src/Linear/Vector.hs

   1 {-# LANGUAGE FlexibleContexts #-}
   2 {-# LANGUAGE FlexibleInstances #-}
   3 {-# LANGUAGE MultiParamTypeClasses #-}
   4 {-# LANGUAGE NoImplicitPrelude #-}
   5 {-# LANGUAGE ScopedTypeVariables #-}
   6 {-# LANGUAGE TypeFamilies #-}
   7
   8 module Linear.Vector (
   9   module Data.Vector.Fixed.Boxed,
  10   Vec1,
  11   (!?),
  12   delete,
  13   element_sum )
  14 where
  15
  16 import qualified Algebra.Additive as Additive ( C )
  17 import qualified Algebra.Ring as Ring ( C )
  18 import Data.Vector.Fixed (
  19   Dim,
  20   N1,
  21   S,
  22   Vector(..),
  23   fromList,
  24   toList )
  25 import qualified Data.Vector.Fixed as V (
  26   (!),
  27   foldl,
  28   length )
  29 import Data.Vector.Fixed.Boxed (
  30   Vec,
  31   Vec2,
  32   Vec3,
  33   Vec4,
  34   Vec5 )
  35 import NumericPrelude hiding ( abs )
  36
  37 type Vec1 = Vec N1
  38
  39
  40
  41 -- | Safe indexing.
  42 --
  43 --   Examples:
  44 --
  45 --   >>> import Data.Vector.Fixed (mk3)
  46 --   >>> let v1 = mk3 1 2 3 :: Vec3 Int
  47 --   >>> v1 !? 2
  48 --   Just 3
  49 --   >>> v1 !? 3
  50 --   Nothing
  51 --
  52 (!?) :: (Vector v a) => v a -> Int -> Maybe a
  53 (!?) v1 idx
  54   | idx < 0 || idx >= V.length v1 = Nothing
  55   | otherwise                     = Just $ v1 V.! idx
  56
  57
  58 -- | Remove an element of the given vector.
  59 --
  60 --   Examples:
  61 --
  62 --   >>> import Data.Vector.Fixed (mk3)
  63 --   >>> let b = mk3 1 2 3 :: Vec3 Int
  64 --   >>> delete b 1 :: Vec2 Int
  65 --   fromList [1,3]
  66 --
  67 delete :: (Vector v a,
  68            Vector w a,
  69            Dim v ~ S (Dim w))
  70        => v a
  71        -> Int
  72        -> w a
  73 delete v1 idx =
  74   fromList (lhalf ++ rhalf')
  75   where
  76     (lhalf, rhalf) = splitAt idx (toList v1)
  77     rhalf' = tail rhalf
  78
  79
  80 -- | We provide our own sum because V.sum relies on a Num instance
  81 --   from the Prelude that we don't have.
  82 --
  83 --   Examples:
  84 --
  85 --   >>> import Data.Vector.Fixed (mk3)
  86 --   >>> let b = mk3 1 2 3 :: Vec3 Int
  87 --   >>> element_sum b
  88 --   6
  89 --
  90 element_sum :: (Additive.C a, Ring.C a, Vector v a) => v a -> a
  91 element_sum = V.foldl (+) (fromInteger 0)