{-
Copyright (C) 2011 Dr. Alistair Ward
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see .
-}
{- |
[@AUTHOR@] Dr. Alistair Ward
[@DESCRIPTION@] Miscellaneous statistical functions.
-}
module Factory.Math.Statistics(
-- * Functions
mean,
nCr,
nPr
) where
import Control.Arrow((***))
import Control.Parallel(par, pseq)
import qualified Data.List
--import qualified Factory.Data.PrimeFactors as Data.PrimeFactors
--import Factory.Data.PrimeFactors((>/<), (>*<))
import qualified Factory.Math.Factorial as Math.Factorial
import qualified Factory.Math.Implementations.Factorial as Math.Implementations.Factorial
-- | Determines the of the supplied numbers.
mean :: (Real r, Fractional f) => [r] -> f
mean [] = error "Factory.Math.Statistics.mean:\tundefined result for specified null-list"
mean l = uncurry (/) . (realToFrac *** fromIntegral) $ foldr (\s -> (+ s) *** succ) (0, 0 :: Int) l
-- | The number of unordered combinations of /r/ objects taken from /n/; .
nCr :: (Math.Factorial.Algorithm factorialAlgorithm, Integral i)
=> factorialAlgorithm
-> i -- ^ The total number of items from which to select.
-> i -- ^ The number of iterms in a sample.
-> i -- ^ The number of combinations.
nCr _ 0 _ = 1
nCr _ _ 0 = 1
nCr factorialAlgorithm n r
| n < 0 = error $ "Factory.Math.Statistics.nCr:\tinvalid n; " ++ show n
| r < 0 = error $ "Factory.Math.Statistics.nCr:\tinvalid r; " ++ show r
| n < r = 0
{-
| otherwise = uncurry div $ product' *** product' $ Math.Implementations.Factorial.primeFactors n >/< (
Math.Implementations.Factorial.primeFactors r >*< Math.Implementations.Factorial.primeFactors (n - r)
) where
product' = Data.PrimeFactors.product' (recip 2) 10
-}
| otherwise = numerator `par` (denominator `pseq` numerator `div` denominator)
where
[smaller, bigger] = Data.List.sort [r, n - r]
numerator = Math.Implementations.Factorial.risingFactorial (bigger + 1) (n - bigger)
denominator = Math.Factorial.factorial factorialAlgorithm smaller
-- | The number of permutations of /r/ objects taken from /n/; .
nPr :: Integral i
=> i -- ^ The total number of items from which to select.
-> i -- ^ The number of items in a sample.
-> i -- ^ The number of permutations.
nPr 0 _ = 1
nPr _ 0 = 1
nPr n r
| n < 0 = error $ "Factory.Math.Statistics.nPr:\tinvalid n; " ++ show n
| r < 0 = error $ "Factory.Math.Statistics.nPr:\tinvalid r; " ++ show r
| n < r = 0
| otherwise = Math.Implementations.Factorial.fallingFactorial n r