# -*- coding: utf-8 -*-
#
# secante.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 secante(F, x0=1.0, xminus1=0.0, errto=0.001, imax=100):
    """
    return the root of a function (using the Secant Method)

    secante(F, x0=1.0, xminus1=0.0, errto=0.001, imax=100)
    
    * F: Function where find the roots
    * x0: next point (estimative)
    * xminus: xi-1, used to define another bound
    * errto: tolerated error
    * imax: max of iterations allowed

    Author: Pedro Garcia <sawp@sawp.com.br>
    see: http://www.sawp.com.br
    License: Creative Commons
         <http://creativecommons.org/licenses/by-nc-nd/2.5/br/>

    Dec 2009
    """

    iterCount = 0
    errno = errto + 1
    x1 = x0
    x0 = xminus1

    while errno > errto and iterCount < imax:
        xminus1 = x0
        x0 = x1

        # in Newton-Raphson will be x1 = x0 - G(x0)/diffG(x0)
        # in fixed point will be x1 = G(x0)
        x1 = x0 - (F(x0)*(xminus1 - x0))/(F(xminus1) - F(x0))

        iterCount += 1

        if x1 != 0:
            errno = fabs((x1 - x0)/x1)

    return x1

if __name__ == "__main__":
    print secante((lambda x: exp(-x) - x), 0, 1, 0.0001,100)