# -*- coding: utf-8 -*-
#
# newtonRaphson.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 newtonRaphson(G, diffG, x0, errto, imax):
    """
    return the root of a function (using the Newton-Raphson Method)

    newtonRaphson(fun, diffFun, x0, errto, imax)
    
    * fun: Function where find the roots
    * diffFun: analytic derivative of fun
    * x0: next point (estimative)
    * 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
    """

    x1 = x0 - G(x0)/diffG(x0) # fixed point x1 = G(x0)
    iterCount = 0
    errno = fabs((x1 - x0)/x1)

    while errno > errto and iterCount < imax:
		x0 = x1
		x1 = x0 - G(x0)/diffG(x0) # in fixed point will be x1 = G(x0)
		iterCount += 1

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

    return x1

if __name__ == "__main__":
    f = lambda x: exp(-x) - x
    d2f = lambda x: -exp(-x) - 1
    print newtonRaphson(f, d2f, 1.2, 0.0001, 100)

    f = lambda x: exp(-x) + x/5.0 - 1.0
    df = lambda x: -exp(-x) + .20
    print newtonRaphson(f, df, 1234e+10, 1e-14, 10000)