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

-- |
--   Module      :  ELynx.Tree.Distribution.TimeOfOrigin
--   Description :  Distribution of time of origin for birth and death trees
--   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 time of origin for birth and death trees. See corollary 3.3
-- in the paper cited above.
module ELynx.Tree.Distribution.TimeOfOrigin
  ( TimeOfOriginDistribution (..),
    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 time of origin for a phylogenetic tree evolving under
-- the birth and death process and conditioned on observing n leaves today.
data TimeOfOriginDistribution = TOD
  { -- | Number of leaves of the tree.
    TimeOfOriginDistribution -> Int
todTN :: Int,
    -- | Birth rate.
    TimeOfOriginDistribution -> Double
todLa :: Rate,
    -- | Death rate.
    TimeOfOriginDistribution -> Double
todMu :: Rate
  }
  deriving (TimeOfOriginDistribution -> TimeOfOriginDistribution -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: TimeOfOriginDistribution -> TimeOfOriginDistribution -> Bool
$c/= :: TimeOfOriginDistribution -> TimeOfOriginDistribution -> Bool
== :: TimeOfOriginDistribution -> TimeOfOriginDistribution -> Bool
$c== :: TimeOfOriginDistribution -> TimeOfOriginDistribution -> Bool
Eq, Typeable, Typeable TimeOfOriginDistribution
TimeOfOriginDistribution -> DataType
TimeOfOriginDistribution -> Constr
(forall b. Data b => b -> b)
-> TimeOfOriginDistribution -> TimeOfOriginDistribution
forall a.
Typeable a
-> (forall (c :: * -> *).
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-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
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    Monad m =>
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-> Data a
forall u.
Int
-> (forall d. Data d => d -> u) -> TimeOfOriginDistribution -> u
forall u.
(forall d. Data d => d -> u) -> TimeOfOriginDistribution -> [u]
forall r r'.
(r -> r' -> r)
-> r
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forall r r'.
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Monad m =>
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(forall b r. Data b => c (b -> r) -> c r)
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-> (forall g. g -> c g)
-> TimeOfOriginDistribution
-> c TimeOfOriginDistribution
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c TimeOfOriginDistribution)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c TimeOfOriginDistribution)
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> TimeOfOriginDistribution -> m TimeOfOriginDistribution
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> TimeOfOriginDistribution -> m TimeOfOriginDistribution
gmapMp :: forall (m :: * -> *).
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(forall d. Data d => d -> m d)
-> TimeOfOriginDistribution -> m TimeOfOriginDistribution
$cgmapMp :: forall (m :: * -> *).
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(forall d. Data d => d -> m d)
-> TimeOfOriginDistribution -> m TimeOfOriginDistribution
gmapM :: forall (m :: * -> *).
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(forall d. Data d => d -> m d)
-> TimeOfOriginDistribution -> m TimeOfOriginDistribution
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> TimeOfOriginDistribution -> m TimeOfOriginDistribution
gmapQi :: forall u.
Int
-> (forall d. Data d => d -> u) -> TimeOfOriginDistribution -> u
$cgmapQi :: forall u.
Int
-> (forall d. Data d => d -> u) -> TimeOfOriginDistribution -> u
gmapQ :: forall u.
(forall d. Data d => d -> u) -> TimeOfOriginDistribution -> [u]
$cgmapQ :: forall u.
(forall d. Data d => d -> u) -> TimeOfOriginDistribution -> [u]
gmapQr :: forall r r'.
(r' -> r -> r)
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$cgmapQr :: forall r r'.
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gmapT :: (forall b. Data b => b -> b)
-> TimeOfOriginDistribution -> TimeOfOriginDistribution
$cgmapT :: (forall b. Data b => b -> b)
-> TimeOfOriginDistribution -> TimeOfOriginDistribution
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dataTypeOf :: TimeOfOriginDistribution -> DataType
$cdataTypeOf :: TimeOfOriginDistribution -> DataType
toConstr :: TimeOfOriginDistribution -> Constr
$ctoConstr :: TimeOfOriginDistribution -> Constr
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c TimeOfOriginDistribution
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c TimeOfOriginDistribution
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(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> TimeOfOriginDistribution
-> c TimeOfOriginDistribution
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> TimeOfOriginDistribution
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Data, forall x.
Rep TimeOfOriginDistribution x -> TimeOfOriginDistribution
forall x.
TimeOfOriginDistribution -> Rep TimeOfOriginDistribution x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x.
Rep TimeOfOriginDistribution x -> TimeOfOriginDistribution
$cfrom :: forall x.
TimeOfOriginDistribution -> Rep TimeOfOriginDistribution x
Generic)

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

-- | Cumulative distribution function Corollary 3.3.
cumulative :: TimeOfOriginDistribution -> Time -> Double
cumulative :: TimeOfOriginDistribution -> Double -> Double
cumulative (TOD Int
n Double
l Double
m) Double
x
  | Double
x forall a. Ord a => a -> a -> Bool
<= Double
0 = Double
0
  | Bool
otherwise = Double
te forall a. Floating a => a -> a -> a
** forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n
  where
    d :: Double
d = Double
l forall a. Num a => a -> a -> a
- Double
m
    te :: Double
te = Double
l forall a. Num a => a -> a -> a
* (Double
1.0 forall a. Num a => a -> a -> a
- forall a. Floating a => a -> a
exp (-Double
d forall a. Num a => a -> a -> a
* Double
x)) forall a. Fractional a => a -> a -> a
/ (Double
l forall a. Num a => a -> a -> a
- Double
m forall a. Num a => a -> a -> a
* forall a. Floating a => a -> a
exp (-Double
d forall a. Num a => a -> a -> a
* Double
x))

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

-- | The density function Eq. (5).
density :: TimeOfOriginDistribution -> Time -> Double
density :: TimeOfOriginDistribution -> Double -> Double
density (TOD Int
nn Double
l Double
m) Double
x
  | Double
x forall a. Ord a => a -> a -> Bool
< Double
0 = Double
0
  | Bool
otherwise = Double
n forall a. Num a => a -> a -> a
* Double
l forall a. Floating a => a -> a -> a
** Double
n forall a. Num a => a -> a -> a
* Double
d forall a. Floating a => a -> a -> a
** Double
2 forall a. Num a => a -> a -> a
* Double
t1 forall a. Floating a => a -> a -> a
** (Double
n forall a. Num a => a -> a -> a
- Double
1.0) forall a. Num a => a -> a -> a
* Double
ex forall a. Fractional a => a -> a -> a
/ (Double
t2 forall a. Floating a => a -> a -> a
** (Double
n forall a. Num a => a -> a -> a
+ Double
1.0))
  where
    d :: Double
d = Double
l forall a. Num a => a -> a -> a
- Double
m
    n :: Double
n = forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
nn
    ex :: Double
ex = forall a. Floating a => a -> a
exp (-Double
d forall a. Num a => a -> a -> a
* Double
x)
    t1 :: Double
t1 = Double
1.0 forall a. Num a => a -> a -> a
- Double
ex
    t2 :: Double
t2 = Double
l forall a. Num a => a -> a -> a
- Double
m forall a. Num a => a -> a -> a
* Double
ex

-- | The inverted cumulative probability distribution 'cumulative'. See also
-- 'D.ContDistr'.
quantile :: TimeOfOriginDistribution -> Double -> Time
quantile :: TimeOfOriginDistribution -> Double -> Double
quantile (TOD Int
n' Double
l Double
m) 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
1.0 forall a. Fractional a => a -> a -> a
/ Double
d forall a. Num a => a -> a -> a
* forall a. Floating a => a -> a
log (Double
t1 forall a. Fractional a => a -> a -> a
/ Double
t2)
  | Bool
otherwise =
      forall a. HasCallStack => [Char] -> a
error forall a b. (a -> b) -> a -> b
$
        [Char]
"PointProcess.quantile: p must be in [0,1] range. Got: "
          forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> [Char]
show Double
p
          forall a. [a] -> [a] -> [a]
++ [Char]
"."
  where
    d :: Double
d = Double
l forall a. Num a => a -> a -> a
- Double
m
    n :: Double
n = forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n'
    t1 :: Double
t1 = Double
l forall a. Num a => a -> a -> a
* (Double
1.0 forall a. Num a => a -> a -> a
- Double
p forall a. Floating a => a -> a -> a
** (Double
1.0 forall a. Fractional a => a -> a -> a
/ Double
n))
    t2 :: Double
t2 = Double
l forall a. Num a => a -> a -> a
- Double
p forall a. Floating a => a -> a -> a
** (Double
1.0 forall a. Fractional a => a -> a -> a
/ Double
n) forall a. Num a => a -> a -> a
* Double
m

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