Module:Harmonic entropy: Difference between revisions
Deprecating ET parsing and backslash ratio: those were ET-specific and not interval-specific. Functionality moved into Module:ET |
m harmonic_entropy() implemented |
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return u._round(result, prec) | return u._round(result, prec) | ||
end | end | ||
end | |||
-- compute Shannon harmonic entropy for an interval of `c` cents | |||
-- `c`, `deviation`: in cents | |||
-- `ratios`: an array of rational numbers | |||
-- `norm`: a function of rational numbers | |||
function p.harmonic_entropy(c, ratios, deviation, norm) | |||
deviation = deviation or 17 | |||
norm = norm or function(ratio) | |||
return math.sqrt(rat.beneditti_height(ratio)) | |||
end | |||
local function S(x) | |||
return math.exp(-x*x / (2*deviation*deviation)) / (deviation * math.sqrt(2*math.pi)) | |||
end | |||
local function Q(ratio) | |||
return S(rat.cents(ratio) - c) / norm(ratio) | |||
end | |||
local Q_norm = 0 | |||
for i, ratio in ipairs(ratios) do | |||
Q_norm = Q_norm + Q(ratio) | |||
end | |||
local function P(ratio) | |||
return Q(ratio) / Q_norm | |||
end | |||
local entropy = 0 | |||
for i, ratio in ipairs(ratios) do | |||
local P_i = P(ratio) | |||
if P_i > 1e-5 then | |||
entropy = entropy - P_i * math.log(P_i) / math.log(2) | |||
end | |||
end | |||
return entropy | |||
end | end | ||
return p | return p | ||