{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}

-- |
--   Module      :  ELynx.Tree.Distribution.BirthDeathCriticalNoTime
--   Description :  Birth and death distribution
--   Copyright   :  2021 Dominik Schrempf
--   License     :  GPL-3.0-or-later
--
--   Maintainer  :  dominik.schrempf@gmail.com
--   Stability   :  unstable
--   Portability :  portable
--
-- Creation date: Tue Feb 13 13:16:18 2018.
--
-- See Gernhard, T. (2008). The conditioned reconstructed process. Journal of
-- Theoretical Biology, 253(4), 769–778. http://doi.org/10.1016/j.jtbi.2008.04.005.
--
-- Distribution of the values of the point process such that it corresponds to
-- reconstructed trees under the birth and death process; critical birth and death
-- process with lambda=mu.
module ELynx.Tree.Distribution.BirthDeathCriticalNoTime
  ( BirthDeathCriticalNoTimeDistribution (..),
    cumulative,
    density,
    quantile,
  )
where

import Data.Data
  ( Data,
    Typeable,
  )
import ELynx.Tree.Distribution.Types
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D

-- | Distribution of the values of the point process such that it corresponds to
-- a reconstructed tree of the birth and death process.
newtype BirthDeathCriticalNoTimeDistribution = BDCNTD
  { -- | Birth and death rate.
    BirthDeathCriticalNoTimeDistribution -> Double
bdcntdLa :: Rate
  }
  deriving (BirthDeathCriticalNoTimeDistribution
-> BirthDeathCriticalNoTimeDistribution -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: BirthDeathCriticalNoTimeDistribution
-> BirthDeathCriticalNoTimeDistribution -> Bool
$c/= :: BirthDeathCriticalNoTimeDistribution
-> BirthDeathCriticalNoTimeDistribution -> Bool
== :: BirthDeathCriticalNoTimeDistribution
-> BirthDeathCriticalNoTimeDistribution -> Bool
$c== :: BirthDeathCriticalNoTimeDistribution
-> BirthDeathCriticalNoTimeDistribution -> Bool
Eq, Typeable, Typeable BirthDeathCriticalNoTimeDistribution
BirthDeathCriticalNoTimeDistribution -> DataType
BirthDeathCriticalNoTimeDistribution -> Constr
(forall b. Data b => b -> b)
-> BirthDeathCriticalNoTimeDistribution
-> BirthDeathCriticalNoTimeDistribution
forall a.
Typeable a
-> (forall (c :: * -> *).
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gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> BirthDeathCriticalNoTimeDistribution
-> m BirthDeathCriticalNoTimeDistribution
$cgmapMo :: forall (m :: * -> *).
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-> m BirthDeathCriticalNoTimeDistribution
gmapMp :: forall (m :: * -> *).
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-> m BirthDeathCriticalNoTimeDistribution
$cgmapMp :: forall (m :: * -> *).
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gmapM :: forall (m :: * -> *).
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gmapQi :: forall u.
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gmapQ :: forall u.
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dataTypeOf :: BirthDeathCriticalNoTimeDistribution -> DataType
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toConstr :: BirthDeathCriticalNoTimeDistribution -> Constr
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gunfold :: forall (c :: * -> *).
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gfoldl :: forall (c :: * -> *).
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Data, forall x.
Rep BirthDeathCriticalNoTimeDistribution x
-> BirthDeathCriticalNoTimeDistribution
forall x.
BirthDeathCriticalNoTimeDistribution
-> Rep BirthDeathCriticalNoTimeDistribution x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x.
Rep BirthDeathCriticalNoTimeDistribution x
-> BirthDeathCriticalNoTimeDistribution
$cfrom :: forall x.
BirthDeathCriticalNoTimeDistribution
-> Rep BirthDeathCriticalNoTimeDistribution x
Generic)

instance D.Distribution BirthDeathCriticalNoTimeDistribution where
  cumulative :: BirthDeathCriticalNoTimeDistribution -> Double -> Double
cumulative = BirthDeathCriticalNoTimeDistribution -> Double -> Double
cumulative

-- | Cumulative distribution function section 2.1.2, second formula.
cumulative :: BirthDeathCriticalNoTimeDistribution -> Time -> Double
cumulative :: BirthDeathCriticalNoTimeDistribution -> Double -> Double
cumulative (BDCNTD Double
l) Double
x
  | Double
x forall a. Ord a => a -> a -> Bool
<= Double
0 = Double
0
  | Bool
otherwise = Double
x forall a. Num a => a -> a -> a
* Double
l forall a. Fractional a => a -> a -> a
/ (Double
1.0 forall a. Num a => a -> a -> a
+ Double
x forall a. Num a => a -> a -> a
* Double
l)

instance D.ContDistr BirthDeathCriticalNoTimeDistribution where
  density :: BirthDeathCriticalNoTimeDistribution -> Double -> Double
density = BirthDeathCriticalNoTimeDistribution -> Double -> Double
density
  quantile :: BirthDeathCriticalNoTimeDistribution -> Double -> Double
quantile = BirthDeathCriticalNoTimeDistribution -> Double -> Double
quantile

-- | Density function section 2.1.2, first formula; t cancels out because it is
-- expected to be much larger than 1.0; because t \in [0, \infty].
density :: BirthDeathCriticalNoTimeDistribution -> Time -> Double
density :: BirthDeathCriticalNoTimeDistribution -> Double -> Double
density (BDCNTD Double
l) Double
x
  | Double
x forall a. Ord a => a -> a -> Bool
< Double
0 = Double
0
  | Bool
otherwise = Double
l forall a. Fractional a => a -> a -> a
/ ((Double
1.0 forall a. Num a => a -> a -> a
+ Double
x forall a. Num a => a -> a -> a
* Double
l) forall a. Floating a => a -> a -> a
** Double
2)

-- | Inverted cumulative probability distribution 'cumulative'. See also
-- 'D.ContDistr'.
quantile :: BirthDeathCriticalNoTimeDistribution -> Double -> Time
quantile :: BirthDeathCriticalNoTimeDistribution -> Double -> Double
quantile (BDCNTD Double
l) Double
p
  | Double
p forall a. Ord a => a -> a -> Bool
>= Double
0 Bool -> Bool -> Bool
&& Double
p forall a. Ord a => a -> a -> Bool
<= Double
1 =
      Double
p forall a. Fractional a => a -> a -> a
/ (Double
l forall a. Num a => a -> a -> a
- Double
l forall a. Num a => a -> a -> a
* Double
p)
  | Bool
otherwise =
      forall a. HasCallStack => [Char] -> a
error forall a b. (a -> b) -> a -> b
$ [Char]
"PointProcess.quantile: p must be in [0,1]. Got: " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> [Char]
show Double
p forall a. [a] -> [a] -> [a]
++ [Char]
"."

instance D.ContGen BirthDeathCriticalNoTimeDistribution where
  genContVar :: forall g (m :: * -> *).
StatefulGen g m =>
BirthDeathCriticalNoTimeDistribution -> g -> m Double
genContVar = forall d g (m :: * -> *).
(ContDistr d, StatefulGen g m) =>
d -> g -> m Double
D.genContinuous