```{-# OPTIONS_GHC -fglasgow-exts #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Numeric.GSL.Distribution.Discrete
-- Copyright   :  (c) A. V. H. McPhail 2010
--
-- Maintainer  :  haskell.vivian.mcphail <at> gmail <dot> com
-- Stability   :  provisional
-- Portability :  uses ffi
--
-- GSL discrete random distribution functions
--
-- <http://www.gnu.org/software/gsl/manual/>
--
-----------------------------------------------------------------------------

module Numeric.GSL.Distribution.Discrete (
OneParamDist(..)
, TwoParamDist(..), ThreeParamDist(..)
, MultiParamDist(..)
, DistFunc(..)
, random_1p, density_1p
, random_2p, density_2p
, random_3p, density_3p
, random_mp, density_mp
) where

-----------------------------------------------------------------------------

import Data.Packed.Vector
--import Data.Packed.Matrix hiding(toLists)
import Data.Packed.Development

--import Numeric.LinearAlgebra.Linear

import Foreign hiding(shift)
--import Foreign.ForeignPtr
--import Foreign.Marshal.Alloc(alloca)
--import Foreign.C.Types(CInt,CUInt,CChar)
import Foreign.C.Types(CInt,CUInt)
--import Foreign.C.String(newCString,peekCString)

--import GHC.ForeignPtr           (mallocPlainForeignPtrBytes)

--import GHC.Base
--import GHC.IOBase

--import Prelude hiding(reverse)

import Numeric.GSL.Distribution.Common

-----------------------------------------------------------------------------

data OneParamDist = Poisson     -- ^ mean
| Bernoulli   -- ^ probability
| Geometric   -- ^ probability
| Logarithmic -- ^ probability
deriving Enum

data TwoParamDist = Binomial     -- ^ probability, successes
| NegBinomial  -- ^ probability, successes
| Pascal       -- ^ probability, n
deriving Enum

data ThreeParamDist = HyperGeometric    -- ^ number type 1, number type 2, samples
deriving Enum

data MultiParamDist = Multinomial   -- ^ trials, probabilities
deriving Enum

-----------------------------------------------------------------------------

fromei x = fromIntegral (fromEnum x) :: CInt

-----------------------------------------------------------------------------

-- | draw a sample from a one parameter distribution
random_1p :: OneParamDist    -- ^ distribution type
-> Int             -- ^ random seed
-> Double          -- ^ parameter
-> Int             -- ^ result
random_1p d s p = unsafePerformIO \$
alloca \$ \r -> do
check "random1p" \$ distribution_discrete_one_param (fromIntegral s) (fromei d) p r
r' <- peek r
return \$ fromIntegral r'

-- | probability of a variate take a value outside the argument
density_1p :: OneParamDist   -- ^ density type
-> DistFunc       -- ^ distribution function type
-> Double         -- ^ parameter
-> Int            -- ^ value
-> Double         -- ^ result
density_1p d f p x = unsafePerformIO \$ do
case d of
Poisson     -> no_inverse f d p x
Geometric   -> no_inverse f d p x
Logarithmic -> pdf_only f d p x
Bernoulli   -> pdf_only f d p x
_           -> distribution_dist_one_param (fromei f) (fromei d) (fromIntegral x) p
where pdf_only f' d' p' x' = if f' /= Density
then error "no CDF"
else distribution_dist_one_param (fromei f') (fromei d') (fromIntegral x') p'
no_inverse f' d' p' x' = if (f' == LowInv || f' == UppInv)
then error "No inverse CDF"
else distribution_dist_one_param (fromei f') (fromei d') (fromIntegral x') p'

foreign import ccall "distribution-aux.h discrete1" distribution_discrete_one_param :: CInt -> CInt -> Double -> Ptr CUInt -> IO CInt
foreign import ccall "distribution-aux.h discrete1_dist" distribution_dist_one_param :: CInt -> CInt -> CUInt -> Double -> IO Double

-----------------------------------------------------------------------------

-- | draw a sample from a two parameter distribution
random_2p :: TwoParamDist    -- ^ distribution type
-> Int             -- ^ random seed
-> Double          -- ^ parameter 1
-> Int             -- ^ parameter 2
-> Int             -- ^ result
random_2p d s p1 p2  = unsafePerformIO \$
alloca \$ \r -> do
check "random2p" \$ distribution_discrete_two_param (fromIntegral s) (fromei d) p1 (fromIntegral p2) r
r' <- peek r
return \$ fromIntegral r'

-- | probability of a variate take a value outside the argument
density_2p :: TwoParamDist   -- ^ density type
-> DistFunc       -- ^ distribution function type
-> Double         -- ^ parameter 1
-> Int            -- ^ parameter 2
-> Int            -- ^ value
-> Double         -- ^ result
density_2p d f p1 p2 x = unsafePerformIO \$ do
case d of
_            -> no_inverse f d p1 p2 x
where no_inverse f' d' p1' p2' x' = if (f' == LowInv || f' == UppInv)
then error "distribution has no inverse CDF"
else distribution_dist_two_param (fromei f') (fromei d') (fromIntegral x') p1' (fromIntegral p2')

foreign import ccall "distribution-aux.h discrete2" distribution_discrete_two_param :: CInt -> CInt -> Double -> CUInt -> Ptr CUInt -> IO CInt
foreign import ccall "distribution-aux.h discrete2_dist" distribution_dist_two_param :: CInt -> CInt -> CUInt -> Double -> CUInt -> IO Double

-----------------------------------------------------------------------------

-- | draw a sample from a three parameter distribution
random_3p :: ThreeParamDist  -- ^ distribution type
-> Int             -- ^ random seed
-> Int             -- ^ parameter 1
-> Int             -- ^ parameter 2
-> Int             -- ^ parameter 3
-> Int          -- ^ result
random_3p d s p1 p2 p3 = unsafePerformIO \$
alloca \$ \r -> do
check "random_3p" \$ distribution_discrete_three_param (fromIntegral s) (fromei d) (fromIntegral p1) (fromIntegral p2) (fromIntegral p3) r
r' <- peek r
return \$ fromIntegral r'

-- | probability of a variate take a value outside the argument
density_3p :: ThreeParamDist   -- ^ density type
-> DistFunc       -- ^ distribution function type
-> Int            -- ^ parameter 1
-> Int            -- ^ parameter 2
-> Int            -- ^ parameter 3
-> Int            -- ^ value
-> Double         -- ^ result
density_3p d f p1 p2 p3 x = unsafePerformIO \$ do
case d of
HyperGeometric -> no_inverse f d p1 p2 p3 x
where no_inverse f' d' p1' p2' p3' x' = if (f' == LowInv || f' == UppInv)
then error "No inverse CDF"
else distribution_dist_three_param (fromei f') (fromei d') (fromIntegral x') (fromIntegral p1') (fromIntegral p2') (fromIntegral p3')

foreign import ccall "distribution-aux.h discrete3" distribution_discrete_three_param :: CInt -> CInt -> CUInt -> CUInt -> CUInt -> Ptr CUInt -> IO CInt
foreign import ccall "distribution-aux.h discrete3_dist" distribution_dist_three_param :: CInt -> CInt -> CUInt -> CUInt -> CUInt -> CUInt -> IO Double

-----------------------------------------------------------------------------

-- | draw a sample from a three parameter distribution
random_mp :: MultiParamDist  -- ^ distribution type
-> Int             -- ^ random seed
-> Int             -- ^ trials
-> Vector Double   -- ^ parameters
-> Vector Int      -- ^ result
random_mp d s t p = unsafePerformIO \$ do
r <- createVector \$ dim p
app2 (distribution_discrete_multi_param (fromIntegral s) (fromei d) (fromIntegral t)) vec p vec r "random_mp"
return \$ mapVector (\x -> (fromIntegral x) :: Int) r

-- | probability of a variate take a value outside the argument
density_mp :: MultiParamDist   -- ^ density type
-> DistFunc       -- ^ distribution function type
-> Vector Double  -- ^ parameters
-> Vector Int     -- ^ values
-> Double         -- ^ result
density_mp d f p q = unsafePerformIO \$ do
case d of
Multinomial -> density_only f d p q
where density_only f' d' p' q' = if f' /= Density
then error "distribution has no CDF"
else alloca \$ \r -> do
app2 (distribution_dist_multi_param (fromei f') (fromei d') r) vec p' vec (mapVector (\x -> (fromIntegral x) :: CUInt) q') "density_mp"
r' <- peek r
return r'

foreign import ccall "distribution-aux.h discrete_mp" distribution_discrete_multi_param :: CInt -> CInt -> CUInt -> CInt -> Ptr Double -> CInt -> Ptr CUInt -> IO CInt
foreign import ccall "distribution-aux.h discrete_mp_dist" distribution_dist_multi_param :: CInt -> CInt -> Ptr Double -> CInt -> Ptr Double -> CInt -> Ptr CUInt -> IO CInt

-----------------------------------------------------------------------------
-----------------------------------------------------------------------------
-----------------------------------------------------------------------------
```