# Creator _Sabyasachi

import numpy as np
import matplotlib.pyplot as plot

total_iteration = 1
number_of_iteration = 1


def plotting(z):
    to_return = (z / (1 - z)) * (np.sqrt(6 / (2 + z))) - .05
    return to_return


def graph(k):
    y = plotting(k)
    plot.figure(figsize=(5, 5))
    plot.plot(k, y)
    plot.grid()
    plot.show()


def secant_method(func, first_guess, second_guess, relative_error, max_iteration):
    global total_iteration
    p = 0.0
    if func(first_guess) * func(second_guess) > 0:
        return None

    while total_iteration < max_iteration and np.abs(second_guess - first_guess) > relative_error:
        try:
            a = first_guess
            b = second_guess
            p = (a*func(b) - b*func(a))/(func(b) - func(a))
        except ZeroDivisionError:
            print("Error! - Divided by zero")
            exit(-1)
        first_guess = second_guess
        second_guess = p
        total_iteration += 1
    if abs(func(second_guess)) > relative_error:
        print("Secant fails after ", total_iteration, " number of iteration")
        total_iteration = -1
    return p


def false_position_method(func, lower_bracket, upper_bracket, app_error, max_iteration):
    global number_of_iteration
    fa = func(lower_bracket)

    while number_of_iteration <= max_iteration:
        a = lower_bracket
        b = upper_bracket
        p = (a * func(b) - b * func(a)) / (func(b) - func(a))
        fp = func(p)

        if fp == 0 or np.abs(func(p)) <= app_error:
            return p
        elif fp * fa >= 0:
            fa = fp
            lower_bracket = p
        else:
            upper_bracket = p
        number_of_iteration += 1

    return None


x = np.arange(-1.9, 1, 0.1)
graph(x)
tolerable_error = 5e-3

iteration_counter = int(input("Enter the maximum number of iteration for Secant and False Position Method : "))
initial_guess = float(input("Enter 1st initial guess for Secant Method : "))
initial_guess_2 = float(input("Enter 2nd initial guess for Secant Method : "))
lower_bound = float(input("Enter lower bound of the bracket for False Position Method : "))
upper_bound = float(input("Enter upper bound of the bracket for False Position Method : "))

sect_method = secant_method(plotting, initial_guess, initial_guess_2, tolerable_error, iteration_counter)

print()
print("Showing the result for Secant Method :")
if total_iteration > 0:
    print("Result found between the given interval ")
    print("Result :", sect_method, " iteration:", total_iteration)
else:
    print("No result found between the given interval :'( \nGood Luck!")

fpm = false_position_method(plotting, lower_bound, upper_bound, tolerable_error, iteration_counter)
print("Showing the result for FP Method :")

if number_of_iteration > 0:
    print("Result found between the given interval ")
    print("Result :", fpm, " iteration:", number_of_iteration)
else:
    print("No result found between the given interval :'( \nGood Luck!")