src/Vector.hs

   1 {-# LANGUAGE FlexibleInstances #-}
   2
   3 -- | The 'Vector' class represents elements of a normed vector
   4 --   space. We define instances for all common numeric types.
   5 module Vector
   6 where
   7
   8 import Data.Number.BigFloat
   9
  10 class (Num a) => Vector a where
  11   norm_2 :: RealFrac b => a -> b
  12   norm_infty :: RealFrac b => a -> b
  13
  14 -- Define instances for common numeric types.
  15 instance Vector Integer where
  16   norm_2 = fromInteger
  17   norm_infty = fromInteger
  18
  19 instance Vector Rational where
  20   norm_2 = fromRational
  21   norm_infty = fromRational
  22
  23 instance Epsilon e => Vector (BigFloat e) where
  24   norm_2 = fromRational . toRational
  25   norm_infty = fromRational . toRational
  26
  27 instance Vector Double where
  28   norm_2 = fromRational . toRational
  29   norm_infty = fromRational . toRational