146 lines
3.3 KiB
Nim
146 lines
3.3 KiB
Nim
import std/math
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import std/sugar
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import std/random
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import std/sequtils
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randomize()
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## Basic math functions
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proc factorial(n: int): int =
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if n == 0 or n < 0:
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return 1
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else:
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return n * factorial(n - 1)
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proc sine(x: float): float =
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let n = 8
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# ^ Taylor will converge really quickly
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# notice that the factorial of 17 is
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# already pretty gigantic
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var acc = 0.0
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for i in 0..n:
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var k = 2*i + 1
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var taylor = pow(-1, i.float) * pow(x, k.float) / factorial(k).float
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acc = acc + taylor
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return acc
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## Log function
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## <https://en.wikipedia.org/wiki/Natural_logarithm#High_precision>
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## Arithmetic-geomtric mean
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proc ag(x: float, y: float): float =
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let n = 32 # just some high number
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var a = (x + y)/2.0
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var b = sqrt(x * y)
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for i in 0..n:
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let temp = a
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a = (a+b)/2.0
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b = sqrt(b*temp)
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return a
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## Find m such that x * 2^m > 2^precision/2
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proc find_m(x:float): float =
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var m = 0.0;
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let precision = 64 # bits
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let c = pow(2.0, precision.float / 2.0)
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while x * pow(2.0, m) < c:
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m = m + 1
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return m
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proc log(x: float): float =
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let m = find_m(x)
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let s = x * pow(2.0, m)
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let ln2 = 0.6931471805599453
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return ( PI / (2.0 * ag(1, 4.0/s)) ) - m * ln2
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## Test these functions
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## echo factorial(5)
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## echo sine(1.0)
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## echo log(0.1)
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## echo log(2.0)
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## echo log(3.0)
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## echo pow(2.0, 32.float)
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## Distribution functions
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## Normal
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## <https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Basic_form>
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proc ur_normal(): float =
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let u1 = rand(1.0)
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let u2 = rand(1.0)
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let z = sqrt(-2.0 * log(u1)) * sine(2 * PI * u2)
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return z
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proc normal(mean: float, sigma: float): float =
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return (mean + sigma * ur_normal())
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proc lognormal(logmean: float, logsigma: float): float =
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let answer = pow(E, normal(logmean, logsigma))
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return answer
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proc to(low: float, high: float): float =
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let normal95confidencePoint = 1.6448536269514722
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let loglow = log(low)
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let loghigh = log(high)
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let logmean = (loglow + loghigh)/2
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let logsigma = (loghigh - loglow) / (2.0 * normal95confidencePoint);
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return lognormal(logmean, logsigma)
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## echo ur_normal()
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## echo normal(10, 20)
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## echo lognormal(2, 4)
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## echo to(10, 90)
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## Manipulate samples
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proc make_samples(f: () -> float, n: int): seq[float] =
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result = toSeq(1..n).map(_ => f())
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return result
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proc mixture(sxs: seq[seq[float]], ps: seq[float], n: int): seq[float] =
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assert sxs.len == ps.len
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var ws: seq[float]
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var sum = 0.0
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for i, p in ps:
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sum = sum + p
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ws.add(sum)
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ws = ws.map(w => w/sum)
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proc get_mixture_sample(): float =
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let r = rand(1.0)
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var i = ws.len - 1
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for j, w in ws:
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if r < w:
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i = j
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break
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## only occasion when ^ doesn't assign i
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## is when r is exactly 1
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## which would correspond to choosing the last item in ws
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## which is why i is initialized to ws.len
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let xs = sxs[i]
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let l = xs.len-1
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let k = rand(0..l)
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return xs[k]
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return toSeq(1..n).map(_ => get_mixture_sample())
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## Actual model
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let n = 1000000
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let p_a = 0.8
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let p_b = 0.5
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let p_c = p_a * p_b
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let weights = @[ 1.0 - p_c, p_c/2.0, p_c/4.0, p_c/4.0 ]
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let fs = [ () => 0.0, () => 1.0, () => to(1.0, 3.0), () => to(2.0, 10.0) ]
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let dists = fs.map(f => make_samples(f, n))
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let result = mixture(dists, weights, n)
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let mean_result = foldl(result, a + b, 0.0) / float(result.len)
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# echo result
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echo mean_result
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