src/Linear/Vector.hs

   1 {-# LANGUAGE FlexibleContexts #-}
   2 {-# LANGUAGE FlexibleInstances #-}
   3 {-# LANGUAGE MultiParamTypeClasses #-}
   4 {-# LANGUAGE ScopedTypeVariables #-}
   5 {-# LANGUAGE TypeFamilies #-}
   6
   7 module Linear.Vector
   8 where
   9
  10 import Data.Vector.Fixed (
  11   Dim,
  12   Fun(..),
  13   N1,
  14   N2,
  15   N3,
  16   N4,
  17   S,
  18   Vector(..),
  19   construct,
  20   fromList,
  21   inspect,
  22   toList,
  23   )
  24 import qualified Data.Vector.Fixed as V (
  25   length,
  26   )
  27
  28
  29 -- * Low-dimension vector wrappers.
  30 --
  31 -- These wrappers are instances of 'Vector', so they inherit all of
  32 -- the userful instances defined above. But, they use fixed
  33 -- constructors, so you can pattern match out the individual
  34 -- components.
  35
  36 data D1 a = D1 a deriving (Show, Eq)
  37 type instance Dim D1 = N1
  38 instance Vector D1 a where
  39   inspect (D1 x) (Fun f) = f x
  40   construct = Fun D1
  41
  42 data D2 a = D2 a a deriving (Show, Eq)
  43 type instance Dim D2 = N2
  44 instance Vector D2 a where
  45   inspect (D2 x y) (Fun f) = f x y
  46   construct = Fun D2
  47
  48 data D3 a = D3 a a a deriving (Show, Eq)
  49 type instance Dim D3 = N3
  50 instance Vector D3 a where
  51   inspect (D3 x y z) (Fun f) = f x y z
  52   construct = Fun D3
  53
  54 data D4 a = D4 a a a a deriving (Show, Eq)
  55 type instance Dim D4 = N4
  56 instance Vector D4 a where
  57   inspect (D4 w x y z) (Fun f) = f w x y z
  58   construct = Fun D4
  59
  60
  61 -- | Unsafe indexing.
  62 --
  63 --   Examples:
  64 --
  65 --   >>> let v1 = D2 1 2
  66 --   >>> v1 ! 1
  67 --   2
  68 --
  69 (!) :: (Vector v a) => v a -> Int -> a
  70 (!) v1 idx = (toList v1) !! idx
  71
  72 -- | Safe indexing.
  73 --
  74 --   Examples:
  75 --
  76 --   >>> let v1 = D3 1 2 3
  77 --   >>> v1 !? 2
  78 --   Just 3
  79 --   >>> v1 !? 3
  80 --   Nothing
  81 --
  82 (!?) :: (Vector v a) => v a -> Int -> Maybe a
  83 (!?) v1 idx
  84   | idx < 0 || idx >= V.length v1 = Nothing
  85   | otherwise                     = Just $ v1 ! idx
  86
  87
  88 -- | Remove an element of the given vector.
  89 --
  90 --   Examples:
  91 --
  92 --   >>> let b = D3 1 2 3
  93 --   >>> delete b 1 :: D2 Int
  94 --   D2 1 3
  95 --
  96 delete :: (Vector v a, Vector w a, Dim v ~ S (Dim w)) => v a -> Int -> w a
  97 delete v1 idx =
  98   fromList $ (lhalf ++ rhalf')
  99   where
 100     (lhalf, rhalf) = splitAt idx (toList v1)
 101     rhalf' = tail rhalf