import numpy as np
# the package numpy is only required for the definition of the
# exponential function below

# function defining the fixed point iteration
# NB: there is no convergence/divergence check, the function
# simply applies n iterations of the fixed point iteration with
# starting value s for the function g
# it can happen that convergence is reached well before the
# number of iterations, but the iteration may also diverge
def fix_iter(g,s,n):
    x = start_point
    for k in range(1,n):
        x = g(x)
    return x

## a small experiment with the function from the lecture
# definition of the function
def fix_fun(x):
    return np.exp(x)/3

# you may freely change starting point and number of iterations
start_point = 0
n_iter = 50

# run the iteration (and display the result)
fix_iter(fix_fun,start_point,n_iter)