import numpy as np
from math import sqrt
from scipy.misc import derivative

def newton_method(x, x1, function):
    return x-(function(x)/derivative(function, x))


def drying_method(x0, x1, function):
    return (x0*function(x1)-x1*function(x0))/(function(x1)-function(x0))

def bissection(x0,x1,function,precision=1e-3):
    if x0 > x1:
        x0,x1 = x1,x0
    k = 0
    mei = (x0+x1)/2.0
    while abs(x1-x0)>=precision and abs(function(mei))>=precision:
        k += 1
        if function(mei)*function(x0)<=0:
            x1 = mei
        else:
            x0 = mei
        mei = (x0+x1)/2.0
        # print str(mei)
    return mei,k


def fixed_point_template(x0,x1,iteration_function,function,precision=1e-3):
    k = 0
    x = iteration_function(x0,x1,function)
    while abs(x-x1)>=precision and abs(function(x1))>=precision:
        k += 1
        x0,x1 = x1, x
        x = iteration_function(x0,x1,function)
    return x,k




def chaos_function(x):
    return (8 - sqrt(400-x**2)) * sqrt(900-x**2) + 8 * sqrt(400-x**2)
    # return ((8/sqrt(400-x**2)) - 1) * sqrt(900-x**2) + 8

def carlos_function(x):
    return (sqrt(400-x**2)*sqrt(900-x**2))/(sqrt(400-x**2)+sqrt(900-x**2))-8



# x,n = bissection(1.0,20.0,chaos_function)
x0,x1 = 8,20
# try:
#
# except Exception:
#     print "Errou"

x,n = fixed_point_template(x0,x1,drying_method,chaos_function)
print "Chaos:raiz:"+str(x)+", iterations:"+str(n)

# x,n = fixed_point_template(x0,x1,newton_method,carlos_function)
# print "Carlo:raiz:"+str(x)+", iterations:"+str(n)








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