Statistics.hs

{-
	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 <http://www.gnu.org/licenses/>.
-}
{- |
 [@AUTHOR@]	Dr. Alistair Ward

 [@DESCRIPTION@]	Defines /QuickCheck/-properties for "Math.Statistics".
-}

module Factory.Test.QuickCheck.Statistics(
-- * Functions
	quickChecks
) where

import qualified	Data.List
import qualified	Data.Numbers.Primes
import qualified	Factory.Math.Implementations.Factorial	as Math.Implementations.Factorial
import qualified	Factory.Math.Statistics			as Math.Statistics
import			Factory.Test.QuickCheck.Factorial()
import qualified	Test.QuickCheck
import			Test.QuickCheck((==>))

-- | Defines invariant properties.
quickChecks :: IO ()
quickChecks	=
	Test.QuickCheck.quickCheck `mapM_` [prop_nC0, prop_nC1, prop_sum]
	>> Test.QuickCheck.quickCheck `mapM_` [prop_symmetry, prop_prime]
	>> Test.QuickCheck.quickCheck `mapM_` [prop_nP0, prop_nP1]
	>> Test.QuickCheck.quickCheck prop_balance	where
		prop_nC0, prop_nC1, prop_sum :: Math.Implementations.Factorial.Algorithm -> Integer -> Test.QuickCheck.Property
		prop_nC0 algorithm n	= Test.QuickCheck.label "prop_nC0" $ Math.Statistics.nCr algorithm (abs n) 0 == 1

		prop_nC1 algorithm i	= Test.QuickCheck.label "prop_nC1" $ Math.Statistics.nCr algorithm n 1 == n	where
			n	= 1 + abs i

		prop_sum algorithm i	= Test.QuickCheck.label "prop_sum" $ sum (Math.Statistics.nCr algorithm n `map` [0 .. n]) == 2 ^ n	where
			n	= 1 + abs i

		prop_symmetry, prop_prime :: Math.Implementations.Factorial.Algorithm -> (Integer, Integer) -> Test.QuickCheck.Property
		prop_symmetry algorithm (i, j)	= Test.QuickCheck.label "prop_symmetry" $ Math.Statistics.nCr algorithm n r == Math.Statistics.nCr algorithm n (n - r)	where
			[r, n]		= Data.List.sort $ map abs [i, j]

		prop_prime algorithm (i, j)	= r `notElem` [0, n]	==> Test.QuickCheck.label "prop_prime" $ (Math.Statistics.nCr algorithm n r `mod` n) == 0	where
			n	= Data.Numbers.Primes.primes !! fromIntegral (i `mod` 500000)
			r	= j `mod` n	--Ensure r is smaller than n.

		prop_nP0, prop_nP1 :: Integer -> Test.QuickCheck.Property
		prop_nP0 n	= Test.QuickCheck.label "prop_nP0" $ Math.Statistics.nPr (abs n) 0 == 1

		prop_nP1 i	= Test.QuickCheck.label "prop_nP1" $ Math.Statistics.nPr n 1 == n	where
			n	= 1 + abs i

		prop_balance :: [Integer] -> Test.QuickCheck.Property
		prop_balance l	= not (null l)	==> Test.QuickCheck.label "prop_balance" . (< 1e-11 {-rounding errors-}) . abs . sum $ map (\i -> fromIntegral i - (Math.Statistics.mean l :: Double)) l