mirror of
https://github.com/sys4-fr/server-nalc.git
synced 2024-11-14 06:20:32 +01:00
150 lines
3.3 KiB
Lua
Executable File
150 lines
3.3 KiB
Lua
Executable File
local statistics = {}
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local ROOT_2 = math.sqrt(2.0)
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-- Approximations for erf(x) and erfInv(x) from
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-- https://en.wikipedia.org/wiki/Error_function
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local erf
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local erf_inv
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local A = 8 * (math.pi - 3.0)/(3.0 * math.pi * (4.0 - math.pi))
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local B = 4.0 / math.pi
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local C = 2.0/(math.pi * A)
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local D = 1.0 / A
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erf = function(x)
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if x == 0 then return 0; end
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local xSq = x * x
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local aXSq = A * xSq
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local v = math.sqrt(1.0 - math.exp(-xSq * (B + aXSq) / (1.0 + aXSq)))
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return (x > 0 and v) or -v
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end
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erf_inv = function(x)
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if x == 0 then return 0; end
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if x <= -1 or x >= 1 then return nil; end
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local y = math.log(1 - x * x)
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local u = C + 0.5 * y
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local v = math.sqrt(math.sqrt(u * u - D * y) - u)
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return (x > 0 and v) or -v
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end
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local function std_normal(u)
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return ROOT_2 * erf_inv(2.0 * u - 1.0)
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end
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local poisson
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local cdf_table = {}
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local function generate_cdf(lambda_index, lambda)
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local max = math.ceil(4 * lambda)
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local pdf = math.exp(-lambda)
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local cdf = pdf
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local t = { [0] = pdf }
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for i = 1, max - 1 do
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pdf = pdf * lambda / i
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cdf = cdf + pdf
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t[i] = cdf
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end
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return t
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end
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for li = 1, 100 do
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cdf_table[li] = generate_cdf(li, 0.25 * li)
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end
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poisson = function(lambda, max)
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if max < 2 then
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return (math.random() < math.exp(-lambda) and 0) or 1
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elseif lambda >= 2 * max then
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return max
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end
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local u = math.random()
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local lambda_index = math.floor(4 * lambda + 0.5)
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local cdfs = cdf_table[lambda_index]
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if cdfs then
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lambda = 0.25 * lambda_index
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if u < cdfs[0] then return 0; end
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if max > #cdfs then max = #cdfs + 1 else max = math.floor(max); end
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if u >= cdfs[max - 1] then return max; end
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if max > 4 then -- Binary search
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local s = 0
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while s + 1 < max do
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local m = math.floor(0.5 * (s + max))
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if u < cdfs[m] then max = m; else s = m; end
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end
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else
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for i = 1, max - 1 do
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if u < cdfs[i] then return i; end
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end
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end
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return max
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else
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local x = lambda + math.sqrt(lambda) * std_normal(u)
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return (x < 0.5 and 0) or (x >= max - 0.5 and max) or math.floor(x + 0.5)
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end
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end
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-- Error function.
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statistics.erf = erf
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-- Inverse error function.
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statistics.erf_inv = erf_inv
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--- Standard normal distribution function (mean 0, standard deviation 1).
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--
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-- @return
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-- Any real number (actually between -3.0 and 3.0).
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--
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statistics.std_normal = function()
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local u = math.random()
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if u < 0.001 then
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return -3.0
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elseif u > 0.999 then
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return 3.0
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end
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return std_normal(u)
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end
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--- Standard normal distribution function (mean 0, standard deviation 1).
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--
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-- @param mu
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-- The distribution mean.
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-- @param sigma
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-- The distribution standard deviation.
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-- @return
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-- Any real number (actually between -3*sigma and 3*sigma).
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--
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statistics.normal = function(mu, sigma)
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local u = math.random()
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if u < 0.001 then
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return mu - 3.0 * sigma
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elseif u > 0.999 then
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return mu + 3.0 * sigma
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end
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return mu + sigma * std_normal(u)
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end
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--- Poisson distribution function.
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--
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-- @param lambda
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-- The distribution mean and variance.
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-- @param max
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-- The distribution maximum.
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-- @return
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-- An integer between 0 and max (both inclusive).
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--
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statistics.poisson = function(lambda, max)
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lambda, max = tonumber(lambda), tonumber(max)
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if not lambda or not max or lambda <= 0 or max < 1 then return 0; end
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return poisson(lambda, max)
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end
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return statistics |