vector.shape = (4,) uses transpose incorrectly. result = matrix + vector.reshape(3,1) where matrix.shape = (3,4) and vector.shape = (4,) reshapes vector wrongly.

3. Final Answer:

   result = matrix + vector where matrix.shape = (3,4) and vector.shape = (4,) -> Option C

4. Quick Check:

   Vector shape matches columns for row-wise addition [OK]

Hint: Add vector matching columns to matrix rows for broadcasting [OK]

Common Mistakes:

• Using vector shape matching rows instead of columns
• Trying to transpose 1D vector which has no effect
• Reshaping vector incorrectly before addition

3. What is the output of the following code?

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

medium

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

B. [[11 22 33]
[14 25 36]
[10 20 30]]

C. [[10 20 30]
[10 20 30]]

D. ValueError due to shape mismatch

Solution

1. Step 1: Understand shapes of A and B

   A has shape (2,3), B has shape (3,). B will broadcast across rows of A.

2. Step 2: Perform element-wise addition

   Each row of A adds B: [1+10, 2+20, 3+30] = [11, 22, 33], [4+10, 5+20, 6+30] = [14, 25, 36].

3. Final Answer:

   [[11 22 33] [14 25 36]] -> Option A

4. Quick Check:

   Broadcast adds vector to each matrix row [OK]

Hint: Add vector to each matrix row when vector shape matches columns [OK]

Common Mistakes:

• Expecting an extra row in output
• Confusing broadcasting with stacking arrays
• Thinking shape mismatch causes error here

4. Identify the error in this code snippet:

import numpy as np
X = np.array([[1, 2], [3, 4], [5, 6]])
y = np.array([10, 20, 30])
result = X + y

medium

A. y should be reshaped to (3,1) before addition

B. No error, code runs fine

C. X and y must have the same number of columns

D. Shapes (3,2) and (3,) cannot broadcast together

Solution

1. Step 1: Check shapes of X and y

   X shape is (3,2), y shape is (3,). Broadcasting rules require trailing dimensions to match or be 1.

2. Step 2: Analyze broadcasting compatibility

   Here, last dims are 2 (X) and 1 (y) after broadcasting rules, so y broadcasts along columns. The addition works without error.

3. Final Answer:

   No error, code runs fine -> Option B

4. Quick Check:

   Broadcasting allows (3,2) + (3,) by treating (3,) as (3,1) [OK]

Hint: Trailing dimensions must match or be 1 for broadcasting [OK]

Common Mistakes:

• Assuming broadcasting works if first dims match
• Not checking trailing dimension compatibility
• Thinking reshaping y to (3,1) fixes addition here

5. Given a 2D array M of shape (4,3) and a 1D array v of shape (4,), how can you add v to each column of M using broadcasting?

hard

A. M + v.T

B. M + v

C. M + v.reshape(1,4)

D. M + v.reshape(4,1)

Solution

1. Step 1: Understand shapes and desired operation

   M is (4,3), v is (4,). To add v to each column, v must be reshaped to (4,1) to broadcast along columns.

2. Step 2: Check each option

   M + v.reshape(4,1) reshapes v to (4,1), allowing broadcasting with M (4,3). M + v tries to add (4,) to (4,3) which broadcasts incorrectly. M + v.reshape(1,4) reshapes v to (1,4), incompatible. M + v.T uses transpose on 1D array which has no effect.

3. Final Answer:

   M + v.reshape(4,1) -> Option D

4. Quick Check:

   Reshape vector to (rows,1) to add to columns [OK]

Hint: Reshape vector to (rows,1) to add to matrix columns [OK]

Common Mistakes:

• Adding vector without reshaping when shapes differ
• Using reshape(1, rows) instead of (rows,1)
• Assuming transpose changes 1D array shape