src/Normed.hs

   1 {-# LANGUAGE FlexibleInstances #-}
   2 {-# LANGUAGE RebindableSyntax #-}
   3
   4 -- | The 'Normed' class represents elements of a normed vector
   5 --   space. We define instances for all common numeric types.
   6 module Normed
   7 where
   8
   9 import BigFloat
  10
  11 import NumericPrelude hiding (abs)
  12 import Algebra.Absolute (abs)
  13 import qualified Algebra.Absolute as Absolute
  14 import qualified Algebra.Algebraic as Algebraic
  15 import qualified Algebra.RealField as RealField
  16 import qualified Algebra.ToInteger as ToInteger
  17
  18 class Normed a where
  19   norm_p :: (ToInteger.C c, Algebraic.C b, Absolute.C b) => c -> a -> b
  20   norm_infty :: (RealField.C b) => a -> b
  21
  22   -- | The "usual" norm. Defaults to the Euclidean norm.
  23   norm :: (Algebraic.C b, Absolute.C b) => a -> b
  24   norm = norm_p (2 :: Integer)
  25
  26 -- Define instances for common numeric types.
  27 instance Normed Integer where
  28   norm_p _ = abs . fromInteger
  29   norm_infty = abs . fromInteger
  30
  31 instance Normed Rational where
  32   norm_p _ = abs . fromRational'
  33   norm_infty = abs . fromRational'
  34
  35 instance Epsilon e => Normed (BigFloat e) where
  36   norm_p _ = abs . fromRational' . toRational
  37   norm_infty = abs . fromRational' . toRational
  38
  39 instance Normed Float where
  40   norm_p _ = abs . fromRational' . toRational
  41   norm_infty = abs . fromRational' . toRational
  42
  43 instance Normed Double where
  44   norm_p _ = abs . fromRational' . toRational
  45   norm_infty = abs . fromRational' . toRational