#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Aug 26 22:42:51 2024

@author: amriksen
"""
import math
import sympy as sp
from colorama import Fore, Back, Style # for colored printed text
import sys


# Define the symbol
x = sp.Symbol('x')


# Newton-Raphsson method for root finding problems -- single variable case 
def my_Newtons_Method(f, f_prime, x0, tolerance=1e-10, max_iterations=10):
    xn = x0
    errors = []
    root_approx = []

    for n in range(max_iterations):
        fxn = f.subs(x, xn)
        fpxn = f_prime.subs(x, xn)
        
        if fpxn == 0:
            print("Zero derivative. No solution found.")
            return None, errors
        
        xn_new = xn - fxn / fpxn
        # Calculate the error as the absolute difference between successive approximations
        error = abs(xn_new - xn)
        errors.append(error)
        root_approx.append(xn_new)

        print(f"Iteration {n+1}: x = {xn_new}, Error = {error}")
    
        # Check for convergence
        if error < tolerance:
            print(f"Converged to {xn_new} after {n+1} iterations.")
            break
    
        xn = xn_new
        
    return xn, errors, root_approx



# Fixed-point iteration function
def my_Fixed_Point_Iteration_Method(g_numeric, x0, tolerance=1e-10, max_iterations=10):
    xn = x0
    errors = []
    root_approx = []
    for n in range(max_iterations):
        xn_new = g_numeric(xn)
        print(f"Iteration {n+1}: x = {xn_new}")
        
        # Calculate the error as the absolute difference between successive approximations
        error = abs(xn_new - xn)
        errors.append(error)
        root_approx.append(xn_new)

        print(f"Iteration {n+1}: x = {xn_new}, Error = {error}")
    
        # Check for convergence
        if error < tolerance:
            print(f"Converged to {xn_new} after {n+1} iterations.")
            break
        
        xn = xn_new
    
    if error > tolerance:
        print(Fore.YELLOW + "\n ERROR:  " + "Maximum iterations reached without convergence!\n" + Style.RESET_ALL)
        sys.exit(1)
    return xn, errors, root_approx