"""
The Gumbell distribution
=========================

Generate the exercise results on the Gumbell distribution
"""
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt


def gumbell_dist(arr):
    return -np.log(-np.log(arr))

years_nb = 21
wspeeds = np.load('sprog-windspeeds.npy')
max_speeds = np.array([arr.max() for arr in np.array_split(wspeeds, years_nb)])
sorted_max_speeds = np.sort(max_speeds)

cprob = (np.arange(years_nb, dtype=np.float32) + 1)/(years_nb + 1)
gprob = gumbell_dist(cprob)
speed_spline = sp.interpolate.UnivariateSpline(gprob, sorted_max_speeds, k=1)
nprob = gumbell_dist(np.linspace(1e-3, 1-1e-3, 100))
fitted_max_speeds = speed_spline(nprob)

fifty_prob = gumbell_dist(49./50.)
fifty_wind = speed_spline(fifty_prob)

plt.figure()
plt.plot(sorted_max_speeds, gprob, 'o')
plt.plot(fitted_max_speeds, nprob, 'g--')
plt.plot([fifty_wind], [fifty_prob], 'o', ms=8., mfc='y', mec='y')
plt.plot([fifty_wind, fifty_wind], [plt.axis()[2], fifty_prob], 'k--')
plt.text(35, -1, r'$V_{50} = %.2f \, m/s$' % fifty_wind)
plt.xlabel('Annual wind speed maxima [$m/s$]')
plt.ylabel('Gumbell cumulative probability')
plt.show()