Gamma.hs

{-
 -      ``Data/Random/Distribution/Gamma''
 -
 -  needs cleanup, verification, and automagic selection of appropriate
 -  algorithms, and proper citations.
 -
 -  should eliminate spurious 'border crossings' betweer RVars and sampleFrom
 -  perhaps Distribution class should have as its basis a function of type
 -  (d t -> RVar t)
 -}
{-# LANGUAGE
    MultiParamTypeClasses,
    FlexibleInstances, FlexibleContexts,
    UndecidableInstances
  #-}

module Data.Random.Distribution.Gamma where

import Data.Random.Source
import Data.Random.RVar
import Data.Random.Distribution
import Data.Random.Distribution.Uniform
import Data.Random.Distribution.Normal

import Control.Monad

    -- translated from gsl source - seems to be best I've found by far.
    -- originally comes from Marsaglia & Tang, "A Simple Method for
    -- generating gamma variables", ACM Transactions on Mathematical
    -- Software, Vol 26, No 3 (2000), p363-372.
realFloatGamma :: RealFloat a => a -> a -> RVar a
realFloatGamma a b
    | a < 1 
    = do
        u <- realFloatStdUniform
        x <- realFloatGamma (1 + a) b
        return (x * u ** recip a)
    | otherwise
    = go
        where
            d = a - (1 / 3)
            c = recip (3 * sqrt d) -- (1 / 3) / sqrt d
            
            go = do
                x <- realFloatStdNormal
                let cx = c * x
                    v = (1 + cx) ^ 3
                    
                    x_2 = x * x
                    x_4 = x_2 * x_2
                
                if cx <= (-1)
                    then go
                    else do
                        u <- realFloatStdUniform
                        
                        if         u < 1 - 0.0331 * x_4
                            || log u < 0.5 * x_2  + d * (1 - v + log v)
                            then return (b * d * v)
                            else go

realFloatErlang :: (Integral a, RealFloat b) => a -> RVar b
realFloatErlang a = realFloatGamma (fromIntegral a) 1

gamma :: (Distribution Gamma a) => a -> a -> RVar a
gamma a b = sample (Gamma a b)

erlang :: (Distribution Gamma a, Integral b, Num a) => b -> a -> RVar a
erlang a b = sample (Gamma (fromIntegral a) b)

data Gamma a = Gamma a a

instance RealFloat a => Distribution Gamma a where
    rvar (Gamma a b) = realFloatGamma a b