Performance tips and vectorization in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of vectorized operation with NumPy arrays

What is the output of this code snippet using NumPy vectorization?

SciPy

import numpy as np
arr = np.array([1, 2, 3, 4])
result = arr * 2 + 1
print(result.tolist())

A [4, 6, 8, 10]

B [1, 3, 5, 7]

C [3, 5, 7, 9]

D [2, 4, 6, 8]

💡 Hint

Remember vectorized operations apply element-wise.

Each element in the array is multiplied by 2, then 1 is added. So 1*2+1=3, 2*2+1=5, etc.

❓ data_output

intermediate

Resulting shape after vectorized matrix multiplication

Given two NumPy arrays A with shape (3, 4) and B with shape (4, 2), what is the shape of the result after np.dot(A, B)?

SciPy

import numpy as np
A = np.ones((3, 4))
B = np.ones((4, 2))
result = np.dot(A, B)
print(result.shape)

A (3, 2)

B (4, 4)

C (3, 4)

D (2, 3)

💡 Hint

Matrix multiplication shape rule: (m,n) dot (n,p) = (m,p).

The dot product of (3,4) and (4,2) results in shape (3,2).

🔧 Debug

advanced

Identify the error in vectorized code using SciPy sparse matrix

What error will this code raise when executed?

SciPy

from scipy.sparse import csr_matrix
import numpy as np

sparse_mat = csr_matrix([[1, 0], [0, 2]])
result = sparse_mat * np.array([1, 2, 3])

A IndexError: index out of bounds

B TypeError: unsupported operand type(s) for *: 'csr_matrix' and 'list'

C No error, outputs a sparse matrix

D ValueError: dimension mismatch

💡 Hint

Check the shapes of the sparse matrix and the array for multiplication compatibility.

The sparse matrix shape is (2,2) but the array has shape (3,), so multiplication fails due to dimension mismatch.

🚀 Application

advanced

Choosing vectorized approach for element-wise operation

You want to compute the square root of each element in a large NumPy array efficiently. Which approach is fastest and uses vectorization?

A Use list comprehension with math.sqrt for each element.

B Use np.sqrt(array) to compute all square roots at once.

C Use a for loop to compute sqrt for each element individually.

D Convert array to list and use map with math.sqrt.

💡 Hint

Vectorized NumPy functions are optimized for array operations.

np.sqrt is a vectorized function that applies sqrt element-wise efficiently without Python loops.

🧠 Conceptual

expert

Why vectorization improves performance in SciPy and NumPy?

Which explanation best describes why vectorization improves performance in SciPy and NumPy?

A Vectorization reduces Python-level loops by using optimized C/Fortran code that runs faster.

B Vectorization increases memory usage but slows down computation due to overhead.

C Vectorization replaces all functions with GPU code by default.

D Vectorization allows parallel execution on multiple CPUs automatically without any code changes.

💡 Hint

Think about how vectorized operations avoid slow Python loops.

Vectorization uses compiled code underneath to perform operations on whole arrays at once, avoiding slow Python loops.