import numpy as np
import matplotlib.pyplot as plt

def bisection(f, a, b, eps):
    fa = f(a)
    if fa * f(b) > 0:
        return None, 0
        # Alternativ: raise ValueError(
        # f'Ingen fortegnsskifte i [{a:g},{b:g}]')

    i = 0  # iterasjonsteller
    while b - a > eps:
        i += 1
        m = (a + b)/2.0
        fm = f(m)
        if fa * fm <= 0:
            b = m  # roten er i venstre  halvdel av [a,b]
        else:
            a = m  # roten er i h?yre halvdel av [a,b]
            fa = fm
    return m, i



def f(x):
    return np.sin(x) * np.exp(-0.1 * x)

#first, plot the function:
x = np.linspace(0, 20, 101)
plt.plot(x, f(x))
plt.show()

#solve f(x) = 0, for starting interval [0.1, 5]
x_val, iter = bisection(f, a=0.1, b=5, eps=1E-5)

print(f'Found approximate root x = {x_val:g} with f(x) = {f(x_val):g}, in {iter} iterations')

"""
Terminal> python halveringsmetoden.py 
Found approximate root x = 3.14159 with f(x) = -2.37995e-07, in 19 iterations
"""