src/TwoTuple.hs

   1 -- | Implement ordered pairs all over again for fun (and to make sure
   2 --   that we can manipulate them algebraically). Also require (as
   3 --   opposed to the built-in ordered pairs) that the elements have
   4 --   matching types.
   5 --
   6 module TwoTuple
   7 where
   8
   9 import Vector
  10
  11
  12 data TwoTuple a = TwoTuple a a
  13   deriving (Eq)
  14
  15 instance (Show a) => Show (TwoTuple a) where
  16   show (TwoTuple x y) = "(" ++ (show x) ++ ", " ++ (show y) ++ ")"
  17
  18 instance Functor TwoTuple where
  19   f `fmap` (TwoTuple x1 y1) = TwoTuple (f x1) (f y1)
  20
  21 instance (RealFloat a) => Vector (TwoTuple a) where
  22   -- The standard Euclidean 2-norm. We need RealFloat for the square
  23   -- root.
  24   norm_2 (TwoTuple x y) = fromRational $ toRational (sqrt(x^2 + y^2))
  25
  26   -- The infinity norm, i.e. the maximum entry.
  27   norm_infty (TwoTuple x y) =
  28     fromRational $ max absx absy
  29     where
  30       absx = abs (toRational x)
  31       absy = abs (toRational y)
  32
  33 -- | It's not correct to use Num here, but I really don't want to have
  34 --   to define my own addition and subtraction.
  35 instance Num a => Num (TwoTuple a) where
  36   -- Standard componentwise addition.
  37   (TwoTuple x1 y1) + (TwoTuple x2 y2) =
  38     TwoTuple (x1 + x2) (y1 + y2)
  39
  40   -- Standard componentwise subtraction.
  41   (TwoTuple x1 y1) - (TwoTuple x2 y2) =
  42     TwoTuple (x1 - x2) (y1 - y2)
  43
  44   -- Left undefined to prevent mistakes. One sane definition
  45   -- would be componentwise multiplication.
  46   (*) _ _ = error "multiplication of vectors is undefined"
  47
  48   abs _ = error "absolute value of vectors is undefined"
  49
  50   signum _ = error "signum of vectors is undefined"
  51
  52   fromInteger x = TwoTuple (fromInteger x) (fromInteger x)