{-# LANGUAGE FlexibleInstances #-}

-- | The 'Vector' class represents elements of a normed vector
--   space. We define instances for all common numeric types.
module Vector
where

import Data.Number.BigFloat

class (Num a) => Vector a where
  norm_2 :: RealFrac b => a -> b
  norm_infty :: RealFrac b => a -> b

-- Define instances for common numeric types.
instance Vector Integer where
  norm_2 = fromInteger
  norm_infty = fromInteger

instance Vector Rational where
  norm_2 = fromRational
  norm_infty = fromRational

instance Epsilon e => Vector (BigFloat e) where
  norm_2 = fromRational . toRational
  norm_infty = fromRational . toRational

instance Vector Double where
  norm_2 = fromRational . toRational
  norm_infty = fromRational . toRational