Create a custom ufunc in NumPy to compute x^2+2x+1

Last update on April 30 2025 12:56:23 (UTC/GMT +8 hours)

7. Custom Ufunc: Quadratic Expression

Custom ufunc with Multiple Operations:

Write a NumPy program that creates a custom ufunc that computes x^2 + 2x + 1 for each element in a NumPy array.

Sample Solution:

Python Code:

import numpy as np

# Define a custom function to compute x^2 + 2x + 1
def compute_expression(x):
    return x**2 + 2*x + 1

# Create a ufunc from the custom function using np.frompyfunc
compute_ufunc = np.frompyfunc(compute_expression, 1, 1)

# Create a 1D NumPy array of integers
array_1d = np.array([1, 2, 3, 4, 5])

# Apply the custom ufunc to the 1D array
result_array = compute_ufunc(array_1d)

# Print the original array and the resulting array
print('Original 1D array:', array_1d)
print('Resulting array after applying compute_ufunc:', result_array)

Output:

Original 1D array: [1 2 3 4 5]
Resulting array after applying compute_ufunc: [4 9 16 25 36]

Explanation:

Import Libraries:

Imported numpy as "np" for array creation and manipulation.

Define Custom Function:

Defined a custom function compute_expression that takes an input x and returns x^2+2x+1.

Create ufunc:

Create a ufunc from the custom function using np.frompyfunc. The function takes the custom function, the number of input arguments (1), and the number of output arguments (1).

Create 1D NumPy Array:

Create a 1D NumPy array named array_1d with integers [1, 2, 3, 4, 5].

Apply Custom ufunc:

Apply the custom ufunc compute_ufunc to the 1D array to obtain the result.

Print Results:

Print the original 1D array and the resulting array after applying the custom "ufunc".

For more Practice: Solve these Related Problems:

Write a Numpy program to define a custom ufunc that computes x² + 2x + 1 and then test it on an array with both positive and negative values.
Write a Numpy program to create a custom ufunc for x² + 2x + 1 and chain it with np.sqrt to compute the square root of the result.
Write a Numpy program to implement a custom ufunc for a quadratic function and compare its output with a vectorized expression of the same formula.
Write a Numpy program to define and apply a custom ufunc for x² + 2x + 1 on a large random array, then profile its performance.

Go to:

Previous: Create array using np.where based on condition in NumPy.
Next: Apply np.exp, np.log, and np.sqrt ufuncs to transform a NumPy array.

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