Vectorization over loops in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is vectorization in the context of numpy?

Vectorization means performing operations on whole arrays at once instead of using loops to process elements one by one. It makes code faster and simpler.

beginner

Why is vectorization faster than using loops in numpy?

Because numpy uses optimized C code and parallel processing under the hood, it can handle whole arrays at once, avoiding slow Python loops.

beginner

Example: How to add two arrays element-wise using vectorization?

Use the '+' operator directly on numpy arrays. For example, if a = np.array([1,2]) and b = np.array([3,4]), then a + b gives np.array([4,6]).

intermediate

What is a common mistake when switching from loops to vectorized numpy code?

Trying to use Python loops inside numpy operations or forgetting that numpy operations work element-wise on arrays, not on single elements.

beginner

How does vectorization improve code readability?

Vectorized code is shorter and clearer because it expresses operations on whole arrays directly, avoiding complex loop structures.

What does vectorization help you avoid in numpy?

A Importing numpy

B Using numpy arrays

C Using functions

D Writing explicit loops over array elements

Vectorization lets you perform operations on whole arrays without writing loops.

Which of these is a vectorized operation in numpy?

A for i in range(len(a)): c[i] = a[i] + b[i]

B c = a + b

C while i < len(a): c[i] = a[i] + b[i]

D c = [] for x in a: c.append(x)

Adding two arrays directly with '+' is vectorized.

Why is vectorized numpy code usually faster?

A It uses optimized C code and avoids Python loops

B It uses Python loops

C It uses more memory

D It runs slower but looks nicer

Numpy vectorization uses fast C code and avoids slow Python loops.

What happens if you try to add two numpy arrays of different shapes without broadcasting?

A It raises an error

B It returns zeros

C It ignores the smaller array

D It works fine

Numpy raises a ValueError if shapes are incompatible for broadcasting.

Which numpy function can help apply a vectorized operation to each element?

A np.loop

B np.for_each

C np.vectorize

D np.iter

np.vectorize wraps a function to apply it element-wise on arrays.

Explain in your own words why vectorization is preferred over loops in numpy.

Think about how numpy handles arrays internally.

Describe how you would convert a loop that adds two arrays element-wise into a vectorized numpy operation.

Focus on replacing the loop with a single numpy expression.

Practice

1. What is the main advantage of using vectorization in numpy instead of loops?

easy

A. It makes the code run faster by doing many operations at once.

B. It uses more memory but slows down the code.

C. It makes the code harder to read and understand.

D. It requires writing more lines of code.

Solution

1. Step 1: Understand vectorization concept

   Vectorization means applying operations on whole arrays at once, not one element at a time.

2. Step 2: Compare speed and simplicity

   This approach uses optimized numpy functions that run faster than explicit loops.

3. Final Answer:

   It makes the code run faster by doing many operations at once. -> Option A

4. Quick Check:

   Vectorization = faster code [OK]

Hint: Vectorization speeds up code by handling arrays at once [OK]

Common Mistakes:

• Thinking vectorization slows code
• Believing vectorization needs more code
• Confusing vectorization with loops

2. Which of the following numpy codes correctly replaces a loop to add 5 to each element in array a?

easy

A. a + 5

B. for i in a: i = i + 5

C. np.add(a, 5, out=a)

D. a.append(5)

Solution

1. Step 1: Identify vectorized addition

   Using np.add(a, 5, out=a) adds 5 to every element in array a efficiently.

2. Step 2: Check other options

   a + 5 works but returns a new array, for i in a: i = i + 5 does not change a, and a.append(5) is invalid for numpy arrays.

3. Final Answer:

   np.add(a, 5, out=a) -> Option C

4. Quick Check:

   np.add = vectorized add [OK]

Hint: Use numpy functions like np.add for vectorized operations [OK]

Common Mistakes:

• Using loops that don't modify array
• Trying list methods on numpy arrays
• Confusing array addition with append

3. What is the output of this code?

import numpy as np
arr = np.array([1, 2, 3])
result = arr * 2
print(result)

medium

A. [2 4 6]

B. [1 2 3 1 2 3]

C. [3 4 5]

D. Error: cannot multiply array by int

Solution

1. Step 1: Understand array multiplication

   Multiplying a numpy array by a number multiplies each element by that number.

2. Step 2: Calculate element-wise multiplication

   Each element in [1, 2, 3] is multiplied by 2, resulting in [2, 4, 6].

3. Final Answer:

   [2 4 6] -> Option A

4. Quick Check:

   Array * number = element-wise multiply [OK]

Hint: Array * number multiplies each element [OK]

Common Mistakes:

• Thinking it concatenates arrays
• Expecting an error on multiplication
• Confusing element-wise with matrix multiply

4. Identify the error in this code that tries to add 10 to each element of arr using a loop:

import numpy as np
arr = np.array([1, 2, 3])
for i in arr:
    i = i + 10
print(arr)

medium

A. Syntax error in for loop.

B. Loop variable i does not modify original array elements.

C. Array arr is not defined.

D. Cannot add integer to numpy array elements.

Solution

1. Step 1: Understand loop variable behavior

   Variable i is a copy of each element, so changing i does not change arr.

2. Step 2: Explain why array remains unchanged

   The original array arr stays the same because the loop does not assign back to array elements.

3. Final Answer:

   Loop variable i does not modify original array elements. -> Option B

4. Quick Check:

   Loop var copy ≠ array change [OK]

Hint: Loop vars are copies; assign to array to change [OK]

Common Mistakes:

• Assuming loop changes array automatically
• Thinking syntax error exists
• Believing numpy disallows int addition

5. You have a numpy array data = np.array([1, 2, 3, 4, 5]). You want to create a new array where each element is squared if it is even, otherwise doubled. Which vectorized code achieves this?

hard

A. data * 2 if data % 2 else data ** 2

B. [x**2 if x%2==0 else x*2 for x in data]

C. for i in range(len(data)): data[i] = data[i]**2 if data[i]%2==0 else data[i]*2

D. np.where(data % 2 == 0, data**2, data*2)

Solution

1. Step 1: Understand vectorized conditional with np.where

   np.where(condition, x, y) returns array choosing x where condition is true, else y.

2. Step 2: Apply condition for even and odd elements

   Condition data % 2 == 0 checks even numbers; squares them, else doubles.

3. Step 3: Check other options

   [x**2 if x%2==0 else x*2 for x in data] uses list comprehension (not vectorized), C uses loop (not vectorized), D is invalid syntax.

4. Final Answer:

   np.where(data % 2 == 0, data**2, data*2) -> Option D

5. Quick Check:

   np.where = vectorized if-else [OK]

Hint: Use np.where for vectorized if-else conditions [OK]

Common Mistakes:

• Using loops or list comprehensions instead of vectorization
• Writing invalid syntax for conditional operations
• Confusing element-wise operations with scalar