monte carlo integration of functions on subset of the real line

mc1.py

"""
    Monte Carlo integration of functions on subsets of the real line,
    using uniform probability distributions
"""
import math
import random


def montecarlo(f, g, a, b):
    """
    :param f: the integral function
    :param g: the integrand function
    :param a: integration lower point
    :param b: integration upper point
    :return: None
    """
    if f is not None:
        actual = f(b) - f(a)
        print(f"actual integral: {actual}")
    else:
        print("No analytical integral given. Cannot compute actual integral compare.")

    N = 10**6
    M = 10
    sm = 0.
    for j in range(M):
        for i in range(N):
            x = random.uniform(a, b)
            sm += g(x)
        computed = 1.0 * sm / (N*(j+1)) * (b - a)
        rel_err = abs(computed - actual) / actual if f is not None else 'n/a'
        print(f"finished. computed {computed} rel. error: {rel_err}")
    print('-' * 4)

def example1():
    f = math.sin
    g = math.cos
    a, b = 0.0, math.pi / 2
    montecarlo(f, g, a, b)

def example2():
    f = math.log
    g = lambda x: 1. / x
    a, b = 6., 11.
    montecarlo(f, g, a, b)

example1()
example2()