module Arithmetic where

import qualified Algebra.Field as Field
import qualified Algebra.Ring as Ring
import NumericPrelude.Numeric
import NumericPrelude.Base hiding (id)

import Prelude ()


det2 :: (Ring.C a) => ((a, a), (a, a)) -> a
det2 ((a00,a01), (a10,a11)) = a00*a11 - a10*a01

solve2 ::
   (Field.C a) =>
   ((a, a), (a, a)) -> (a, a) -> (a, a)
solve2 a@(a0,a1) b =
   let d = det2 a
   in  (det2 (b,a1) / d, det2 (a0,b) / d)

linearRegression :: (Field.C a) => [(a,a)] -> (a, a)
linearRegression xys =
   let (xs,ys) = unzip xys
       s = sum xs
       s2 = sum $ map (^2) xs
   in  solve2
          ((fromIntegral $ length xs, s), (s, s2))
          (sum ys, sum $ zipWith (*) xs ys)