{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE DeriveDataTypeable    #-}
{-# LANGUAGE DeriveFoldable        #-}
{-# LANGUAGE DeriveGeneric         #-}
{-# LANGUAGE DeriveTraversable     #-}
{-# LANGUAGE FlexibleContexts      #-}
{-# LANGUAGE FlexibleInstances     #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables   #-}
{-# LANGUAGE TemplateHaskell       #-}
{-# LANGUAGE TypeFamilies          #-}
{-# LANGUAGE ViewPatterns          #-}
-- |
-- Monoids for calculating various statistics in constant space
module Data.Monoid.Statistics.Numeric (
    -- * Mean & Variance
    -- ** Number of elements
    CountG(..)
  , Count
  , asCount
    -- ** Mean algorithms
    -- ** Default algorithms
  , Mean
  , asMean
  , WMean
  , asWMean
    -- *** Mean
  , MeanNaive(..)
  , asMeanNaive
  , MeanKBN(..)
  , asMeanKBN
    -- *** Weighted mean
  , WMeanNaive(..)
  , asWMeanNaive
  , WMeanKBN(..)
  , asWMeanKBN
    -- ** Variance
  , Variance(..)
  , asVariance
    -- * Maximum and minimum
  , Max(..)
  , Min(..)
  , MaxD(..)
  , MinD(..)
    -- * Binomial trials
  , BinomAcc(..)
  , asBinomAcc
    -- * Rest
  , Weighted(..)
    -- * References
    -- $references
  ) where

import Control.Monad.Catch          (MonadThrow(..))
import Data.Data                    (Typeable,Data)
import Data.Vector.Unboxed          (Unbox)
import Data.Vector.Unboxed.Deriving (derivingUnbox)
import Numeric.Sum
import GHC.Generics                 (Generic)

import Data.Monoid.Statistics.Class


----------------------------------------------------------------
-- Statistical monoids
----------------------------------------------------------------

-- | Calculate number of elements in the sample.
newtype CountG a = CountG { CountG a -> a
calcCountN :: a }
                  deriving (Int -> CountG a -> ShowS
[CountG a] -> ShowS
CountG a -> String
(Int -> CountG a -> ShowS)
-> (CountG a -> String) -> ([CountG a] -> ShowS) -> Show (CountG a)
forall a. Show a => Int -> CountG a -> ShowS
forall a. Show a => [CountG a] -> ShowS
forall a. Show a => CountG a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [CountG a] -> ShowS
$cshowList :: forall a. Show a => [CountG a] -> ShowS
show :: CountG a -> String
$cshow :: forall a. Show a => CountG a -> String
showsPrec :: Int -> CountG a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> CountG a -> ShowS
Show,CountG a -> CountG a -> Bool
(CountG a -> CountG a -> Bool)
-> (CountG a -> CountG a -> Bool) -> Eq (CountG a)
forall a. Eq a => CountG a -> CountG a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: CountG a -> CountG a -> Bool
$c/= :: forall a. Eq a => CountG a -> CountG a -> Bool
== :: CountG a -> CountG a -> Bool
$c== :: forall a. Eq a => CountG a -> CountG a -> Bool
Eq,Eq (CountG a)
Eq (CountG a)
-> (CountG a -> CountG a -> Ordering)
-> (CountG a -> CountG a -> Bool)
-> (CountG a -> CountG a -> Bool)
-> (CountG a -> CountG a -> Bool)
-> (CountG a -> CountG a -> Bool)
-> (CountG a -> CountG a -> CountG a)
-> (CountG a -> CountG a -> CountG a)
-> Ord (CountG a)
CountG a -> CountG a -> Bool
CountG a -> CountG a -> Ordering
CountG a -> CountG a -> CountG a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
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-> (a -> a -> Bool)
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-> Ord a
forall a. Ord a => Eq (CountG a)
forall a. Ord a => CountG a -> CountG a -> Bool
forall a. Ord a => CountG a -> CountG a -> Ordering
forall a. Ord a => CountG a -> CountG a -> CountG a
min :: CountG a -> CountG a -> CountG a
$cmin :: forall a. Ord a => CountG a -> CountG a -> CountG a
max :: CountG a -> CountG a -> CountG a
$cmax :: forall a. Ord a => CountG a -> CountG a -> CountG a
>= :: CountG a -> CountG a -> Bool
$c>= :: forall a. Ord a => CountG a -> CountG a -> Bool
> :: CountG a -> CountG a -> Bool
$c> :: forall a. Ord a => CountG a -> CountG a -> Bool
<= :: CountG a -> CountG a -> Bool
$c<= :: forall a. Ord a => CountG a -> CountG a -> Bool
< :: CountG a -> CountG a -> Bool
$c< :: forall a. Ord a => CountG a -> CountG a -> Bool
compare :: CountG a -> CountG a -> Ordering
$ccompare :: forall a. Ord a => CountG a -> CountG a -> Ordering
$cp1Ord :: forall a. Ord a => Eq (CountG a)
Ord,Typeable)

type Count = CountG Int

-- | Type restricted 'id'
asCount :: CountG a -> CountG a
asCount :: CountG a -> CountG a
asCount = CountG a -> CountG a
forall a. a -> a
id

instance Integral a => Semigroup (CountG a) where
  CountG a
i <> :: CountG a -> CountG a -> CountG a
<> CountG a
j = a -> CountG a
forall a. a -> CountG a
CountG (a
i a -> a -> a
forall a. Num a => a -> a -> a
+ a
j)

instance Integral a => Monoid (CountG a) where
  mempty :: CountG a
mempty  = a -> CountG a
forall a. a -> CountG a
CountG a
0
  mappend :: CountG a -> CountG a -> CountG a
mappend = CountG a -> CountG a -> CountG a
forall a. Semigroup a => a -> a -> a
(<>)

instance (Integral a) => StatMonoid (CountG a) b where
  singletonMonoid :: b -> CountG a
singletonMonoid b
_            = a -> CountG a
forall a. a -> CountG a
CountG a
1
  addValue :: CountG a -> b -> CountG a
addValue        (CountG a
n) b
_ = a -> CountG a
forall a. a -> CountG a
CountG (a
n a -> a -> a
forall a. Num a => a -> a -> a
+ a
1)


instance CalcCount (CountG Int) where
  calcCount :: CountG Int -> Int
calcCount = CountG Int -> Int
forall a. CountG a -> a
calcCountN



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

-- | Type alias for currently recommended algorithms for calculation
--   of mean. It should be default choice
type Mean = MeanKBN

asMean :: Mean -> Mean
asMean :: Mean -> Mean
asMean = Mean -> Mean
forall a. a -> a
id

-- | Type alias for currently recommended algorithms for calculation
--   of weighted mean. It should be default choice
type WMean = WMeanKBN

asWMean :: WMean -> WMean
asWMean :: WMean -> WMean
asWMean = WMean -> WMean
forall a. a -> a
id


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

-- | Incremental calculation of mean. It tracks separately number of
--   elements and running sum. Note that summation of floating point
--   numbers loses precision and genrally use 'MeanKBN' is
--   recommended.
data MeanNaive = MeanNaive !Int !Double
             deriving (Int -> MeanNaive -> ShowS
[MeanNaive] -> ShowS
MeanNaive -> String
(Int -> MeanNaive -> ShowS)
-> (MeanNaive -> String)
-> ([MeanNaive] -> ShowS)
-> Show MeanNaive
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [MeanNaive] -> ShowS
$cshowList :: [MeanNaive] -> ShowS
show :: MeanNaive -> String
$cshow :: MeanNaive -> String
showsPrec :: Int -> MeanNaive -> ShowS
$cshowsPrec :: Int -> MeanNaive -> ShowS
Show,MeanNaive -> MeanNaive -> Bool
(MeanNaive -> MeanNaive -> Bool)
-> (MeanNaive -> MeanNaive -> Bool) -> Eq MeanNaive
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: MeanNaive -> MeanNaive -> Bool
$c/= :: MeanNaive -> MeanNaive -> Bool
== :: MeanNaive -> MeanNaive -> Bool
$c== :: MeanNaive -> MeanNaive -> Bool
Eq,Typeable,Typeable MeanNaive
DataType
Constr
Typeable MeanNaive
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> MeanNaive -> c MeanNaive)
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-> (forall r r'.
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    -> r -> (forall d. Data d => d -> r') -> MeanNaive -> r)
-> (forall u. (forall d. Data d => d -> u) -> MeanNaive -> [u])
-> (forall u.
    Int -> (forall d. Data d => d -> u) -> MeanNaive -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> MeanNaive -> m MeanNaive)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> MeanNaive -> m MeanNaive)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> MeanNaive -> m MeanNaive)
-> Data MeanNaive
MeanNaive -> DataType
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    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> a -> m a)
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    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> MeanNaive -> u
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forall (t :: * -> * -> *) (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MeanNaive)
$cMeanNaive :: Constr
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gmapMo :: (forall d. Data d => d -> m d) -> MeanNaive -> m MeanNaive
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$cgmapM :: forall (m :: * -> *).
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(forall d. Data d => d -> m d) -> MeanNaive -> m MeanNaive
gmapQi :: Int -> (forall d. Data d => d -> u) -> MeanNaive -> u
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MeanNaive -> u
gmapQ :: (forall d. Data d => d -> u) -> MeanNaive -> [u]
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> MeanNaive -> [u]
gmapQr :: (r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> MeanNaive -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
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gmapQl :: (r -> r' -> r)
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$cgmapQl :: forall r r'.
(r -> r' -> r)
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gmapT :: (forall b. Data b => b -> b) -> MeanNaive -> MeanNaive
$cgmapT :: (forall b. Data b => b -> b) -> MeanNaive -> MeanNaive
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MeanNaive)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MeanNaive)
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$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c MeanNaive)
dataTypeOf :: MeanNaive -> DataType
$cdataTypeOf :: MeanNaive -> DataType
toConstr :: MeanNaive -> Constr
$ctoConstr :: MeanNaive -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MeanNaive
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MeanNaive
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(forall d b. Data d => c (d -> b) -> d -> c b)
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Data,(forall x. MeanNaive -> Rep MeanNaive x)
-> (forall x. Rep MeanNaive x -> MeanNaive) -> Generic MeanNaive
forall x. Rep MeanNaive x -> MeanNaive
forall x. MeanNaive -> Rep MeanNaive x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x. Rep MeanNaive x -> MeanNaive
$cfrom :: forall x. MeanNaive -> Rep MeanNaive x
Generic)

asMeanNaive :: MeanNaive -> MeanNaive
asMeanNaive :: MeanNaive -> MeanNaive
asMeanNaive = MeanNaive -> MeanNaive
forall a. a -> a
id


instance Semigroup MeanNaive where
  MeanNaive Int
0  Double
_  <> :: MeanNaive -> MeanNaive -> MeanNaive
<> MeanNaive
m               = MeanNaive
m
  MeanNaive
m               <> MeanNaive Int
0  Double
_  = MeanNaive
m
  MeanNaive Int
n1 Double
s1 <> MeanNaive Int
n2 Double
s2 = Int -> Double -> MeanNaive
MeanNaive (Int
n1Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
n2) (Double
s1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
s2)

instance Monoid MeanNaive where
  mempty :: MeanNaive
mempty  = Int -> Double -> MeanNaive
MeanNaive Int
0 Double
0
  mappend :: MeanNaive -> MeanNaive -> MeanNaive
mappend = MeanNaive -> MeanNaive -> MeanNaive
forall a. Semigroup a => a -> a -> a
(<>)

instance Real a => StatMonoid MeanNaive a where
  addValue :: MeanNaive -> a -> MeanNaive
addValue (MeanNaive Int
n Double
m) a
x = Int -> Double -> MeanNaive
MeanNaive (Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1) (Double
m Double -> Double -> Double
forall a. Num a => a -> a -> a
+ a -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac a
x)
  {-# INLINE addValue #-}

instance CalcCount MeanNaive where
  calcCount :: MeanNaive -> Int
calcCount (MeanNaive Int
n Double
_) = Int
n
instance CalcMean MeanNaive where
  calcMean :: MeanNaive -> m Double
calcMean (MeanNaive Int
0 Double
_) = SampleError -> m Double
forall (m :: * -> *) e a. (MonadThrow m, Exception e) => e -> m a
throwM (SampleError -> m Double) -> SampleError -> m Double
forall a b. (a -> b) -> a -> b
$ String -> SampleError
EmptySample String
"Data.Monoid.Statistics.Numeric.MeanNaive: calcMean"
  calcMean (MeanNaive Int
n Double
s) = Double -> m Double
forall (m :: * -> *) a. Monad m => a -> m a
return (Double
s Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n)


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

-- | Incremental calculation of mean. It tracks separately number of
--   elements and running sum. It uses algorithm for compensated
--   summation which works with mantissa of double size at cost of
--   doing more operations. This means that it's usually possible to
--   compute sum (and therefore mean) within 1 ulp.
data MeanKBN = MeanKBN !Int {-# UNPACK #-} !KBNSum
             deriving (Int -> Mean -> ShowS
[Mean] -> ShowS
Mean -> String
(Int -> Mean -> ShowS)
-> (Mean -> String) -> ([Mean] -> ShowS) -> Show Mean
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Mean] -> ShowS
$cshowList :: [Mean] -> ShowS
show :: Mean -> String
$cshow :: Mean -> String
showsPrec :: Int -> Mean -> ShowS
$cshowsPrec :: Int -> Mean -> ShowS
Show,Mean -> Mean -> Bool
(Mean -> Mean -> Bool) -> (Mean -> Mean -> Bool) -> Eq Mean
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Mean -> Mean -> Bool
$c/= :: Mean -> Mean -> Bool
== :: Mean -> Mean -> Bool
$c== :: Mean -> Mean -> Bool
Eq,Typeable,Typeable Mean
DataType
Constr
Typeable Mean
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Mean -> c Mean)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c Mean)
-> (Mean -> Constr)
-> (Mean -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c Mean))
-> (forall (t :: * -> * -> *) (c :: * -> *).
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    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Mean))
-> ((forall b. Data b => b -> b) -> Mean -> Mean)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Mean -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Mean -> r)
-> (forall u. (forall d. Data d => d -> u) -> Mean -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> Mean -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Mean -> m Mean)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Mean -> m Mean)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Mean -> m Mean)
-> Data Mean
Mean -> DataType
Mean -> Constr
(forall b. Data b => b -> b) -> Mean -> Mean
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Mean -> c Mean
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Mean
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
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    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
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    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
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-> (forall r r'.
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    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> Mean -> u
forall u. (forall d. Data d => d -> u) -> Mean -> [u]
forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Mean -> r
forall r r'.
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forall (m :: * -> *).
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forall (c :: * -> *).
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-> (forall r. r -> c r) -> Constr -> c Mean
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
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forall (t :: * -> *) (c :: * -> *).
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forall (t :: * -> * -> *) (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Mean)
$cMeanKBN :: Constr
$tMeanKBN :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> Mean -> m Mean
$cgmapMo :: forall (m :: * -> *).
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$cgmapMp :: forall (m :: * -> *).
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(forall d. Data d => d -> m d) -> Mean -> m Mean
gmapM :: (forall d. Data d => d -> m d) -> Mean -> m Mean
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Mean -> m Mean
gmapQi :: Int -> (forall d. Data d => d -> u) -> Mean -> u
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Mean -> u
gmapQ :: (forall d. Data d => d -> u) -> Mean -> [u]
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> Mean -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Mean -> r
$cgmapQr :: forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Mean -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Mean -> r
$cgmapQl :: forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Mean -> r
gmapT :: (forall b. Data b => b -> b) -> Mean -> Mean
$cgmapT :: (forall b. Data b => b -> b) -> Mean -> Mean
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Mean)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Mean)
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c Mean)
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Mean)
dataTypeOf :: Mean -> DataType
$cdataTypeOf :: Mean -> DataType
toConstr :: Mean -> Constr
$ctoConstr :: Mean -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Mean
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Mean
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Mean -> c Mean
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Mean -> c Mean
$cp1Data :: Typeable Mean
Data,(forall x. Mean -> Rep Mean x)
-> (forall x. Rep Mean x -> Mean) -> Generic Mean
forall x. Rep Mean x -> Mean
forall x. Mean -> Rep Mean x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x. Rep Mean x -> Mean
$cfrom :: forall x. Mean -> Rep Mean x
Generic)

asMeanKBN :: MeanKBN -> MeanKBN
asMeanKBN :: Mean -> Mean
asMeanKBN = Mean -> Mean
forall a. a -> a
id


instance Semigroup MeanKBN where
  MeanKBN Int
0  KBNSum
_  <> :: Mean -> Mean -> Mean
<> Mean
m             = Mean
m
  Mean
m             <> MeanKBN Int
0  KBNSum
_  = Mean
m
  MeanKBN Int
n1 KBNSum
s1 <> MeanKBN Int
n2 KBNSum
s2 = Int -> KBNSum -> Mean
MeanKBN (Int
n1Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
n2) (KBNSum
s1 KBNSum -> KBNSum -> KBNSum
forall a. Semigroup a => a -> a -> a
<> KBNSum
s2)

instance Monoid MeanKBN where
  mempty :: Mean
mempty  = Int -> KBNSum -> Mean
MeanKBN Int
0 KBNSum
forall a. Monoid a => a
mempty
  mappend :: Mean -> Mean -> Mean
mappend = Mean -> Mean -> Mean
forall a. Semigroup a => a -> a -> a
(<>)
  
instance Real a => StatMonoid MeanKBN a where
  addValue :: Mean -> a -> Mean
addValue (MeanKBN Int
n KBNSum
m) a
x = Int -> KBNSum -> Mean
MeanKBN (Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1) (KBNSum -> a -> KBNSum
forall m a. StatMonoid m a => m -> a -> m
addValue KBNSum
m a
x)
  {-# INLINE addValue #-}

instance CalcCount MeanKBN where
  calcCount :: Mean -> Int
calcCount (MeanKBN Int
n KBNSum
_) = Int
n
instance CalcMean MeanKBN where
  calcMean :: Mean -> m Double
calcMean (MeanKBN Int
0 KBNSum
_) = SampleError -> m Double
forall (m :: * -> *) e a. (MonadThrow m, Exception e) => e -> m a
throwM (SampleError -> m Double) -> SampleError -> m Double
forall a b. (a -> b) -> a -> b
$ String -> SampleError
EmptySample String
"Data.Monoid.Statistics.Numeric.MeanKBN: calcMean"
  calcMean (MeanKBN Int
n KBNSum
s) = Double -> m Double
forall (m :: * -> *) a. Monad m => a -> m a
return (KBNSum -> Double
kbn KBNSum
s Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n)


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

-- | Incremental calculation of weighed mean.
data WMeanNaive = WMeanNaive
  !Double  -- Weight
  !Double  -- Weighted sum
  deriving (Int -> WMeanNaive -> ShowS
[WMeanNaive] -> ShowS
WMeanNaive -> String
(Int -> WMeanNaive -> ShowS)
-> (WMeanNaive -> String)
-> ([WMeanNaive] -> ShowS)
-> Show WMeanNaive
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [WMeanNaive] -> ShowS
$cshowList :: [WMeanNaive] -> ShowS
show :: WMeanNaive -> String
$cshow :: WMeanNaive -> String
showsPrec :: Int -> WMeanNaive -> ShowS
$cshowsPrec :: Int -> WMeanNaive -> ShowS
Show,WMeanNaive -> WMeanNaive -> Bool
(WMeanNaive -> WMeanNaive -> Bool)
-> (WMeanNaive -> WMeanNaive -> Bool) -> Eq WMeanNaive
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: WMeanNaive -> WMeanNaive -> Bool
$c/= :: WMeanNaive -> WMeanNaive -> Bool
== :: WMeanNaive -> WMeanNaive -> Bool
$c== :: WMeanNaive -> WMeanNaive -> Bool
Eq,Typeable,Typeable WMeanNaive
DataType
Constr
Typeable WMeanNaive
-> (forall (c :: * -> *).
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-> Data WMeanNaive
WMeanNaive -> DataType
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forall u. Int -> (forall d. Data d => d -> u) -> WMeanNaive -> u
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forall (c :: * -> *).
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forall (t :: * -> *) (c :: * -> *).
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(forall d. Data d => c (t d)) -> Maybe (c WMeanNaive)
forall (t :: * -> * -> *) (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c WMeanNaive)
$cWMeanNaive :: Constr
$tWMeanNaive :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> WMeanNaive -> m WMeanNaive
$cgmapMo :: forall (m :: * -> *).
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(forall d. Data d => d -> m d) -> WMeanNaive -> m WMeanNaive
gmapMp :: (forall d. Data d => d -> m d) -> WMeanNaive -> m WMeanNaive
$cgmapMp :: forall (m :: * -> *).
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(forall d. Data d => d -> m d) -> WMeanNaive -> m WMeanNaive
gmapM :: (forall d. Data d => d -> m d) -> WMeanNaive -> m WMeanNaive
$cgmapM :: forall (m :: * -> *).
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(forall d. Data d => d -> m d) -> WMeanNaive -> m WMeanNaive
gmapQi :: Int -> (forall d. Data d => d -> u) -> WMeanNaive -> u
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> WMeanNaive -> u
gmapQ :: (forall d. Data d => d -> u) -> WMeanNaive -> [u]
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> WMeanNaive -> [u]
gmapQr :: (r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> WMeanNaive -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> WMeanNaive -> r
gmapQl :: (r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> WMeanNaive -> r
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> WMeanNaive -> r
gmapT :: (forall b. Data b => b -> b) -> WMeanNaive -> WMeanNaive
$cgmapT :: (forall b. Data b => b -> b) -> WMeanNaive -> WMeanNaive
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c WMeanNaive)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c WMeanNaive)
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c WMeanNaive)
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c WMeanNaive)
dataTypeOf :: WMeanNaive -> DataType
$cdataTypeOf :: WMeanNaive -> DataType
toConstr :: WMeanNaive -> Constr
$ctoConstr :: WMeanNaive -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c WMeanNaive
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c WMeanNaive
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> WMeanNaive -> c WMeanNaive
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> WMeanNaive -> c WMeanNaive
$cp1Data :: Typeable WMeanNaive
Data,(forall x. WMeanNaive -> Rep WMeanNaive x)
-> (forall x. Rep WMeanNaive x -> WMeanNaive) -> Generic WMeanNaive
forall x. Rep WMeanNaive x -> WMeanNaive
forall x. WMeanNaive -> Rep WMeanNaive x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x. Rep WMeanNaive x -> WMeanNaive
$cfrom :: forall x. WMeanNaive -> Rep WMeanNaive x
Generic)

asWMeanNaive :: WMeanNaive -> WMeanNaive
asWMeanNaive :: WMeanNaive -> WMeanNaive
asWMeanNaive = WMeanNaive -> WMeanNaive
forall a. a -> a
id


instance Semigroup WMeanNaive where
  WMeanNaive Double
w1 Double
s1 <> :: WMeanNaive -> WMeanNaive -> WMeanNaive
<> WMeanNaive Double
w2 Double
s2 = Double -> Double -> WMeanNaive
WMeanNaive (Double
w1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
w2) (Double
s1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
s2)

instance Monoid WMeanNaive where
  mempty :: WMeanNaive
mempty  = Double -> Double -> WMeanNaive
WMeanNaive Double
0 Double
0
  mappend :: WMeanNaive -> WMeanNaive -> WMeanNaive
mappend = WMeanNaive -> WMeanNaive -> WMeanNaive
forall a. Semigroup a => a -> a -> a
(<>)

instance (Real w, Real a) => StatMonoid WMeanNaive (Weighted w a) where
  addValue :: WMeanNaive -> Weighted w a -> WMeanNaive
addValue (WMeanNaive Double
n Double
s) (Weighted w
w a
a)
    = Double -> Double -> WMeanNaive
WMeanNaive (Double
n Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
w') (Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
+ (Double
w' Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
a'))
    where
      w' :: Double
w' = w -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac w
w
      a' :: Double
a' = a -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac a
a
  {-# INLINE addValue #-}

instance CalcMean WMeanNaive where
  calcMean :: WMeanNaive -> m Double
calcMean (WMeanNaive Double
w Double
s)
    | Double
w Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<= Double
0    = SampleError -> m Double
forall (m :: * -> *) e a. (MonadThrow m, Exception e) => e -> m a
throwM (SampleError -> m Double) -> SampleError -> m Double
forall a b. (a -> b) -> a -> b
$ String -> SampleError
EmptySample String
"Data.Monoid.Statistics.Numeric.WMeanNaive: calcMean"
    | Bool
otherwise = Double -> m Double
forall (m :: * -> *) a. Monad m => a -> m a
return (Double
s Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
w)

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

-- | Incremental calculation of weighed mean. Sum of both weights and
--   elements is calculated using Kahan-Babuška-Neumaier summation.
data WMeanKBN = WMeanKBN
  {-# UNPACK #-} !KBNSum  -- Weight
  {-# UNPACK #-} !KBNSum  -- Weighted sum
  deriving (Int -> WMean -> ShowS
[WMean] -> ShowS
WMean -> String
(Int -> WMean -> ShowS)
-> (WMean -> String) -> ([WMean] -> ShowS) -> Show WMean
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [WMean] -> ShowS
$cshowList :: [WMean] -> ShowS
show :: WMean -> String
$cshow :: WMean -> String
showsPrec :: Int -> WMean -> ShowS
$cshowsPrec :: Int -> WMean -> ShowS
Show,WMean -> WMean -> Bool
(WMean -> WMean -> Bool) -> (WMean -> WMean -> Bool) -> Eq WMean
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: WMean -> WMean -> Bool
$c/= :: WMean -> WMean -> Bool
== :: WMean -> WMean -> Bool
$c== :: WMean -> WMean -> Bool
Eq,Typeable,Typeable WMean
DataType
Constr
Typeable WMean
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> WMean -> c WMean)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c WMean)
-> (WMean -> Constr)
-> (WMean -> DataType)
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-> (forall (t :: * -> * -> *) (c :: * -> *).
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-> ((forall b. Data b => b -> b) -> WMean -> WMean)
-> (forall r r'.
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-> (forall r r'.
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-> (forall u. (forall d. Data d => d -> u) -> WMean -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> WMean -> u)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> WMean -> m WMean)
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    (forall d. Data d => d -> m d) -> WMean -> m WMean)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> WMean -> m WMean)
-> Data WMean
WMean -> DataType
WMean -> Constr
(forall b. Data b => b -> b) -> WMean -> WMean
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> WMean -> c WMean
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-> (forall r. r -> c r) -> Constr -> c WMean
forall a.
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-> (forall (t :: * -> * -> *) (c :: * -> *).
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-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
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-> (forall r r'.
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-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
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-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> a -> m a)
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-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> WMean -> u
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forall r r'.
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(forall d. Data d => d -> m d) -> WMean -> m WMean
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forall (t :: * -> * -> *) (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c WMean)
$cWMeanKBN :: Constr
$tWMeanKBN :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> WMean -> m WMean
$cgmapMo :: forall (m :: * -> *).
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$cgmapM :: forall (m :: * -> *).
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gmapQi :: Int -> (forall d. Data d => d -> u) -> WMean -> u
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> WMean -> u
gmapQ :: (forall d. Data d => d -> u) -> WMean -> [u]
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> WMean -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WMean -> r
$cgmapQr :: forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WMean -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WMean -> r
$cgmapQl :: forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WMean -> r
gmapT :: (forall b. Data b => b -> b) -> WMean -> WMean
$cgmapT :: (forall b. Data b => b -> b) -> WMean -> WMean
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c WMean)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c WMean)
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c WMean)
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c WMean)
dataTypeOf :: WMean -> DataType
$cdataTypeOf :: WMean -> DataType
toConstr :: WMean -> Constr
$ctoConstr :: WMean -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c WMean
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c WMean
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> WMean -> c WMean
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> WMean -> c WMean
$cp1Data :: Typeable WMean
Data,(forall x. WMean -> Rep WMean x)
-> (forall x. Rep WMean x -> WMean) -> Generic WMean
forall x. Rep WMean x -> WMean
forall x. WMean -> Rep WMean x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x. Rep WMean x -> WMean
$cfrom :: forall x. WMean -> Rep WMean x
Generic)

asWMeanKBN :: WMeanKBN -> WMeanKBN
asWMeanKBN :: WMean -> WMean
asWMeanKBN = WMean -> WMean
forall a. a -> a
id


instance Semigroup WMeanKBN where
  WMeanKBN KBNSum
n1 KBNSum
s1 <> :: WMean -> WMean -> WMean
<> WMeanKBN KBNSum
n2 KBNSum
s2 = KBNSum -> KBNSum -> WMean
WMeanKBN (KBNSum
n1 KBNSum -> KBNSum -> KBNSum
forall a. Semigroup a => a -> a -> a
<> KBNSum
n2) (KBNSum
s1 KBNSum -> KBNSum -> KBNSum
forall a. Semigroup a => a -> a -> a
<> KBNSum
s2)

instance Monoid WMeanKBN where
  mempty :: WMean
mempty  = KBNSum -> KBNSum -> WMean
WMeanKBN KBNSum
forall a. Monoid a => a
mempty KBNSum
forall a. Monoid a => a
mempty
  mappend :: WMean -> WMean -> WMean
mappend = WMean -> WMean -> WMean
forall a. Semigroup a => a -> a -> a
(<>)

instance (Real w, Real a) => StatMonoid WMeanKBN (Weighted w a) where
  addValue :: WMean -> Weighted w a -> WMean
addValue (WMeanKBN KBNSum
n KBNSum
m) (Weighted w
w a
a)
    = KBNSum -> KBNSum -> WMean
WMeanKBN (KBNSum -> Double -> KBNSum
forall s. Summation s => s -> Double -> s
add KBNSum
n Double
w') (KBNSum -> Double -> KBNSum
forall s. Summation s => s -> Double -> s
add KBNSum
m (Double
w' Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
a'))
    where
      w' :: Double
w' = w -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac w
w :: Double
      a' :: Double
a' = a -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac a
a :: Double
  {-# INLINE addValue #-}

instance CalcMean WMeanKBN where
  calcMean :: WMean -> m Double
calcMean (WMeanKBN (KBNSum -> Double
kbn -> Double
w) (KBNSum -> Double
kbn -> Double
s))
    | Double
w Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<= Double
0    = SampleError -> m Double
forall (m :: * -> *) e a. (MonadThrow m, Exception e) => e -> m a
throwM (SampleError -> m Double) -> SampleError -> m Double
forall a b. (a -> b) -> a -> b
$ String -> SampleError
EmptySample String
"Data.Monoid.Statistics.Numeric.WMeanKBN: calcMean"
    | Bool
otherwise = Double -> m Double
forall (m :: * -> *) a. Monad m => a -> m a
return (Double
s Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
w)


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

-- | This is algorithm for estimation of mean and variance of sample
--   which uses modified Welford algorithm. It uses KBN summation and
--   provides approximately 2 additional decimal digits
data VarWelfordKBN = VarWelfordKBN
  {-# UNPACK #-} !Int    --  Number of elements in the sample
  {-# UNPACK #-} !KBNSum -- Current sum of elements of sample
  {-# UNPACK #-} !KBNSum -- Current sum of squares of deviations from current mean

asVarWelfordKBN :: VarWelfordKBN -> VarWelfordKBN
asVarWelfordKBN :: VarWelfordKBN -> VarWelfordKBN
asVarWelfordKBN = VarWelfordKBN -> VarWelfordKBN
forall a. a -> a
id


-- | Incremental algorithms for calculation the standard deviation [Chan1979].
data Variance = Variance {-# UNPACK #-} !Int    --  Number of elements in the sample
                         {-# UNPACK #-} !Double -- Current sum of elements of sample
                         {-# UNPACK #-} !Double -- Current sum of squares of deviations from current mean
                deriving (Int -> Variance -> ShowS
[Variance] -> ShowS
Variance -> String
(Int -> Variance -> ShowS)
-> (Variance -> String) -> ([Variance] -> ShowS) -> Show Variance
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Variance] -> ShowS
$cshowList :: [Variance] -> ShowS
show :: Variance -> String
$cshow :: Variance -> String
showsPrec :: Int -> Variance -> ShowS
$cshowsPrec :: Int -> Variance -> ShowS
Show,Variance -> Variance -> Bool
(Variance -> Variance -> Bool)
-> (Variance -> Variance -> Bool) -> Eq Variance
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Variance -> Variance -> Bool
$c/= :: Variance -> Variance -> Bool
== :: Variance -> Variance -> Bool
$c== :: Variance -> Variance -> Bool
Eq,Typeable)

-- | Type restricted 'id '
asVariance :: Variance -> Variance
asVariance :: Variance -> Variance
asVariance = Variance -> Variance
forall a. a -> a
id

instance Semigroup Variance where
  Variance Int
n1 Double
ta Double
sa <> :: Variance -> Variance -> Variance
<> Variance Int
n2 Double
tb Double
sb
    = Int -> Double -> Double -> Variance
Variance (Int
n1Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
n2) (Double
taDouble -> Double -> Double
forall a. Num a => a -> a -> a
+Double
tb) Double
sumsq
    where
      na :: Double
na = Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n1
      nb :: Double
nb = Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n2
      nom :: Double
nom = Double -> Double
sqr (Double
ta Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
nb Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
tb Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
na)
      sumsq :: Double
sumsq | Int
n1 Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
0   = Double
sb
            | Int
n2 Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
0   = Double
sa
            | Bool
otherwise = Double
sa Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
sb Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
nom Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ ((Double
na Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
nb) Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
na Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
nb)

instance Monoid Variance where
  mempty :: Variance
mempty  = Int -> Double -> Double -> Variance
Variance Int
0 Double
0 Double
0
  mappend :: Variance -> Variance -> Variance
mappend = Variance -> Variance -> Variance
forall a. Semigroup a => a -> a -> a
(<>)

instance Real a => StatMonoid Variance a where
  addValue :: Variance -> a -> Variance
addValue (Variance Int
0 Double
_ Double
_) a
x = a -> Variance
forall m a. StatMonoid m a => a -> m
singletonMonoid a
x
  addValue (Variance Int
n Double
t Double
s) (a -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac -> Double
x)
    = Int -> Double -> Double -> Variance
Variance (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1) (Double
t Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
x) (Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double -> Double
sqr (Double
t  Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
n' Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
x) Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ (Double
n' Double -> Double -> Double
forall a. Num a => a -> a -> a
* (Double
n'Double -> Double -> Double
forall a. Num a => a -> a -> a
+Double
1)))
    where
      n' :: Double
n' = Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n
  {-# INLINE addValue #-}
  singletonMonoid :: a -> Variance
singletonMonoid a
x = Int -> Double -> Double -> Variance
Variance Int
1 (a -> Double
forall a b. (Real a, Fractional b) => a -> b
realToFrac a
x) Double
0
  {-# INLINE singletonMonoid #-}

instance CalcCount Variance where
  calcCount :: Variance -> Int
calcCount (Variance Int
n Double
_ Double
_) = Int
n

instance CalcMean Variance where
  calcMean :: Variance -> m Double
calcMean (Variance Int
0 Double
_ Double
_) = SampleError -> m Double
forall (m :: * -> *) e a. (MonadThrow m, Exception e) => e -> m a
throwM (SampleError -> m Double) -> SampleError -> m Double
forall a b. (a -> b) -> a -> b
$ String -> SampleError
EmptySample String
"Data.Monoid.Statistics.Numeric.Variance: calcMean"
  calcMean (Variance Int
n Double
s Double
_) = Double -> m Double
forall (m :: * -> *) a. Monad m => a -> m a
return (Double
s Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n)

instance CalcVariance Variance where
  calcVariance :: Variance -> m Double
calcVariance (Variance Int
n Double
_ Double
s)
    | Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
2     = SampleError -> m Double
forall (m :: * -> *) e a. (MonadThrow m, Exception e) => e -> m a
throwM (SampleError -> m Double) -> SampleError -> m Double
forall a b. (a -> b) -> a -> b
$ String -> String -> SampleError
InvalidSample
                    String
"Data.Monoid.Statistics.Numeric.Variance: calcVariance"
                    String
"Need at least 2 elements"
    | Bool
otherwise = Double -> m Double
forall (m :: * -> *) a. Monad m => a -> m a
return (Double -> m Double) -> Double -> m Double
forall a b. (a -> b) -> a -> b
$! Double
s Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1)
  calcVarianceML :: Variance -> m Double
calcVarianceML (Variance Int
n Double
_ Double
s)
    | Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
1     = SampleError -> m Double
forall (m :: * -> *) e a. (MonadThrow m, Exception e) => e -> m a
throwM (SampleError -> m Double) -> SampleError -> m Double
forall a b. (a -> b) -> a -> b
$ String -> String -> SampleError
InvalidSample
                    String
"Data.Monoid.Statistics.Numeric.Variance: calcVarianceML"
                    String
"Need at least 1 element"
    | Bool
otherwise = Double -> m Double
forall (m :: * -> *) a. Monad m => a -> m a
return (Double -> m Double) -> Double -> m Double
forall a b. (a -> b) -> a -> b
$! Double
s Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n



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

-- | Calculate minimum of sample
newtype Min a = Min { Min a -> Maybe a
calcMin :: Maybe a }
              deriving (Int -> Min a -> ShowS
[Min a] -> ShowS
Min a -> String
(Int -> Min a -> ShowS)
-> (Min a -> String) -> ([Min a] -> ShowS) -> Show (Min a)
forall a. Show a => Int -> Min a -> ShowS
forall a. Show a => [Min a] -> ShowS
forall a. Show a => Min a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Min a] -> ShowS
$cshowList :: forall a. Show a => [Min a] -> ShowS
show :: Min a -> String
$cshow :: forall a. Show a => Min a -> String
showsPrec :: Int -> Min a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> Min a -> ShowS
Show,Min a -> Min a -> Bool
(Min a -> Min a -> Bool) -> (Min a -> Min a -> Bool) -> Eq (Min a)
forall a. Eq a => Min a -> Min a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Min a -> Min a -> Bool
$c/= :: forall a. Eq a => Min a -> Min a -> Bool
== :: Min a -> Min a -> Bool
$c== :: forall a. Eq a => Min a -> Min a -> Bool
Eq,Eq (Min a)
Eq (Min a)
-> (Min a -> Min a -> Ordering)
-> (Min a -> Min a -> Bool)
-> (Min a -> Min a -> Bool)
-> (Min a -> Min a -> Bool)
-> (Min a -> Min a -> Bool)
-> (Min a -> Min a -> Min a)
-> (Min a -> Min a -> Min a)
-> Ord (Min a)
Min a -> Min a -> Bool
Min a -> Min a -> Ordering
Min a -> Min a -> Min a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall a. Ord a => Eq (Min a)
forall a. Ord a => Min a -> Min a -> Bool
forall a. Ord a => Min a -> Min a -> Ordering
forall a. Ord a => Min a -> Min a -> Min a
min :: Min a -> Min a -> Min a
$cmin :: forall a. Ord a => Min a -> Min a -> Min a
max :: Min a -> Min a -> Min a
$cmax :: forall a. Ord a => Min a -> Min a -> Min a
>= :: Min a -> Min a -> Bool
$c>= :: forall a. Ord a => Min a -> Min a -> Bool
> :: Min a -> Min a -> Bool
$c> :: forall a. Ord a => Min a -> Min a -> Bool
<= :: Min a -> Min a -> Bool
$c<= :: forall a. Ord a => Min a -> Min a -> Bool
< :: Min a -> Min a -> Bool
$c< :: forall a. Ord a => Min a -> Min a -> Bool
compare :: Min a -> Min a -> Ordering
$ccompare :: forall a. Ord a => Min a -> Min a -> Ordering
$cp1Ord :: forall a. Ord a => Eq (Min a)
Ord,Typeable,Typeable (Min a)
DataType
Constr
Typeable (Min a)
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Min a -> c (Min a))
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Min a))
-> (Min a -> Constr)
-> (Min a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c (Min a)))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)))
-> ((forall b. Data b => b -> b) -> Min a -> Min a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r)
-> (forall u. (forall d. Data d => d -> u) -> Min a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> Min a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Min a -> m (Min a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Min a -> m (Min a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Min a -> m (Min a))
-> Data (Min a)
Min a -> DataType
Min a -> Constr
(forall d. Data d => c (t d)) -> Maybe (c (Min a))
(forall b. Data b => b -> b) -> Min a -> Min a
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Min a -> c (Min a)
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Min a)
forall a. Data a => Typeable (Min a)
forall a. Data a => Min a -> DataType
forall a. Data a => Min a -> Constr
forall a. Data a => (forall b. Data b => b -> b) -> Min a -> Min a
forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> Min a -> u
forall a u. Data a => (forall d. Data d => d -> u) -> Min a -> [u]
forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> Min a -> m (Min a)
forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Min a -> m (Min a)
forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Min a)
forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Min a -> c (Min a)
forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (Min a))
forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a))
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> Min a -> u
forall u. (forall d. Data d => d -> u) -> Min a -> [u]
forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Min a -> m (Min a)
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Min a -> m (Min a)
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Min a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Min a -> c (Min a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (Min a))
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a))
$cMin :: Constr
$tMin :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> Min a -> m (Min a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Min a -> m (Min a)
gmapMp :: (forall d. Data d => d -> m d) -> Min a -> m (Min a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Min a -> m (Min a)
gmapM :: (forall d. Data d => d -> m d) -> Min a -> m (Min a)
$cgmapM :: forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> Min a -> m (Min a)
gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u
$cgmapQi :: forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> Min a -> u
gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u]
$cgmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> Min a -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
$cgmapQr :: forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
$cgmapQl :: forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r
gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a
$cgmapT :: forall a. Data a => (forall b. Data b => b -> b) -> Min a -> Min a
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a))
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (Min a))
$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (Min a))
dataTypeOf :: Min a -> DataType
$cdataTypeOf :: forall a. Data a => Min a -> DataType
toConstr :: Min a -> Constr
$ctoConstr :: forall a. Data a => Min a -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Min a)
$cgunfold :: forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Min a)
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Min a -> c (Min a)
$cgfoldl :: forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Min a -> c (Min a)
$cp1Data :: forall a. Data a => Typeable (Min a)
Data,(forall x. Min a -> Rep (Min a) x)
-> (forall x. Rep (Min a) x -> Min a) -> Generic (Min a)
forall x. Rep (Min a) x -> Min a
forall x. Min a -> Rep (Min a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (Min a) x -> Min a
forall a x. Min a -> Rep (Min a) x
$cto :: forall a x. Rep (Min a) x -> Min a
$cfrom :: forall a x. Min a -> Rep (Min a) x
Generic)

instance Ord a => Semigroup (Min a) where
  Min (Just a
a) <> :: Min a -> Min a -> Min a
<> Min (Just a
b) = Maybe a -> Min a
forall a. Maybe a -> Min a
Min (a -> Maybe a
forall a. a -> Maybe a
Just (a -> Maybe a) -> a -> Maybe a
forall a b. (a -> b) -> a -> b
$! a -> a -> a
forall a. Ord a => a -> a -> a
min a
a a
b)
  Min Maybe a
a        <> Min Maybe a
Nothing  = Maybe a -> Min a
forall a. Maybe a -> Min a
Min Maybe a
a
  Min Maybe a
Nothing  <> Min Maybe a
b        = Maybe a -> Min a
forall a. Maybe a -> Min a
Min Maybe a
b

instance Ord a => Monoid (Min a) where
  mempty :: Min a
mempty  = Maybe a -> Min a
forall a. Maybe a -> Min a
Min Maybe a
forall a. Maybe a
Nothing
  mappend :: Min a -> Min a -> Min a
mappend = Min a -> Min a -> Min a
forall a. Semigroup a => a -> a -> a
(<>)

instance (Ord a, a ~ a') => StatMonoid (Min a) a' where
  singletonMonoid :: a' -> Min a
singletonMonoid a'
a = Maybe a' -> Min a'
forall a. Maybe a -> Min a
Min (a' -> Maybe a'
forall a. a -> Maybe a
Just a'
a)


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

-- | Calculate maximum of sample
newtype Max a = Max { Max a -> Maybe a
calcMax :: Maybe a }
              deriving (Int -> Max a -> ShowS
[Max a] -> ShowS
Max a -> String
(Int -> Max a -> ShowS)
-> (Max a -> String) -> ([Max a] -> ShowS) -> Show (Max a)
forall a. Show a => Int -> Max a -> ShowS
forall a. Show a => [Max a] -> ShowS
forall a. Show a => Max a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Max a] -> ShowS
$cshowList :: forall a. Show a => [Max a] -> ShowS
show :: Max a -> String
$cshow :: forall a. Show a => Max a -> String
showsPrec :: Int -> Max a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> Max a -> ShowS
Show,Max a -> Max a -> Bool
(Max a -> Max a -> Bool) -> (Max a -> Max a -> Bool) -> Eq (Max a)
forall a. Eq a => Max a -> Max a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Max a -> Max a -> Bool
$c/= :: forall a. Eq a => Max a -> Max a -> Bool
== :: Max a -> Max a -> Bool
$c== :: forall a. Eq a => Max a -> Max a -> Bool
Eq,Eq (Max a)
Eq (Max a)
-> (Max a -> Max a -> Ordering)
-> (Max a -> Max a -> Bool)
-> (Max a -> Max a -> Bool)
-> (Max a -> Max a -> Bool)
-> (Max a -> Max a -> Bool)
-> (Max a -> Max a -> Max a)
-> (Max a -> Max a -> Max a)
-> Ord (Max a)
Max a -> Max a -> Bool
Max a -> Max a -> Ordering
Max a -> Max a -> Max a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall a. Ord a => Eq (Max a)
forall a. Ord a => Max a -> Max a -> Bool
forall a. Ord a => Max a -> Max a -> Ordering
forall a. Ord a => Max a -> Max a -> Max a
min :: Max a -> Max a -> Max a
$cmin :: forall a. Ord a => Max a -> Max a -> Max a
max :: Max a -> Max a -> Max a
$cmax :: forall a. Ord a => Max a -> Max a -> Max a
>= :: Max a -> Max a -> Bool
$c>= :: forall a. Ord a => Max a -> Max a -> Bool
> :: Max a -> Max a -> Bool
$c> :: forall a. Ord a => Max a -> Max a -> Bool
<= :: Max a -> Max a -> Bool
$c<= :: forall a. Ord a => Max a -> Max a -> Bool
< :: Max a -> Max a -> Bool
$c< :: forall a. Ord a => Max a -> Max a -> Bool
compare :: Max a -> Max a -> Ordering
$ccompare :: forall a. Ord a => Max a -> Max a -> Ordering
$cp1Ord :: forall a. Ord a => Eq (Max a)
Ord,Typeable,Typeable (Max a)
DataType
Constr
Typeable (Max a)
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Max a -> c (Max a))
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Max a))
-> (Max a -> Constr)
-> (Max a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c (Max a)))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)))
-> ((forall b. Data b => b -> b) -> Max a -> Max a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r)
-> (forall u. (forall d. Data d => d -> u) -> Max a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> Max a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Max a -> m (Max a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Max a -> m (Max a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Max a -> m (Max a))
-> Data (Max a)
Max a -> DataType
Max a -> Constr
(forall d. Data d => c (t d)) -> Maybe (c (Max a))
(forall b. Data b => b -> b) -> Max a -> Max a
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Max a -> c (Max a)
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Max a)
forall a. Data a => Typeable (Max a)
forall a. Data a => Max a -> DataType
forall a. Data a => Max a -> Constr
forall a. Data a => (forall b. Data b => b -> b) -> Max a -> Max a
forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> Max a -> u
forall a u. Data a => (forall d. Data d => d -> u) -> Max a -> [u]
forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> Max a -> m (Max a)
forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Max a -> m (Max a)
forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Max a)
forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Max a -> c (Max a)
forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (Max a))
forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a))
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> Max a -> u
forall u. (forall d. Data d => d -> u) -> Max a -> [u]
forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Max a -> m (Max a)
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Max a -> m (Max a)
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Max a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Max a -> c (Max a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (Max a))
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a))
$cMax :: Constr
$tMax :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> Max a -> m (Max a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Max a -> m (Max a)
gmapMp :: (forall d. Data d => d -> m d) -> Max a -> m (Max a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Max a -> m (Max a)
gmapM :: (forall d. Data d => d -> m d) -> Max a -> m (Max a)
$cgmapM :: forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> Max a -> m (Max a)
gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u
$cgmapQi :: forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> Max a -> u
gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u]
$cgmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> Max a -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
$cgmapQr :: forall a r r'.
Data a =>
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
$cgmapQl :: forall a r r'.
Data a =>
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r
gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a
$cgmapT :: forall a. Data a => (forall b. Data b => b -> b) -> Max a -> Max a
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a))
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (Max a))
$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (Max a))
dataTypeOf :: Max a -> DataType
$cdataTypeOf :: forall a. Data a => Max a -> DataType
toConstr :: Max a -> Constr
$ctoConstr :: forall a. Data a => Max a -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Max a)
$cgunfold :: forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Max a)
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Max a -> c (Max a)
$cgfoldl :: forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Max a -> c (Max a)
$cp1Data :: forall a. Data a => Typeable (Max a)
Data,(forall x. Max a -> Rep (Max a) x)
-> (forall x. Rep (Max a) x -> Max a) -> Generic (Max a)
forall x. Rep (Max a) x -> Max a
forall x. Max a -> Rep (Max a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (Max a) x -> Max a
forall a x. Max a -> Rep (Max a) x
$cto :: forall a x. Rep (Max a) x -> Max a
$cfrom :: forall a x. Max a -> Rep (Max a) x
Generic)

instance Ord a => Semigroup (Max a) where
  Max (Just a
a) <> :: Max a -> Max a -> Max a
<> Max (Just a
b) = Maybe a -> Max a
forall a. Maybe a -> Max a
Max (a -> Maybe a
forall a. a -> Maybe a
Just (a -> Maybe a) -> a -> Maybe a
forall a b. (a -> b) -> a -> b
$! a -> a -> a
forall a. Ord a => a -> a -> a
max a
a a
b)
  Max Maybe a
a        <> Max Maybe a
Nothing  = Maybe a -> Max a
forall a. Maybe a -> Max a
Max Maybe a
a
  Max Maybe a
Nothing  <> Max Maybe a
b        = Maybe a -> Max a
forall a. Maybe a -> Max a
Max Maybe a
b

instance Ord a => Monoid (Max a) where
  mempty :: Max a
mempty  = Maybe a -> Max a
forall a. Maybe a -> Max a
Max Maybe a
forall a. Maybe a
Nothing
  mappend :: Max a -> Max a -> Max a
mappend = Max a -> Max a -> Max a
forall a. Semigroup a => a -> a -> a
(<>)

instance (Ord a, a ~ a') => StatMonoid (Max a) a' where
  singletonMonoid :: a' -> Max a
singletonMonoid a'
a = Maybe a' -> Max a'
forall a. Maybe a -> Max a
Max (a' -> Maybe a'
forall a. a -> Maybe a
Just a'
a)


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

-- | Calculate minimum of sample of Doubles. For empty sample returns NaN. Any
--   NaN encountered will be ignored.
newtype MinD = MinD { MinD -> Double
calcMinD :: Double }
              deriving (Int -> MinD -> ShowS
[MinD] -> ShowS
MinD -> String
(Int -> MinD -> ShowS)
-> (MinD -> String) -> ([MinD] -> ShowS) -> Show MinD
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [MinD] -> ShowS
$cshowList :: [MinD] -> ShowS
show :: MinD -> String
$cshow :: MinD -> String
showsPrec :: Int -> MinD -> ShowS
$cshowsPrec :: Int -> MinD -> ShowS
Show,Typeable,Typeable MinD
DataType
Constr
Typeable MinD
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> MinD -> c MinD)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c MinD)
-> (MinD -> Constr)
-> (MinD -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c MinD))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MinD))
-> ((forall b. Data b => b -> b) -> MinD -> MinD)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r)
-> (forall u. (forall d. Data d => d -> u) -> MinD -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> MinD -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> MinD -> m MinD)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MinD -> m MinD)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MinD -> m MinD)
-> Data MinD
MinD -> DataType
MinD -> Constr
(forall b. Data b => b -> b) -> MinD -> MinD
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MinD -> c MinD
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MinD
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> MinD -> u
forall u. (forall d. Data d => d -> u) -> MinD -> [u]
forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r
forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> MinD -> m MinD
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MinD -> m MinD
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MinD
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MinD -> c MinD
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c MinD)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MinD)
$cMinD :: Constr
$tMinD :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> MinD -> m MinD
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MinD -> m MinD
gmapMp :: (forall d. Data d => d -> m d) -> MinD -> m MinD
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MinD -> m MinD
gmapM :: (forall d. Data d => d -> m d) -> MinD -> m MinD
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> MinD -> m MinD
gmapQi :: Int -> (forall d. Data d => d -> u) -> MinD -> u
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MinD -> u
gmapQ :: (forall d. Data d => d -> u) -> MinD -> [u]
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> MinD -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r
$cgmapQr :: forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r
$cgmapQl :: forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MinD -> r
gmapT :: (forall b. Data b => b -> b) -> MinD -> MinD
$cgmapT :: (forall b. Data b => b -> b) -> MinD -> MinD
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MinD)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MinD)
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c MinD)
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c MinD)
dataTypeOf :: MinD -> DataType
$cdataTypeOf :: MinD -> DataType
toConstr :: MinD -> Constr
$ctoConstr :: MinD -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MinD
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MinD
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MinD -> c MinD
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MinD -> c MinD
$cp1Data :: Typeable MinD
Data,(forall x. MinD -> Rep MinD x)
-> (forall x. Rep MinD x -> MinD) -> Generic MinD
forall x. Rep MinD x -> MinD
forall x. MinD -> Rep MinD x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x. Rep MinD x -> MinD
$cfrom :: forall x. MinD -> Rep MinD x
Generic)

instance Eq MinD where
  MinD Double
a == :: MinD -> MinD -> Bool
== MinD Double
b
    | Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
a Bool -> Bool -> Bool
&& Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
b = Bool
True
    | Bool
otherwise          = Double
a Double -> Double -> Bool
forall a. Eq a => a -> a -> Bool
== Double
b

instance Semigroup MinD where
  MinD Double
x <> :: MinD -> MinD -> MinD
<> MinD Double
y
    | Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
x   = Double -> MinD
MinD Double
y
    | Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
y   = Double -> MinD
MinD Double
x
    | Bool
otherwise = Double -> MinD
MinD (Double -> Double -> Double
forall a. Ord a => a -> a -> a
min Double
x Double
y)

-- N.B. forall (x :: Double) (x <= NaN) == False
instance Monoid MinD where
  mempty :: MinD
mempty  = Double -> MinD
MinD (Double
0Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Double
0)
  mappend :: MinD -> MinD -> MinD
mappend = MinD -> MinD -> MinD
forall a. Semigroup a => a -> a -> a
(<>)

instance a ~ Double => StatMonoid MinD a where
  singletonMonoid :: a -> MinD
singletonMonoid = a -> MinD
Double -> MinD
MinD



-- | Calculate maximum of sample. For empty sample returns NaN. Any
--   NaN encountered will be ignored.
newtype MaxD = MaxD { MaxD -> Double
calcMaxD :: Double }
              deriving (Int -> MaxD -> ShowS
[MaxD] -> ShowS
MaxD -> String
(Int -> MaxD -> ShowS)
-> (MaxD -> String) -> ([MaxD] -> ShowS) -> Show MaxD
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [MaxD] -> ShowS
$cshowList :: [MaxD] -> ShowS
show :: MaxD -> String
$cshow :: MaxD -> String
showsPrec :: Int -> MaxD -> ShowS
$cshowsPrec :: Int -> MaxD -> ShowS
Show,Typeable,Typeable MaxD
DataType
Constr
Typeable MaxD
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> MaxD -> c MaxD)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c MaxD)
-> (MaxD -> Constr)
-> (MaxD -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c MaxD))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MaxD))
-> ((forall b. Data b => b -> b) -> MaxD -> MaxD)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r)
-> (forall u. (forall d. Data d => d -> u) -> MaxD -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> MaxD -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> MaxD -> m MaxD)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MaxD -> m MaxD)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> MaxD -> m MaxD)
-> Data MaxD
MaxD -> DataType
MaxD -> Constr
(forall b. Data b => b -> b) -> MaxD -> MaxD
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxD -> c MaxD
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MaxD
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> MaxD -> u
forall u. (forall d. Data d => d -> u) -> MaxD -> [u]
forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r
forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> MaxD -> m MaxD
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MaxD -> m MaxD
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MaxD
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxD -> c MaxD
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c MaxD)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MaxD)
$cMaxD :: Constr
$tMaxD :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> MaxD -> m MaxD
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MaxD -> m MaxD
gmapMp :: (forall d. Data d => d -> m d) -> MaxD -> m MaxD
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> MaxD -> m MaxD
gmapM :: (forall d. Data d => d -> m d) -> MaxD -> m MaxD
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> MaxD -> m MaxD
gmapQi :: Int -> (forall d. Data d => d -> u) -> MaxD -> u
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> MaxD -> u
gmapQ :: (forall d. Data d => d -> u) -> MaxD -> [u]
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> MaxD -> [u]
gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r
$cgmapQr :: forall r r'.
(r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r
gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r
$cgmapQl :: forall r r'.
(r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MaxD -> r
gmapT :: (forall b. Data b => b -> b) -> MaxD -> MaxD
$cgmapT :: (forall b. Data b => b -> b) -> MaxD -> MaxD
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MaxD)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c MaxD)
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c MaxD)
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c MaxD)
dataTypeOf :: MaxD -> DataType
$cdataTypeOf :: MaxD -> DataType
toConstr :: MaxD -> Constr
$ctoConstr :: MaxD -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MaxD
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c MaxD
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxD -> c MaxD
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> MaxD -> c MaxD
$cp1Data :: Typeable MaxD
Data,(forall x. MaxD -> Rep MaxD x)
-> (forall x. Rep MaxD x -> MaxD) -> Generic MaxD
forall x. Rep MaxD x -> MaxD
forall x. MaxD -> Rep MaxD x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x. Rep MaxD x -> MaxD
$cfrom :: forall x. MaxD -> Rep MaxD x
Generic)

instance Eq MaxD where
  MaxD Double
a == :: MaxD -> MaxD -> Bool
== MaxD Double
b
    | Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
a Bool -> Bool -> Bool
&& Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
b = Bool
True
    | Bool
otherwise          = Double
a Double -> Double -> Bool
forall a. Eq a => a -> a -> Bool
== Double
b

instance Semigroup MaxD where
  MaxD Double
x <> :: MaxD -> MaxD -> MaxD
<> MaxD Double
y
    | Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
x   = Double -> MaxD
MaxD Double
y
    | Double -> Bool
forall a. RealFloat a => a -> Bool
isNaN Double
y   = Double -> MaxD
MaxD Double
x
    | Bool
otherwise = Double -> MaxD
MaxD (Double -> Double -> Double
forall a. Ord a => a -> a -> a
max Double
x Double
y)

instance Monoid MaxD where
  mempty :: MaxD
mempty  = Double -> MaxD
MaxD (Double
0Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Double
0)
  mappend :: MaxD -> MaxD -> MaxD
mappend = MaxD -> MaxD -> MaxD
forall a. Semigroup a => a -> a -> a
(<>)

instance a ~ Double => StatMonoid MaxD a where
  singletonMonoid :: a -> MaxD
singletonMonoid = a -> MaxD
Double -> MaxD
MaxD


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

-- | Accumulator for binomial trials.
data BinomAcc = BinomAcc { BinomAcc -> Int
binomAccSuccess :: !Int
                         , BinomAcc -> Int
binomAccTotal   :: !Int
                         }
  deriving (Int -> BinomAcc -> ShowS
[BinomAcc] -> ShowS
BinomAcc -> String
(Int -> BinomAcc -> ShowS)
-> (BinomAcc -> String) -> ([BinomAcc] -> ShowS) -> Show BinomAcc
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [BinomAcc] -> ShowS
$cshowList :: [BinomAcc] -> ShowS
show :: BinomAcc -> String
$cshow :: BinomAcc -> String
showsPrec :: Int -> BinomAcc -> ShowS
$cshowsPrec :: Int -> BinomAcc -> ShowS
Show,BinomAcc -> BinomAcc -> Bool
(BinomAcc -> BinomAcc -> Bool)
-> (BinomAcc -> BinomAcc -> Bool) -> Eq BinomAcc
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: BinomAcc -> BinomAcc -> Bool
$c/= :: BinomAcc -> BinomAcc -> Bool
== :: BinomAcc -> BinomAcc -> Bool
$c== :: BinomAcc -> BinomAcc -> Bool
Eq,Eq BinomAcc
Eq BinomAcc
-> (BinomAcc -> BinomAcc -> Ordering)
-> (BinomAcc -> BinomAcc -> Bool)
-> (BinomAcc -> BinomAcc -> Bool)
-> (BinomAcc -> BinomAcc -> Bool)
-> (BinomAcc -> BinomAcc -> Bool)
-> (BinomAcc -> BinomAcc -> BinomAcc)
-> (BinomAcc -> BinomAcc -> BinomAcc)
-> Ord BinomAcc
BinomAcc -> BinomAcc -> Bool
BinomAcc -> BinomAcc -> Ordering
BinomAcc -> BinomAcc -> BinomAcc
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
min :: BinomAcc -> BinomAcc -> BinomAcc
$cmin :: BinomAcc -> BinomAcc -> BinomAcc
max :: BinomAcc -> BinomAcc -> BinomAcc
$cmax :: BinomAcc -> BinomAcc -> BinomAcc
>= :: BinomAcc -> BinomAcc -> Bool
$c>= :: BinomAcc -> BinomAcc -> Bool
> :: BinomAcc -> BinomAcc -> Bool
$c> :: BinomAcc -> BinomAcc -> Bool
<= :: BinomAcc -> BinomAcc -> Bool
$c<= :: BinomAcc -> BinomAcc -> Bool
< :: BinomAcc -> BinomAcc -> Bool
$c< :: BinomAcc -> BinomAcc -> Bool
compare :: BinomAcc -> BinomAcc -> Ordering
$ccompare :: BinomAcc -> BinomAcc -> Ordering
$cp1Ord :: Eq BinomAcc
Ord,Typeable,Typeable BinomAcc
DataType
Constr
Typeable BinomAcc
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> BinomAcc -> c BinomAcc)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c BinomAcc)
-> (BinomAcc -> Constr)
-> (BinomAcc -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c BinomAcc))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c BinomAcc))
-> ((forall b. Data b => b -> b) -> BinomAcc -> BinomAcc)
-> (forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> BinomAcc -> r)
-> (forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> BinomAcc -> r)
-> (forall u. (forall d. Data d => d -> u) -> BinomAcc -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> BinomAcc -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc)
-> Data BinomAcc
BinomAcc -> DataType
BinomAcc -> Constr
(forall b. Data b => b -> b) -> BinomAcc -> BinomAcc
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> BinomAcc -> c BinomAcc
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c BinomAcc
forall a.
Typeable a
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> BinomAcc -> u
forall u. (forall d. Data d => d -> u) -> BinomAcc -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> BinomAcc -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> BinomAcc -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c BinomAcc
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> BinomAcc -> c BinomAcc
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c BinomAcc)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c BinomAcc)
$cBinomAcc :: Constr
$tBinomAcc :: DataType
gmapMo :: (forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
gmapMp :: (forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
gmapM :: (forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> BinomAcc -> m BinomAcc
gmapQi :: Int -> (forall d. Data d => d -> u) -> BinomAcc -> u
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> BinomAcc -> u
gmapQ :: (forall d. Data d => d -> u) -> BinomAcc -> [u]
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> BinomAcc -> [u]
gmapQr :: (r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> BinomAcc -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> BinomAcc -> r
gmapQl :: (r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> BinomAcc -> r
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> BinomAcc -> r
gmapT :: (forall b. Data b => b -> b) -> BinomAcc -> BinomAcc
$cgmapT :: (forall b. Data b => b -> b) -> BinomAcc -> BinomAcc
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c BinomAcc)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c BinomAcc)
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c BinomAcc)
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c BinomAcc)
dataTypeOf :: BinomAcc -> DataType
$cdataTypeOf :: BinomAcc -> DataType
toConstr :: BinomAcc -> Constr
$ctoConstr :: BinomAcc -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c BinomAcc
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c BinomAcc
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> BinomAcc -> c BinomAcc
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> BinomAcc -> c BinomAcc
$cp1Data :: Typeable BinomAcc
Data,(forall x. BinomAcc -> Rep BinomAcc x)
-> (forall x. Rep BinomAcc x -> BinomAcc) -> Generic BinomAcc
forall x. Rep BinomAcc x -> BinomAcc
forall x. BinomAcc -> Rep BinomAcc x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cto :: forall x. Rep BinomAcc x -> BinomAcc
$cfrom :: forall x. BinomAcc -> Rep BinomAcc x
Generic)

-- | Type restricted 'id'
asBinomAcc :: BinomAcc -> BinomAcc
asBinomAcc :: BinomAcc -> BinomAcc
asBinomAcc = BinomAcc -> BinomAcc
forall a. a -> a
id

instance Semigroup BinomAcc where
  BinomAcc Int
n1 Int
m1 <> :: BinomAcc -> BinomAcc -> BinomAcc
<> BinomAcc Int
n2 Int
m2 = Int -> Int -> BinomAcc
BinomAcc (Int
n1Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
n2) (Int
m1Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
m2)

instance Monoid BinomAcc where
  mempty :: BinomAcc
mempty  = Int -> Int -> BinomAcc
BinomAcc Int
0 Int
0
  mappend :: BinomAcc -> BinomAcc -> BinomAcc
mappend = BinomAcc -> BinomAcc -> BinomAcc
forall a. Semigroup a => a -> a -> a
(<>)

instance StatMonoid BinomAcc Bool where
  addValue :: BinomAcc -> Bool -> BinomAcc
addValue (BinomAcc Int
nS Int
nT) Bool
True  = Int -> Int -> BinomAcc
BinomAcc (Int
nSInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1) (Int
nTInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)
  addValue (BinomAcc Int
nS Int
nT) Bool
False = Int -> Int -> BinomAcc
BinomAcc  Int
nS    (Int
nTInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)


-- | Value @a@ weighted by weight @w@
data Weighted w a = Weighted w a
              deriving (Int -> Weighted w a -> ShowS
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----------------------------------------------------------------
-- Helpers
----------------------------------------------------------------

sqr :: Double -> Double
sqr :: Double -> Double
sqr Double
x = Double
x Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
x
{-# INLINE sqr #-}


----------------------------------------------------------------
-- Unboxed instances
----------------------------------------------------------------

derivingUnbox "CountG"
  [t| forall a. Unbox a => CountG a -> a |]
  [| calcCountN |]
  [| CountG     |]

derivingUnbox "MeanKBN"
  [t| MeanKBN -> (Int,Double,Double) |]
  [| \(MeanKBN a (KBNSum b c)) -> (a,b,c)   |]
  [| \(a,b,c) -> MeanKBN a (KBNSum b c) |]

derivingUnbox "Variance"
  [t| Variance -> (Int,Double,Double) |]
  [| \(Variance a b c) -> (a,b,c)  |]
  [| \(a,b,c) -> Variance a b c    |]

derivingUnbox "MinD"
  [t| MinD -> Double |]
  [| calcMinD |]
  [| MinD     |]

derivingUnbox "MaxD"
  [t| MaxD -> Double |]
  [| calcMaxD |]
  [| MaxD     |]

derivingUnbox "Weighted"
  [t| forall w a. (Unbox w, Unbox a) => Weighted w a -> (w,a) |]
  [| \(Weighted w a) -> (w,a) |]
  [| \(w,a) -> Weighted w a   |]

derivingUnbox "BinomAcc"
  [t| BinomAcc -> (Int,Int)   |]
  [| \(BinomAcc k n) -> (k,n) |]
  [| \(k,n) -> BinomAcc k n   |]


-- $references
--
-- * [Welford1962] Welford, B.P. (1962) Note on a method for
--   calculating corrected sums of squares and
--   products. /Technometrics/
--   4(3):419-420. <http://www.jstor.org/stable/1266577>
--
-- * [Chan1979] Chan, Tony F.; Golub, Gene H.; LeVeque, Randall
--   J. (1979), Updating Formulae and a Pairwise Algorithm for
--   Computing Sample Variances., Technical Report STAN-CS-79-773,
--   Department of Computer Science, Stanford University. Page 4.