#%%
import numpy as np

# %%
print("Aufgabe 4")

def fixpunkt_iteration(f, x, tol=1e-7):
    x_new = f(x)
    i = 0

    while(np.abs(x_new-x) > tol):
        x = x_new
        x_new = f(x)
        i += 1
    return [x_new, i]

x0 = 1.0

f = lambda x: 1-(1/5)*x
fixpunkt_a, iterationen_a = fixpunkt_iteration(f, x0)

f = np.cos
fixpunkt_b, iterationen_b = fixpunkt_iteration(f, x0)

f = lambda x: np.e**-x
fixpunkt_c, iterationen_c = fixpunkt_iteration(f, x0)

# Ausgabe
print("----------------------------------------------------------------------")
print(__file__)
print("----------------------------------------------------------------------")
print(f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n")
print(f"b) f(x) = cos(x)\nFixpunkt: {fixpunkt_b}\nIterationen: {iterationen_b}\n")
print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")
print("----------------------------------------------------------------------")