np.vectorize() for custom functions in NumPy - Time & Space Complexity

Time Complexity: np.vectorize() for custom functions

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run a custom function on many numbers changes when using np.vectorize().

How does the work grow when we apply the function to bigger arrays?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

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

n = 10
vec_func = np.vectorize(my_func)
arr = np.arange(n)
result = vec_func(arr)

This code applies a custom function to each element of an array using np.vectorize.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Applying my_func to each element of the array.
• How many times: Once for each element in the input array (n times).

How Execution Grows With Input

As the array size grows, the function runs once per element, so the total work grows in direct proportion to the number of elements.

Input Size (n)	Approx. Operations
10	10 function calls
100	100 function calls
1000	1000 function calls

Pattern observation: Doubling the input size roughly doubles the work done.

Final Time Complexity

Time Complexity: O(n)

This means the time to run grows linearly with the number of elements in the array.

Common Mistake

[X] Wrong: "np.vectorize makes the function run faster by doing things all at once like built-in numpy operations."

[OK] Correct: np.vectorize is a convenience tool that still calls the function once per element in Python, so it does not speed up the function itself.

Interview Connect

Understanding how np.vectorize works helps you explain performance when using custom functions on arrays, a useful skill for data tasks and coding interviews.

Self-Check

What if we replaced np.vectorize with a true numpy ufunc? How would the time complexity change?