import math

import soundfile


def level_cross(levels, a, b):
    a_level = 0
    b_level = 0
    if a > b:
        a, b = b, a
    for i in range(len(levels)):
        if a < levels[i]:
            a_level = i
            break
    for i in range(len(levels)):
        if b < levels[i]:
            b_level = i
            break
    return range(a_level, b_level)


data, rate = soundfile.read('sig0001.wav')

umax = max(data)
umin = min(data)
N = 32
deltaU = (umax - umin) / N
Ulevels = [(i - N / 2) * deltaU for i in range(N)]

S = 0
Nlevels = [0 for i in range(len(Ulevels))]

for j in range(1, len(data)):
    increase_list = level_cross(Ulevels, data[j - 1], data[j])
    if increase_list:
        for index in increase_list:
            Nlevels[index] += 1

for value in Nlevels:
    S += value

print(S)
print(*Ulevels)
print(*Nlevels)

chances = [Nlevels[i] / S for i in range(len(Ulevels))]
print(*chances)

Uavg = 0
for i in range(len(chances)):
    Uavg += Ulevels[i] * chances[i]

sigma = 0
for i in range(len(chances)):
    sigma += (Ulevels[i] - Uavg) * (Ulevels[i] - Uavg) * chances[i]
sigma = math.sqrt(sigma)

for i in range(len(chances) - 1, -1, -1):
    if chances[i] == 0:
        del chances[i]
        del Ulevels[i]

H = 0
for i in range(len(chances)):
    H -= chances[i] * math.log(chances[i])

nu = math.exp(H) / math.sqrt(2 * math.pi * sigma * sigma)

print(nu)