# %%
import numpy as np

# %%
print("Aufgabe 4")


def fixpunkt_iteration(f, x=1.0, tol=1e-7, N=1000):
    x_new = f(x)
    i = 0

    while np.abs(x_new - x) > tol:
        if i > N:
            raise RuntimeError("Keine Konvergenz erreicht")

        x = x_new
        x_new = f(x)
        i += 1
    return [x_new, i]


# Ausgabe
print("----------------------------------------------------------------------")
print(__file__)
print("----------------------------------------------------------------------")

f = lambda x: 1 - (1 / 5) * x
try:
    fixpunkt_a, iterationen_a = fixpunkt_iteration(f)
except RuntimeError as error:
    print(f"a) f(x) = 1-(1/5)*x\n{error}")
else:
    print(
        f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n"
    )

f = np.cos
try:
    fixpunkt_b, iterationen_b = fixpunkt_iteration(f)
except RuntimeError as error:
    print(f"b) f(x) = cos(x)\n{error}")
else:
    print(f"b) f(x) = cos(x)\nFixpunkt: {fixpunkt_b}\nIterationen: {iterationen_b}\n")

f = lambda x: np.e**-x
try:
    fixpunkt_c, iterationen_c = fixpunkt_iteration(f)
except RuntimeError as error:
    print(f"c) f(x) = e⁻x\n{error}")
else:
    print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")

print("----------------------------------------------------------------------")

##%
# Parameter
q = 2.0
a_0 = 1.0
pr = 16


# Funktionen
def f(x):
    y = 0.5 * (x + q / x)
    return y


# Iteration
w = 0.0
a = a_0
k = 0

print("----------------------------------------------------------------------")
print(__file__)
print("----------------------------------------------------------------------")
print("Iteration :")
print(f"a_{k} = {a:#.16g}")

while a != w:
    w = a
    k = k + 1
    a = f(a)
    print(f"a_{k} = {a:#.16g}")

# Ausgabe :
print("----------------------------------------------------------------------")
print(f"Wurzel: sqrt({q:#.{pr}g}) = {a:#.{pr}g}")
print("----------------------------------------------------------------------")