import numpy
import matplotlib.pyplot as plt


def evaluate(length, phi0, timestep):  # length in m, phi0 in rad, timestep in s
    tau_quadrat = ((2 * length) / (3 * 9.81))
    phi = phi0
    v_phi = 0
    time = 0
    while phi < numpy.pi / 2:
        a_phi = numpy.sin(phi) / tau_quadrat
        v_phi += timestep * a_phi
        phi += timestep * v_phi
        time += timestep
    return time


# testing the evaluation
prec_test = 0.01
phi0s_test = [0 + prec_test * i for i in range(1, round(2 * numpy.pi / prec_test) + 1)]
sols_test = [evaluate(1.45, phi0, 0.01) for phi0 in phi0s_test]
plt.plot(phi0s_test, sols_test, label='test', ls='', marker='.')
plt.legend()
plt.show()
print('Wir lesen aus dem Grafen ab: 0.81\nSelbst gerechneter Wert:', evaluate(1.45, 0.25, 0.01))


def find_sol(length, phi0, prec):  # length in m, phi0 in rad, prec is the number of decimal places
    prev = None
    for i in range(10):
        sol = evaluate(length, phi0, 0.1 ** i)
        if prev and abs(sol - prev) < 0.5 * 0.1 ** prec:
            break
        prev = sol
    return sol


def find_sols(lengths, phi0s, prec):
    sols = {}
    for length in lengths:
        phi_sols = []
        for phi0 in phi0s:
            phi_sols += [find_sol(length, phi0, prec)]
        sols[length] = [phi0s, phi_sols]
    return sols