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import matplotlib.pyplot as plt
import numpy as np
from numpy import log, exp, sqrt


N_values = [5.0 * 2**i for i in range(0, 32, 4)]


def W(N, ni):
    lnW_max = N * log(N) - 2.0 * N / 2.0 * log(N / 2.0)

    W_list = []
    for _ni in ni:
        ni_t = _ni * log(_ni) if _ni > 0 else 0
        Nni_t = (N - _ni) * log(N - _ni) if N - _ni > 0 else 0

        lnW = N * log(N) - ni_t - Nni_t - lnW_max
        W_list.append(exp(lnW))

    return W_list

plt.title('# of configrations ($_NC_{n_i}$)')
fig, ax = plt.subplots()

for N in N_values:
    N_avg = N * 0.5
    Nrange = 6.0 * sqrt(N)
    logni = np.linspace(log(max([1.0, N_avg - Nrange])), log(N_avg + Nrange), 500)
    ni = exp(logni)
    W_ni = W(N, ni)
    x = ni / N

#    W_ni /= max(W_ni)
    ax.plot(x, W_ni, label = f'N = {N:.2g}', linewidth = 1.0)


ax.set_xlabel('$n_i / N$')
ax.set_ylabel('$W(n_i)$')
ax.set_xlim([0.1, 1.0])
ax.set_xscale('log')
#ax.set_yscale('log')

#for tick in ax.get_xticklabels():
#    tick.set_rotation(45)

ax.legend()
plt.grid(True)

plt.tight_layout()

plt.savefig('plotW.png')

plt.pause(0.1)
input(">>")