{-# LANGUAGE NoImplicitPrelude #-}
module Phladiprelio.General.Distance where
import GHC.Base
import GHC.Real (Fractional(..),Real(..),gcd,quot,(/),fromIntegral)
import GHC.Float (Floating(..),sqrt)
import GHC.List
import Data.List (replicate)
import GHC.Num ((*),(-))
-- | 'toEqLength' changes two given lists of non-negative 'Real' numbers into two lists of equal
-- minimal lengths and also returs its new length and initial lengths of the lists given.
toEqLength :: Real a => [a] -> [a] -> ([a],[a],Int,Int,Int)
toEqLength xs ys
| null xs = ([],[],0,0,0)
| null ys = ([],[],0,0,0)
| otherwise = (ts, vs, lx * ly `quot` dc,lx,ly)
where lx = length xs
ly = length ys
dc = gcd lx ly
ts = concatMap (replicate (ly `quot` dc)) $ xs
vs = concatMap (replicate (lx `quot` dc)) $ ys
-- | 'toEqLengthL' changes two given lists of non-negative 'Real' numbers into two lists of equal
-- minimal lengths and also returs its new length and initial lengths of the lists given. Is
-- intended to be used when the length of the lists are known and given as the first and the second parameters
-- here respectively.
toEqLengthL :: Real a => Int -> Int -> [a] -> [a] -> ([a],[a],Int,Int,Int)
toEqLengthL lx ly xs ys
| lx == 0 = ([],[],0,0,0)
| ly == 0 = ([],[],0,0,0)
| otherwise = (ts, vs, lx * ly `quot` dc,lx,ly)
where dc = gcd lx ly
ts = concatMap (replicate (ly `quot` dc)) $ xs
vs = concatMap (replicate (lx `quot` dc)) $ ys
sumSqrDistNorm :: (Real a, Fractional a) => [a] -> [a] -> a
sumSqrDistNorm xs ys
| lc == 0 = 0
| otherwise = sum (zipWith (\x y -> (x - y) * (x - y)) ts vs) / fromIntegral lc
where (ts, vs, lc, lx, ly) = toEqLength xs ys
-- | 'distanceSqr' is applied on two lists of non-negative 'Real' numbers (preferably, of type
-- 'Double') and returns a special kind of distance that is similar to the statistical distance used
-- in the regression analysis. Is intended to be used e. g. for the PhLADiPreLiO approach. The less
-- is the resulting number, the more \'similar\' are the two lists of non-negative numbers in their
-- distributions. Here, in contrast to the more general 'distanceSqrG', the numbers must be normed
-- to 1.0, so that the largest ones in both listn must be 1.0.
distanceSqr :: (Real a, Floating a, Fractional a) => [a] -> [a] -> a
distanceSqr xs ys = sqrt s
where s = sumSqrDistNorm xs ys
{-# INLINE distanceSqr #-}
-- | 'distanceSqrG' is applied on two lists of non-negative 'Real' numbers (preferably, of type
-- 'Double') and returns a special kind of distance that is similar to the statistical distance used
-- in the regression analysis. Is intended to be used e. g. for the PhLADiPreLiO approach. The less
-- is the resulting number, the more \'similar\' are the two lists of non-negative numbers in their
-- distributions.
distanceSqrG :: (Real a, Floating a, Fractional a) => [a] -> [a] -> a
distanceSqrG xs ys = distanceSqr qs rs
where mx = maximum xs
my = maximum ys
qs = map (/ mx) xs
rs = map (/ my) ys
{-# INLINE distanceSqrG #-}
-- | 'distanceSqrG2' is an partially optimized variant of the 'distanceSqrG' if length of the least
-- common multiplier of the two lists is known and provided as the first argument, besides if it is
-- equal to the length of the second argument, and if maximum element of the second argument here is
-- equal to 1.0.
distanceSqrG2 :: (Real a, Floating a, Fractional a) => Int -> [a] -> [a] -> a
distanceSqrG2 lc xs ys = sqrt (sum (zipWith (\x y -> (x - y) * (x - y)) xs qs) / fromIntegral lc)
where my = maximum ys
rs = map (/ my) ys
lr = length rs
dc = lc `quot` lr
qs = concatMap (replicate dc) rs
{-# INLINE distanceSqrG2 #-}