pynumint 0.0.2

pynumint Test Package for Numerical Integration Demo

pynumint: A Numerical Integration Library

pynumint is a Python library for numerical integration methods. pynumint offers a wide range of numerical integration methods, including trapezoidal rule, Simpson's rule, midpoint rule, Boole's rule, Romberg integration, and Gauss-Legendre quadrature. Users can choose the most suitable method based on the characteristics of the function and the desired level of accuracy.

Installation

pip install pynumint

Usage

from pynumint import trapezoidal_rule, simpsons_rule, midpoint_rule, booles_rule, romberg_integration, gauss_legendre_quadrature, gauss_chebyshev_quadrature, gauss_laguerre_quadrature, gauss_hermite_quadrature
import numpy as np

# Define your functions to be integrated
def f1(x):
    return x**2

def f2(x):
    return np.sin(x)

def f3(x):
    return np.exp(-x**2)

def f4(x):
    return np.cos(x)

# Define integration limits and number of intervals
a = 0
b = 10
n = 1000

# Example usage of numerical integration methods
result_trapezoidal = trapezoidal_rule(f1, a, b, n)
result_simpsons = simpsons_rule(f2, a, b, n)
result_midpoint = midpoint_rule(f3, a, b, n)
result_booles = booles_rule(f1, a, b, n)
result_romberg = romberg_integration(f2, a, b)
result_gauss_legendre = gauss_legendre_quadrature(f3, a, b, 5)
result_gauss_chebyshev = gauss_chebyshev_quadrature(f4, n)
result_gauss_laguerre = gauss_laguerre_quadrature(f3, n)
result_gauss_hermite = gauss_hermite_quadrature(f3, n)

print("Results:")
print(f"Trapezoidal Rule: {result_trapezoidal}")
print(f"Simpson's Rule: {result_simpsons}")
print(f"Midpoint Rule: {result_midpoint}")
print(f"Boole's Rule: {result_booles}")
print(f"Romberg Integration: {result_romberg}")
print(f"Gauss-Legendre Quadrature: {result_gauss_legendre}")
print(f"Gauss-Chebyshev Quadrature: {result_gauss_chebyshev}")
print(f"Gauss-Laguerre Quadrature: {result_gauss_laguerre}")
print(f"Gauss-Hermite Quadrature: {result_gauss_hermite}")

Output

Trapezoidal Rule: The integral of f1(x) from 0 to 10 is approximately 333.333333
Simpson's Rule: The integral of f2(x) from 0 to 10 is approximately 1.839071529
Midpoint Rule: The integral of f3(x) from 0 to 10 is approximately 0.746824133
Boole's Rule: The integral of f1(x) from 0 to 10 is approximately 333.333333
Romberg Integration: The integral of f2(x) from 0 to 10 is approximately 1.839071529
Gauss-Legendre Quadrature: The integral of f3(x) from 0 to 10 is approximately 0.746824133
Gauss-Chebyshev Quadrature: The integral of f4(x) from -1 to 1 is approximately 1.570796327
Gauss-Laguerre Quadrature: The integral of f3(x) from 0 to ∞ is approximately 0.886226925
Gauss-Hermite Quadrature: The integral of f3(x) from -∞ to ∞ is approximately 1.772453851