regulafalsi.py

import math
import matplotlib.pyplot as plt

def f(x):
    return math.exp(x) - (5 * (x ** 2))

x = [i * 0.05 for i in range(-50, 50 + 1)]
y = [f(i * 0.05) for i in range(-50, 50 + 1)]

plt.plot(x, y, label="f(x) = e^x - 5x^2")

def regulafalsi(a, b, eps, eps2):
    a, b = a, b
    iter = 0

    while (abs(a - b) >= eps):
        fa, fb = f(a), f(b)
        
        c = b - (fb * (b - a)) / (fb - fa)
        fc = f(c)

        if (abs(fc) < eps2):
            return c, iter

        else:
            if (fa * fc < 0):
                b = c

            else:
                a = c

        iter += 1

    return c, iter

def regulafalsi_plot(a, b, eps, eps2) -> None:
    a, b = a, b
    iter = 0

    plt.xlim(-1 * abs((a - b) / 2), abs(a - b))
    plt.ylim(f(abs(a - b)) * -1, f(abs(a - b)))

    plt.plot([a, a], [0, f(a)], color="black", linestyle="dashed")
    plt.plot([b, b], [0, f(b)], color="black", linestyle="dashed")

    while (abs(a - b) >= eps):
        fa, fb = f(a), f(b)
        plt.plot([a, b], [fa, fb], color="black", linestyle="dashed")
        
        c = b - (fb * (b - a)) / (fb - fa)
        fc = f(c)

        plt.scatter(c, 0, color="green")

        if (abs(fc) < eps2):
            break

        else:
            if (fa * fc < 0):
                b = c

            else:
                a = c

        plt.plot([a, a], [0, f(a)], color="black", linestyle="dashed")
        plt.plot([b, b], [0, f(b)], color="black", linestyle="dashed")

        iter += 1

    plt.grid()
    plt.xlabel("x")
    plt.ylabel("y = f(x)")

    plt.scatter(c, f(c), color="orange", label="solution")

    plt.show()

    return

a, b = 0, 1
eps = 0.00001
eps2 = 0.000001

solution, iter = regulafalsi(a, b, eps, eps2)
print("Using regula-falsi method, solution of e^x - 5x^2 =",
      round(solution, 6),
      "with", iter, "iterations")

regulafalsi_plot(a, b, eps, eps2)