{-# LANGUAGE CPP #-}
module Factory.Math.Statistics(
getMean,
getRootMeanSquare,
getWeightedMean,
getVariance,
getStandardDeviation,
getAverageAbsoluteDeviation,
getCoefficientOfVariance,
nCr,
nPr
) where
import Control.Arrow((***))
import qualified Control.Exception
import Control.Parallel(par, pseq)
import qualified Data.Foldable
import qualified Data.List
import qualified Factory.Math.Factorial as Math.Factorial
import qualified Factory.Math.Implementations.Factorial as Math.Implementations.Factorial
import qualified Factory.Math.Power as Math.Power
getMean :: (
Data.Foldable.Foldable foldable,
Fractional result,
Real value
)
=> foldable value
-> result
{-# SPECIALISE getMean :: Data.Foldable.Foldable foldable => foldable Double -> Double #-}
#if MIN_TOOL_VERSION_ghc(7,10,0)
{-# SPECIALISE getMean :: Data.Foldable.Foldable foldable => foldable Rational -> Rational #-}
#endif
getMean :: foldable value -> result
getMean foldable value
foldable = Bool -> result -> result
forall a. (?callStack::CallStack) => Bool -> a -> a
Control.Exception.assert (Int
denominator Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
/= Int
0) (result -> result) -> result -> result
forall a b. (a -> b) -> a -> b
$ value -> result
forall a b. (Real a, Fractional b) => a -> b
realToFrac value
numerator result -> result -> result
forall a. Fractional a => a -> a -> a
/ Int -> result
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
denominator where
denominator :: Int
(value
numerator, Int
denominator) = ((value, Int) -> value -> (value, Int))
-> (value, Int) -> foldable value -> (value, Int)
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Data.Foldable.foldl' (
\(value, Int)
acc value
x -> let
acc' :: (value, Int)
acc'@(value
n, Int
d) = (value -> value -> value
forall a. Num a => a -> a -> a
+ value
x) (value -> value) -> (Int -> Int) -> (value, Int) -> (value, Int)
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** Int -> Int
forall a. Enum a => a -> a
succ ((value, Int) -> (value, Int)) -> (value, Int) -> (value, Int)
forall a b. (a -> b) -> a -> b
$ (value, Int)
acc
in value
n value -> (value, Int) -> (value, Int)
`seq` Int
d Int -> (value, Int) -> (value, Int)
`seq` (value, Int)
acc'
) (value
0, Int
0) foldable value
foldable
getRootMeanSquare :: (
Data.Foldable.Foldable foldable,
Floating result,
Real value
)
=> foldable value
-> result
{-# SPECIALISE getRootMeanSquare :: Data.Foldable.Foldable foldable => foldable Double -> Double #-}
getRootMeanSquare :: foldable value -> result
getRootMeanSquare foldable value
foldable = Bool -> result -> result
forall a. (?callStack::CallStack) => Bool -> a -> a
Control.Exception.assert (Int
denominator Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
/= Int
0) (result -> result) -> (result -> result) -> result -> result
forall b c a. (b -> c) -> (a -> b) -> a -> c
. result -> result
forall a. Floating a => a -> a
sqrt (result -> result) -> result -> result
forall a b. (a -> b) -> a -> b
$ value -> result
forall a b. (Real a, Fractional b) => a -> b
realToFrac value
numerator result -> result -> result
forall a. Fractional a => a -> a -> a
/ Int -> result
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
denominator where
denominator :: Int
(value
numerator, Int
denominator) = ((value, Int) -> value -> (value, Int))
-> (value, Int) -> foldable value -> (value, Int)
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Data.Foldable.foldl' (
\(value, Int)
acc value
x -> let
acc' :: (value, Int)
acc'@(value
n, Int
d) = (value -> value -> value
forall a. Num a => a -> a -> a
+ value -> value
forall n. Num n => n -> n
Math.Power.square value
x) (value -> value) -> (Int -> Int) -> (value, Int) -> (value, Int)
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** Int -> Int
forall a. Enum a => a -> a
succ ((value, Int) -> (value, Int)) -> (value, Int) -> (value, Int)
forall a b. (a -> b) -> a -> b
$ (value, Int)
acc
in value
n value -> (value, Int) -> (value, Int)
`seq` Int
d Int -> (value, Int) -> (value, Int)
`seq` (value, Int)
acc'
) (value
0, Int
0) foldable value
foldable
getWeightedMean :: (
Data.Foldable.Foldable foldable,
Fractional result,
Real value,
Real weight
)
=> foldable (value, weight)
-> result
{-# SPECIALISE getWeightedMean :: Data.Foldable.Foldable foldable => foldable (Double, Double) -> Double #-}
#if MIN_TOOL_VERSION_ghc(7,10,0)
{-# SPECIALISE getWeightedMean :: Data.Foldable.Foldable foldable => foldable (Rational, Rational) -> Rational #-}
#endif
getWeightedMean :: foldable (value, weight) -> result
getWeightedMean foldable (value, weight)
foldable = Bool -> result -> result
forall a. (?callStack::CallStack) => Bool -> a -> a
Control.Exception.assert (weight
denominator weight -> weight -> Bool
forall a. Eq a => a -> a -> Bool
/= weight
0) (result -> result) -> result -> result
forall a b. (a -> b) -> a -> b
$ result
numerator result -> result -> result
forall a. Fractional a => a -> a -> a
/ weight -> result
forall a b. (Real a, Fractional b) => a -> b
realToFrac weight
denominator where
(result
numerator, weight
denominator) = ((result, weight) -> (value, weight) -> (result, weight))
-> (result, weight) -> foldable (value, weight) -> (result, weight)
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Data.Foldable.foldl' (
\(result, weight)
acc (value
value, weight
weight) -> if weight
weight weight -> weight -> Bool
forall a. Eq a => a -> a -> Bool
== weight
0
then (result, weight)
acc
else let
acc' :: (result, weight)
acc'@(result
n, weight
d) = (result -> result -> result
forall a. Num a => a -> a -> a
+ weight -> result
forall a b. (Real a, Fractional b) => a -> b
realToFrac weight
weight result -> result -> result
forall a. Num a => a -> a -> a
* value -> result
forall a b. (Real a, Fractional b) => a -> b
realToFrac value
value) (result -> result)
-> (weight -> weight) -> (result, weight) -> (result, weight)
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** (weight -> weight -> weight
forall a. Num a => a -> a -> a
+ weight
weight) ((result, weight) -> (result, weight))
-> (result, weight) -> (result, weight)
forall a b. (a -> b) -> a -> b
$ (result, weight)
acc
in result
n result -> (result, weight) -> (result, weight)
`seq` weight
d weight -> (result, weight) -> (result, weight)
`seq` (result, weight)
acc'
) (result
0, weight
0) foldable (value, weight)
foldable
getDispersionFromMean :: (
Data.Foldable.Foldable foldable,
Fractional result,
Functor foldable,
Real value
) => (Rational -> Rational) -> foldable value -> result
{-# SPECIALISE getDispersionFromMean :: (Data.Foldable.Foldable foldable, Functor foldable) => (Rational -> Rational) -> foldable Double -> Double #-}
#if MIN_TOOL_VERSION_ghc(7,10,0)
{-# SPECIALISE getDispersionFromMean :: (Data.Foldable.Foldable foldable, Functor foldable) => (Rational -> Rational) -> foldable Rational -> Rational #-}
#endif
getDispersionFromMean :: (Rational -> Rational) -> foldable value -> result
getDispersionFromMean Rational -> Rational
weight foldable value
foldable = foldable Rational -> result
forall (foldable :: * -> *) result value.
(Foldable foldable, Fractional result, Real value) =>
foldable value -> result
getMean (foldable Rational -> result) -> foldable Rational -> result
forall a b. (a -> b) -> a -> b
$ (value -> Rational) -> foldable value -> foldable Rational
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Rational -> Rational
weight (Rational -> Rational) -> (value -> Rational) -> value -> Rational
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Rational -> Rational -> Rational
forall a. Num a => a -> a -> a
subtract Rational
mean (Rational -> Rational) -> (value -> Rational) -> value -> Rational
forall b c a. (b -> c) -> (a -> b) -> a -> c
. value -> Rational
forall a. Real a => a -> Rational
toRational) foldable value
foldable where
mean :: Rational
mean = foldable value -> Rational
forall (foldable :: * -> *) result value.
(Foldable foldable, Fractional result, Real value) =>
foldable value -> result
getMean foldable value
foldable
getVariance :: (
Data.Foldable.Foldable foldable,
Fractional variance,
Functor foldable,
Real value
) => foldable value -> variance
{-# SPECIALISE getVariance :: (Data.Foldable.Foldable foldable, Functor foldable) => foldable Double -> Double #-}
#if MIN_TOOL_VERSION_ghc(7,10,0)
{-# SPECIALISE getVariance :: (Data.Foldable.Foldable foldable, Functor foldable) => foldable Rational -> Rational #-}
#endif
getVariance :: foldable value -> variance
getVariance = (Rational -> Rational) -> foldable value -> variance
forall (foldable :: * -> *) result value.
(Foldable foldable, Fractional result, Functor foldable,
Real value) =>
(Rational -> Rational) -> foldable value -> result
getDispersionFromMean Rational -> Rational
forall n. Num n => n -> n
Math.Power.square
getStandardDeviation :: (
Data.Foldable.Foldable foldable,
Floating result,
Functor foldable,
Real value
) => foldable value -> result
{-# SPECIALISE getStandardDeviation :: (Data.Foldable.Foldable foldable, Functor foldable) => foldable Double -> Double #-}
getStandardDeviation :: foldable value -> result
getStandardDeviation = result -> result
forall a. Floating a => a -> a
sqrt (result -> result)
-> (foldable value -> result) -> foldable value -> result
forall b c a. (b -> c) -> (a -> b) -> a -> c
. foldable value -> result
forall (foldable :: * -> *) variance value.
(Foldable foldable, Fractional variance, Functor foldable,
Real value) =>
foldable value -> variance
getVariance
getAverageAbsoluteDeviation :: (
Data.Foldable.Foldable foldable,
Fractional result,
Functor foldable,
Real value
) => foldable value -> result
{-# SPECIALISE getAverageAbsoluteDeviation :: (Data.Foldable.Foldable foldable, Functor foldable) => foldable Double -> Double #-}
#if MIN_TOOL_VERSION_ghc(7,10,0)
{-# SPECIALISE getAverageAbsoluteDeviation :: (Data.Foldable.Foldable foldable, Functor foldable) => foldable Rational -> Rational #-}
#endif
getAverageAbsoluteDeviation :: foldable value -> result
getAverageAbsoluteDeviation = (Rational -> Rational) -> foldable value -> result
forall (foldable :: * -> *) result value.
(Foldable foldable, Fractional result, Functor foldable,
Real value) =>
(Rational -> Rational) -> foldable value -> result
getDispersionFromMean Rational -> Rational
forall n. Num n => n -> n
abs
getCoefficientOfVariance :: (
Data.Foldable.Foldable foldable,
Eq result,
Floating result,
Functor foldable,
Real value
) => foldable value -> result
{-# SPECIALISE getCoefficientOfVariance :: (Data.Foldable.Foldable foldable, Functor foldable) => foldable Double -> Double #-}
getCoefficientOfVariance :: foldable value -> result
getCoefficientOfVariance foldable value
l = Bool -> result -> result
forall a. (?callStack::CallStack) => Bool -> a -> a
Control.Exception.assert (result
mean result -> result -> Bool
forall a. Eq a => a -> a -> Bool
/= result
0) (result -> result) -> result -> result
forall a b. (a -> b) -> a -> b
$ foldable value -> result
forall (foldable :: * -> *) result value.
(Foldable foldable, Floating result, Functor foldable,
Real value) =>
foldable value -> result
getStandardDeviation foldable value
l result -> result -> result
forall a. Fractional a => a -> a -> a
/ result -> result
forall n. Num n => n -> n
abs result
mean where
mean :: result
mean = foldable value -> result
forall (foldable :: * -> *) result value.
(Foldable foldable, Fractional result, Real value) =>
foldable value -> result
getMean foldable value
l
nCr :: (Math.Factorial.Algorithmic factorialAlgorithm, Integral i, Show i)
=> factorialAlgorithm
-> i
-> i
-> i
nCr :: factorialAlgorithm -> i -> i -> i
nCr factorialAlgorithm
_ i
0 i
_ = i
1
nCr factorialAlgorithm
_ i
_ i
0 = i
1
nCr factorialAlgorithm
factorialAlgorithm i
n i
r
| i
n i -> i -> Bool
forall a. Ord a => a -> a -> Bool
< i
r = i
0
| Bool
otherwise = Bool -> i -> i
forall a. (?callStack::CallStack) => Bool -> a -> a
Control.Exception.assert (i
n i -> i -> Bool
forall a. Ord a => a -> a -> Bool
>= i
0 Bool -> Bool -> Bool
&& i
r i -> i -> Bool
forall a. Ord a => a -> a -> Bool
>= i
0) (i -> i) -> i -> i
forall a b. (a -> b) -> a -> b
$ i
numerator i -> i -> i
forall a b. a -> b -> b
`par` (i
denominator i -> i -> i
forall a b. a -> b -> b
`pseq` i
numerator i -> i -> i
forall a. Integral a => a -> a -> a
`div` i
denominator)
where
[i
smaller, i
bigger] = [i] -> [i]
forall a. Ord a => [a] -> [a]
Data.List.sort [i
r, i
n i -> i -> i
forall a. Num a => a -> a -> a
- i
r]
numerator :: i
numerator = i -> i -> i
forall i. (Integral i, Show i) => i -> i -> i
Math.Implementations.Factorial.risingFactorial (i -> i
forall a. Enum a => a -> a
succ i
bigger) (i
n i -> i -> i
forall a. Num a => a -> a -> a
- i
bigger)
denominator :: i
denominator = factorialAlgorithm -> i -> i
forall algorithm i.
(Algorithmic algorithm, Integral i, Show i) =>
algorithm -> i -> i
Math.Factorial.factorial factorialAlgorithm
factorialAlgorithm i
smaller
nPr :: (Integral i, Show i)
=> i
-> i
-> i
nPr :: i -> i -> i
nPr i
0 i
_ = i
1
nPr i
_ i
0 = i
1
nPr i
n i
r
| i
n i -> i -> Bool
forall a. Ord a => a -> a -> Bool
< i
r = i
0
| Bool
otherwise = Bool -> i -> i
forall a. (?callStack::CallStack) => Bool -> a -> a
Control.Exception.assert (i
n i -> i -> Bool
forall a. Ord a => a -> a -> Bool
>= i
0 Bool -> Bool -> Bool
&& i
r i -> i -> Bool
forall a. Ord a => a -> a -> Bool
>= i
0) (i -> i) -> i -> i
forall a b. (a -> b) -> a -> b
$ i -> i -> i
forall i. (Integral i, Show i) => i -> i -> i
Math.Implementations.Factorial.fallingFactorial i
n i
r