When NumPy is not fast enough - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Comparing execution time of NumPy and pure Python loops

What will be the output of the following code snippet that compares the sum of squares using NumPy and a Python loop?

NumPy

import numpy as np
import time

arr = np.arange(1_000_000)

start = time.time()
result_numpy = np.sum(arr ** 2)
end = time.time()
numpy_time = end - start

start = time.time()
result_loop = 0
for x in arr:
    result_loop += x ** 2
end = time.time()
loop_time = end - start

print(f"NumPy sum: {result_numpy}, Time: {numpy_time:.4f} seconds")
print(f"Loop sum: {result_loop}, Time: {loop_time:.4f} seconds")

A

NumPy sum: 333332833333500000, Time: 1.2000 seconds
Loop sum: 333332833333500000, Time: 0.0050 seconds

B

NumPy sum: 333332833333500000, Time: 0.0050 seconds
Loop sum: 333332833333500000, Time: 1.2000 seconds

C

NumPy sum: 500000500000, Time: 0.0050 seconds
Loop sum: 500000500000, Time: 1.2000 seconds

D

NumPy sum: 333332833333500000, Time: 0.0050 seconds
Loop sum: 0, Time: 1.2000 seconds

💡 Hint

NumPy uses optimized C code internally, so it runs much faster than Python loops.

The NumPy sum of squares is correct and computed very fast. The Python loop computes the same sum but takes much longer.

❓ data_output

intermediate

Result shape after applying a slow Python function with np.vectorize

Given the code below, what is the shape of the output array?

NumPy

import numpy as np

def slow_func(x):
    return x ** 2 + 1

vec_func = np.vectorize(slow_func)
arr = np.arange(12).reshape(3,4)
result = vec_func(arr)
print(result.shape)

A (3, 4)

B (12,)

C (4, 3)

D (1, 12)

💡 Hint

np.vectorize preserves the input array shape.

np.vectorize applies the function element-wise and returns an array with the same shape as the input.

🔧 Debug

advanced

Why does this Numba JIT function run slower than NumPy?

Consider this code using Numba's JIT to speed up a function. Why might it run slower than the pure NumPy version?

NumPy

import numpy as np
from numba import jit

@jit(nopython=True)
def sum_squares(arr):
    total = 0
    for i in range(arr.size):
        total += arr[i] ** 2
    return total

arr = np.arange(1_000_000)

import time
start = time.time()
result_numba = sum_squares(arr)
end = time.time()
numba_time = end - start

start = time.time()
result_numpy = np.sum(arr ** 2)
end = time.time()
numpy_time = end - start

print(f"Numba time: {numba_time:.4f} seconds")
print(f"NumPy time: {numpy_time:.4f} seconds")

A Numba runs slower because np.arange is incompatible with Numba.

B Numba runs slower because the JIT compiler is not installed correctly.

C Numba runs slower because the function uses a Python loop instead of vectorized operations.

D Numba runs slower because the function is missing a return statement.

💡 Hint

Numba speeds up loops but cannot beat fully vectorized NumPy operations.

Numba speeds up loops but vectorized NumPy operations are implemented in optimized C code and often run faster than explicit loops, even JIT compiled.

🧠 Conceptual

advanced

When to consider alternatives to NumPy for speed

Which scenario is the best reason to consider alternatives like Numba or Cython instead of pure NumPy?

A When you want to use built-in NumPy functions for matrix multiplication.

B When you want to plot data using matplotlib.

C When you want to load data from CSV files quickly.

D When you need to speed up element-wise operations that cannot be vectorized easily.

💡 Hint

Think about when vectorization is not possible or practical.

NumPy is fast for vectorized operations. For complex element-wise logic that can't be vectorized, tools like Numba or Cython can speed up loops.

🚀 Application

expert

Optimizing a custom function with Numba for large arrays

You have a custom function that applies a complex formula element-wise on a large NumPy array. The pure Python loop is too slow. Which approach will most likely give the best speedup?

A Use Numba's @jit decorator with nopython=True on the loop function.

B Rewrite the function using only Python built-in functions without NumPy.

C Use np.vectorize to apply the function element-wise.

D Convert the array to a list and use a Python list comprehension.

💡 Hint

Consider which method compiles loops to fast machine code.

Numba's JIT with nopython=True compiles loops to fast machine code, giving large speedups for complex element-wise functions on arrays.

Practice

1. Why might NumPy sometimes be too slow for certain tasks?

easy

A. Because it does not support mathematical operations

B. Because it cannot handle arrays larger than 100 elements

C. Because it only works on single-core processors

D. Because it uses Python loops internally which are slow

Solution

1. Step 1: Understand NumPy's speed basis

   NumPy is fast because it uses optimized C code, but Python loops around NumPy operations can slow it down.

2. Step 2: Identify the cause of slowness

   When complex tasks require Python loops or non-vectorized code, speed drops because Python loops are slower than compiled code.

3. Final Answer:

   Because it uses Python loops internally which are slow -> Option D

4. Quick Check:

   Python loops slow NumPy = Because it uses Python loops internally which are slow [OK]

Hint: NumPy is fast with vectorized code, slow with Python loops [OK]

Common Mistakes:

• Thinking NumPy can't handle large arrays
• Believing NumPy only works on single-core CPUs
• Assuming NumPy lacks math operation support

2. Which of the following is the correct way to import Numba to speed up NumPy code?

easy

A. import numba as nb

B. import numba.speedup

C. from numba import jit

D. import numba.jit

Solution

1. Step 1: Recall Numba import syntax

   Numba's just-in-time compiler is accessed by importing jit from numba: from numba import jit.

2. Step 2: Check other options

   Options A, C, and D are invalid imports; 'import numba as nb' imports the whole module but requires nb.jit to use the decorator, while C and D do not exist.

3. Final Answer:

   from numba import jit -> Option C

4. Quick Check:

   Correct Numba import = from numba import jit [OK]

Hint: Use 'from numba import jit' to access speedup decorator [OK]

Common Mistakes:

• Trying to import submodules that don't exist
• Importing whole numba without jit
• Using incorrect import syntax

3. What will be the output of this code snippet?

import numpy as np
from numba import jit

@jit(nopython=True)
def sum_squares(n):
    total = 0
    for i in range(n):
        total += i * i
    return total

print(sum_squares(5))

medium

A. 30

B. 55

C. 10

D. Error due to jit decorator

Solution

1. Step 1: Understand the function logic

   The function sums squares of numbers from 0 to n-1. For n=5, it sums 0²+1²+2²+3²+4² = 0+1+4+9+16 = 30.

2. Step 2: Check jit decorator effect

   The jit decorator speeds up the function but does not change output. No error occurs.

3. Final Answer:

   30 -> Option A

4. Quick Check:

   Sum of squares 0 to 4 = 30 [OK]

Hint: Sum squares 0 to 4 = 30; jit doesn't change output [OK]

Common Mistakes:

• Confusing sum of squares with sum of numbers
• Expecting jit to cause errors
• Miscounting range end

4. Identify the error in this code that tries to speed up a NumPy operation using Numba:

import numpy as np
from numba import jit

@jit
def multiply_array(arr):
    return arr * 2

print(multiply_array(np.array([1, 2, 3])))

medium

A. Numba jit cannot speed up NumPy array operations directly

B. The jit decorator is missing parentheses

C. The function multiply_array must use a loop inside

D. NumPy arrays cannot be passed to jit functions

Solution

1. Step 1: Understand Numba's limitations

   Numba jit speeds up Python loops and scalar operations but does not speed up vectorized NumPy operations directly.

2. Step 2: Analyze the code behavior

   The function returns arr * 2, which is a NumPy vectorized operation. Numba jit won't speed this up; it just calls NumPy internally.

3. Final Answer:

   Numba jit cannot speed up NumPy array operations directly -> Option A

4. Quick Check:

   Numba jit doesn't speed vectorized NumPy ops = Numba jit cannot speed up NumPy array operations directly [OK]

Hint: Numba jit speeds loops, not vectorized NumPy ops [OK]

Common Mistakes:

• Thinking jit decorator syntax is wrong
• Believing jit requires loops inside
• Assuming NumPy arrays can't be used with jit

5. You have a large NumPy array and want to speed up a custom function that applies a complex calculation element-wise. Which approach is best?

hard

A. Use pure Python loops without any acceleration

B. Rewrite the function using Numba jit with a loop over array elements

C. Convert the array to a list and use list comprehensions

D. Use NumPy vectorized operations only, no jit

Solution

1. Step 1: Understand the problem context

   Complex element-wise calculations may not be vectorizable easily with NumPy, so pure vectorized operations might not work.

2. Step 2: Choose the best speedup method

   Using Numba jit with a loop over array elements compiles the loop to fast machine code, speeding up the custom calculation.

3. Step 3: Evaluate other options

   Pure Python loops and list comprehensions are slow; vectorized NumPy ops may not support complex logic.

4. Final Answer:

   Rewrite the function using Numba jit with a loop over array elements -> Option B

5. Quick Check:

   Numba jit + loops = best speedup for complex element-wise ops [OK]

Hint: Use Numba jit with loops for complex element-wise speedup [OK]

Common Mistakes:

• Relying on pure Python loops for speed
• Converting arrays to lists unnecessarily
• Assuming all complex ops can be vectorized