NumPy: Compute the given polynomial values
17. Evaluate Polynomial Values
Write a NumPy program to compute the following polynomial values.
Sample Solution:
Python Code:
# Importing the NumPy library
import numpy as np
# Computing the value of the polynomial [1, -2, 1] when x = 2
print("Polynomial value when x = 2:")
print(np.polyval([1, -2, 1], 2))
# Computing the value of the polynomial [1, -12, 10, 7, -10] when x = 3
print("Polynomial value when x = 3:")
print(np.polyval([1, -12, 10, 7, -10], 3))
Sample Output:
Polynomial value when x = 2: 1 Polynomial value when x = 3: -142
Explanation:
numpy.polyval(p, x) evaluates the polynomial p at x.
np.polyval([1, -2, 1], 2): Here p = [1, -2, 1], so the polynomial is x^2 - 2x + 1. We evaluate this polynomial at x=2, which gives 2^2 - 2*2 + 1 = 1.
np.polyval([1, -12, 10, 7, -10], 3): Here p = [1, -12, 10, 7, -10], so the polynomial is x^4 - 12x^3 + 10x^2 + 7x - 10. We evaluate this polynomial at x=3, which gives 3^4 - 12*3^3 + 10*3^2 + 7*3 - 10 = -142
Pictorial Presentation:
For more Practice: Solve these Related Problems:
- Implement a function that evaluates a polynomial at a given value using np.polyval and returns the result.
- Test the function on multiple input values and verify that the outputs match manual calculations.
- Create a solution that handles polynomials of varying degrees and returns an array of evaluated values.
- Compare the np.polyval output with a custom implementation using Horner’s method for efficiency.
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Python-Numpy Code Editor:
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