# -*- coding: utf-8 -*-
#
# regulafalsi.py
#
#
# Autor: Pedro Garcia Freitas <sawp@sawp.com.br>
# License: Creative Commons
#      <http://creativecommons.org/licenses/by-nc-nd/2.5/br/>
#

from math import fabs, exp

def RegulaFalsi(F, xl, xr, errto=0.01, imax=1000):
    """
    Return the root of a function using Regula Falsi

    RegulaFalsi(fun, xl, xr, imax, errto)
    
    * fun: Function where find the roots
    * xl: left bound of interval
    * xr: right bound of interval
    * imax: max of iterations allowed
    * errto: tolerated error

    Author: Pedro Garcia <sawp@sawp.com.br>
    License: Creative Commons
         <http://creativecommons.org/licenses/by-nc-nd/2.5/br/>
    """
    x = 0
    iterCount = 0
    errno = 1

    fl = F(xl)

    while errno > errto and iterCount < imax:
        xold = x
        iterCount = iterCount + 1

        fr = F(xr)

        # x = (xl+xr)/2.l ponto onde modifica a Bisseccao
        x = xr - fr*(xl-xr)/(fl - fr)

        fx = F(x)
        
        if x != 0:
            errno = fabs((x - xold)/x)

        test = fl * fx

        if test < 0:
            xr = x
        elif test > 0:
            xl = x
            fl = fx
        else:
            errno = 0

    return x

if __name__ == "__main__":
    f = lambda x: exp(-x) - x
    print RegulaFalsi(f, 1.2, 50, 0.0001,100)