#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Apr  2 08:39:37 2025

@author: hundledr-local
"""

def bisection(f,a,b,tol):
 """
  Bisection Method
     Computes an approximation to f(x)=0 given that the 
     root is bracketed in [a,b] with f(a)f(b)<0.
     Will run until TOL is reached, and will output the solution xc
     
    In this version, we assume the function f is passing both the
    value of the function AND its derivative (so it lines up with 
    Newton's Method')
    
"""
 u=f(a)
 fa=u[0]
 u=f(b)
 fb=u[0]
 if fa*fb >= 0:
        print("Root may not be bracketed.")
        return None
 
 iter=0
 while (b-a)/2>tol:
        iter+=1
        c = (a + b)/2
        u = f(c)
        fc=u[0]
        if fc==0:
            print("Found exact solution.")
            return c
        elif fa*fc < 0:
            b=c
            fb=fc
        else:
            a=c
            fa=fc
        
 print('Finished after %3d iterations.\n' % iter )       
 return (a + b)/2

# Example: Finding the root of f(x) = x^3 - 4x - 9 in [2, 3]
def func(x):
    return x**3 + x - 1

root = bisection_method(func, 0, 1, 5e-5)
print(f"Root found: {root:.6f}")