mirror of
https://github.com/sys4-fr/server-nalc.git
synced 2024-12-27 19:20:37 +01:00
175 lines
3.3 KiB
Lua
Executable File
175 lines
3.3 KiB
Lua
Executable File
local statistics = {}
|
|
local ROOT_2 = math.sqrt(2.0)
|
|
|
|
-- Approximations for erf(x) and erfInv(x) from
|
|
-- https://en.wikipedia.org/wiki/Error_function
|
|
|
|
local erf
|
|
local erf_inv
|
|
|
|
local A = 8 * (math.pi - 3.0)/(3.0 * math.pi * (4.0 - math.pi))
|
|
local B = 4.0 / math.pi
|
|
local C = 2.0/(math.pi * A)
|
|
local D = 1.0 / A
|
|
|
|
erf = function(x)
|
|
|
|
if x == 0 then return 0; end
|
|
|
|
local xSq = x * x
|
|
local aXSq = A * xSq
|
|
local v = math.sqrt(1.0 - math.exp(-xSq * (B + aXSq) / (1.0 + aXSq)))
|
|
|
|
return (x > 0 and v) or -v
|
|
end
|
|
|
|
erf_inv = function(x)
|
|
|
|
if x == 0 then return 0; end
|
|
|
|
if x <= -1 or x >= 1 then return nil; end
|
|
|
|
local y = math.log(1 - x * x)
|
|
local u = C + 0.5 * y
|
|
local v = math.sqrt(math.sqrt(u * u - D * y) - u)
|
|
|
|
return (x > 0 and v) or -v
|
|
end
|
|
|
|
local function std_normal(u)
|
|
return ROOT_2 * erf_inv(2.0 * u - 1.0)
|
|
end
|
|
|
|
local poisson
|
|
local cdf_table = {}
|
|
|
|
local function generate_cdf(lambda_index, lambda)
|
|
|
|
local max = math.ceil(4 * lambda)
|
|
local pdf = math.exp(-lambda)
|
|
local cdf = pdf
|
|
local t = { [0] = pdf }
|
|
|
|
for i = 1, max - 1 do
|
|
pdf = pdf * lambda / i
|
|
cdf = cdf + pdf
|
|
t[i] = cdf
|
|
end
|
|
|
|
return t
|
|
end
|
|
|
|
for li = 1, 100 do
|
|
cdf_table[li] = generate_cdf(li, 0.25 * li)
|
|
end
|
|
|
|
poisson = function(lambda, max)
|
|
|
|
if max < 2 then
|
|
return (math.random() < math.exp(-lambda) and 0) or 1
|
|
elseif lambda >= 2 * max then
|
|
return max
|
|
end
|
|
|
|
local u = math.random()
|
|
local lambda_index = math.floor(4 * lambda + 0.5)
|
|
local cdfs = cdf_table[lambda_index]
|
|
|
|
if cdfs then
|
|
|
|
lambda = 0.25 * lambda_index
|
|
|
|
if u < cdfs[0] then return 0; end
|
|
if max > #cdfs then max = #cdfs + 1 else max = math.floor(max); end
|
|
if u >= cdfs[max - 1] then return max; end
|
|
|
|
if max > 4 then -- Binary search
|
|
|
|
local s = 0
|
|
|
|
while s + 1 < max do
|
|
|
|
local m = math.floor(0.5 * (s + max))
|
|
|
|
if u < cdfs[m] then max = m; else s = m; end
|
|
end
|
|
else
|
|
for i = 1, max - 1 do
|
|
if u < cdfs[i] then return i; end
|
|
end
|
|
end
|
|
|
|
return max
|
|
else
|
|
local x = lambda + math.sqrt(lambda) * std_normal(u)
|
|
|
|
return (x < 0.5 and 0) or (x >= max - 0.5 and max) or math.floor(x + 0.5)
|
|
end
|
|
end
|
|
|
|
-- Error function.
|
|
statistics.erf = erf
|
|
|
|
-- Inverse error function.
|
|
statistics.erf_inv = erf_inv
|
|
|
|
--- Standard normal distribution function (mean 0, standard deviation 1).
|
|
--
|
|
-- @return
|
|
-- Any real number (actually between -3.0 and 3.0).
|
|
|
|
statistics.std_normal = function()
|
|
|
|
local u = math.random()
|
|
|
|
if u < 0.001 then
|
|
return -3.0
|
|
elseif u > 0.999 then
|
|
return 3.0
|
|
end
|
|
|
|
return std_normal(u)
|
|
end
|
|
|
|
--- Standard normal distribution function (mean 0, standard deviation 1).
|
|
--
|
|
-- @param mu
|
|
-- The distribution mean.
|
|
-- @param sigma
|
|
-- The distribution standard deviation.
|
|
-- @return
|
|
-- Any real number (actually between -3*sigma and 3*sigma).
|
|
|
|
statistics.normal = function(mu, sigma)
|
|
|
|
local u = math.random()
|
|
|
|
if u < 0.001 then
|
|
return mu - 3.0 * sigma
|
|
elseif u > 0.999 then
|
|
return mu + 3.0 * sigma
|
|
end
|
|
|
|
return mu + sigma * std_normal(u)
|
|
end
|
|
|
|
--- Poisson distribution function.
|
|
--
|
|
-- @param lambda
|
|
-- The distribution mean and variance.
|
|
-- @param max
|
|
-- The distribution maximum.
|
|
-- @return
|
|
-- An integer between 0 and max (both inclusive).
|
|
|
|
statistics.poisson = function(lambda, max)
|
|
|
|
lambda, max = tonumber(lambda), tonumber(max)
|
|
|
|
if not lambda or not max or lambda <= 0 or max < 1 then return 0; end
|
|
|
|
return poisson(lambda, max)
|
|
end
|
|
|
|
return statistics
|