X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FFixedVector.hs;h=402b02eeb531c743f3bd324a8ad3ad4652f8ef3b;hb=fb559d85500b113d9b1c74e8b6e3a033369154b9;hp=531c0fd7b9155a1db0987959f6544fcbf8747cfc;hpb=e73e40c515938df4de629dbc88463c5d88bca7c8;p=numerical-analysis.git

diff --git a/src/FixedVector.hs b/src/FixedVector.hs
index 531c0fd..402b02e 100644
--- a/src/FixedVector.hs
+++ b/src/FixedVector.hs
@@ -8,17 +8,19 @@ module FixedVector
 where
 
 import Data.List (intercalate)
-import Data.Vector.Fixed as V
-import Data.Vector.Fixed.Boxed
+import qualified Data.Vector.Fixed as V
 
 import Normed
 
 -- | The Vn newtype simply wraps (Vector v a) so that we avoid
 --   undecidable instances.
-newtype Vn a = Vn a
+newtype Vn v a = Vn (v a)
 
+-- | Declare the dimension of the wrapper to be the dimension of what
+--   it contains.
+type instance V.Dim (Vn v) = V.Dim v
 
-instance (Show a, Vector v a) => Show (Vn (v a)) where
+instance (Show a, V.Vector v a) => Show (Vn v a) where
   -- | Display vectors as ordinary tuples. This is poor practice, but
   --   these results are primarily displayed interactively and
   --   convenience trumps correctness (said the guy who insists his
@@ -33,7 +35,7 @@ instance (Show a, Vector v a) => Show (Vn (v a)) where
   show (Vn v1) =
     "(" ++ (intercalate "," element_strings) ++ ")"
     where
-      v1l = toList v1
+      v1l = V.toList v1
       element_strings = Prelude.map show v1l
 
 
@@ -51,14 +53,14 @@ instance (Show a, Vector v a) => Show (Vn (v a)) where
 --   >>> v1 == v3
 --   False
 --
-instance (Eq a, Vector v a, Vector v Bool) => Eq (Vn (v a)) where
+instance (Eq a, V.Vector v a, V.Vector v Bool) => Eq (Vn v a) where
   (Vn v1) == (Vn v2) = V.foldl (&&) True (V.zipWith (==) v1 v2)
 
 
 -- | The use of 'Num' here is of course incorrect (otherwise, we
 --   wouldn't have to throw errors). But it's really nice to be able
 --   to use normal addition/subtraction.
-instance (Num a, Vector v a) => Num (Vn (v a)) where
+instance (Num a, V.Vector v a) => Num (Vn v a) where
   -- | Componentwise addition.
   --
   --   Examples:
@@ -87,7 +89,7 @@ instance (Num a, Vector v a) => Num (Vn (v a)) where
   --
   --   Examples:
   --
-  --   >>> let v1 = fromInteger 17 :: Vn (Vec3 Int)
+  --   >>> let v1 = fromInteger 17 :: Vn Vec3 Int
   --   (17,17,17)
   --
   fromInteger x = Vn $ V.replicate (fromInteger x)
@@ -95,10 +97,14 @@ instance (Num a, Vector v a) => Num (Vn (v a)) where
   abs = error "absolute value of vectors is undefined"
   signum = error "signum of vectors is undefined"
 
-instance Functor Vn where
-  fmap f (Vn v1) = Vn (f v1)
 
-instance (RealFloat a, Ord a, Vector v a) => Normed (Vn (v a)) where
+-- | This is probably useless, since the vectors we usually contain
+--   aren't functor instances.
+instance (Functor v) => Functor (Vn v) where
+  fmap f (Vn v1) = Vn (f `fmap` v1)
+
+
+instance (RealFloat a, Ord a, V.Vector v a) => Normed (Vn v a) where
   -- | The infinity norm. We don't use V.maximum here because it
   --   relies on a type constraint that the vector be non-empty and I
   --   don't know how to pattern match it away.
@@ -136,7 +142,7 @@ instance (RealFloat a, Ord a, Vector v a) => Normed (Vn (v a)) where
 --   >>> dot v1 v2
 --   32
 --
-dot :: (Num a, Vector v a) => Vn (v a) -> Vn (v a) -> a
+dot :: (Num a, V.Vector v a) => Vn v a -> Vn v a -> a
 dot (Vn v1) (Vn v2) = V.sum $ V.zipWith (*) v1 v2
 
 
@@ -149,7 +155,7 @@ dot (Vn v1) (Vn v2) = V.sum $ V.zipWith (*) v1 v2
 --   >>> angle v1 v2 == pi/2.0
 --   True
 --
-angle :: (RealFloat a, Vector v a) => Vn (v a) -> Vn (v a) -> a
+angle :: (RealFloat a, V.Vector v a) => Vn v a -> Vn v a -> a
 angle v1 v2 =
   acos theta
   where
@@ -157,6 +163,109 @@ angle v1 v2 =
     norms = (norm v1) * (norm v2)
 
 
+-- | The length of a vector.
+--
+--   Examples:
+--
+--   >>> let v1 = make2d (1,2)
+--   >>> length v1
+--   2
+--
+length :: (V.Vector v a) => Vn v a -> Int
+length (Vn v1) = V.length v1
+
+
+-- | Unsafe indexing.
+--
+--   Examples:
+--
+--   >>> let v1 = make3d (1,2,3)
+--   >>> v1 ! 2
+--   3
+--   >>> v1 ! 3
+--   *** Exception: Data.Vector.Fixed.!: index out of range
+--
+(!) :: (V.Vector v a) => Vn v a -> Int -> a
+(!) (Vn v1) idx = v1 V.! idx
+
+
+-- | Safe indexing.
+--
+--   Examples:
+--
+--   >>> let v1 = make3d (1,2,3)
+--   >>> v1 !? 2
+--   Just 3
+--   >>> v1 !? 3
+--   Nothing
+--
+(!?) :: (V.Vector v a) => Vn v a -> Int -> Maybe a
+(!?) v1@(Vn v2) idx
+  | idx < 0 || idx >= V.length v2 = Nothing
+  | otherwise                     = Just $ v1 ! idx
+
+
+-- | Convert vector to a list.
+--
+--   Examples:
+--
+--   >>> let v1 = make2d (1,2)
+--   >>> toList v1
+--   [1,2]
+--
+toList :: (V.Vector v a) => Vn v a -> [a]
+toList (Vn v1) = V.toList v1
+
+
+-- | Convert a list to a vector.
+--
+--   Examples:
+--
+--   >>> fromList [1,2] :: Vn Vec2D Int
+--   (1,2)
+--
+fromList :: (V.Vector v a) => [a] -> Vn v a
+fromList xs = Vn $ V.fromList xs
+
+-- | Map a function over a vector.
+--
+--   Examples:
+--
+--   >>> let v1 = make2d (1,2)
+--   >>> map (*2) v1
+--   (2,4)
+--
+map :: (V.Vector v a, V.Vector v b) => (a -> b) -> Vn v a -> Vn v b
+map f (Vn vs) = Vn $ V.map f vs
+
+
+
+-- * Low-dimension vector wrappers.
+--
+-- These wrappers are instances of 'Vector', so they inherit all of
+-- the userful instances defined above. But, they use fixed
+-- constructors, so you can pattern match out the individual
+-- components.
+
+data Vec2D a = Vec2D a a
+type instance V.Dim Vec2D = V.N2
+instance V.Vector Vec2D a where
+  inspect (Vec2D x y) (V.Fun f) = f x y
+  construct = V.Fun Vec2D
+
+data Vec3D a = Vec3D a a a
+type instance V.Dim Vec3D = V.N3
+instance V.Vector Vec3D a where
+  inspect (Vec3D x y z) (V.Fun f) = f x y z
+  construct = V.Fun Vec3D
+
+data Vec4D a = Vec4D a a a a
+type instance V.Dim Vec4D = V.N4
+instance V.Vector Vec4D a where
+  inspect (Vec4D w x y z) (V.Fun f) = f w x y z
+  construct = V.Fun Vec4D
+
+
 -- | Convenience function for creating 2d vectors.
 --
 --   Examples:
@@ -164,12 +273,12 @@ angle v1 v2 =
 --   >>> let v1 = make2d (1,2)
 --   >>> v1
 --   (1,2)
+--   >>> let Vn (Vec2D x y) = v1
+--   >>> (x,y)
+--   (1,2)
 --
-make2d :: forall a. (a,a) -> Vn (Vec2 a)
-make2d (x,y) =
-  Vn v1
-  where
-    v1 = vec $ con |> x |> y :: Vec2 a
+make2d :: forall a. (a,a) -> Vn Vec2D a
+make2d (x,y) = Vn (Vec2D x y)
 
 
 -- | Convenience function for creating 3d vectors.
@@ -179,9 +288,24 @@ make2d (x,y) =
 --   >>> let v1 = make3d (1,2,3)
 --   >>> v1
 --   (1,2,3)
+--   >>> let Vn (Vec3D x y z) = v1
+--   >>> (x,y,z)
+--   (1,2,3)
 --
-make3d :: forall a. (a,a,a) -> Vn (Vec3 a)
-make3d (x,y,z) =
-  Vn v1
-  where
-    v1 = vec $ con |> x |> y |> z :: Vec3 a
+make3d :: forall a. (a,a,a) -> Vn Vec3D a
+make3d (x,y,z) = Vn (Vec3D x y z)
+
+
+-- | Convenience function for creating 4d vectors.
+--
+--   Examples:
+--
+--   >>> let v1 = make4d (1,2,3,4)
+--   >>> v1
+--   (1,2,3,4)
+--   >>> let Vn (Vec4D w x y z) = v1
+--   >>> (w,x,y,z)
+--   (1,2,3,4)
+--
+make4d :: forall a. (a,a,a,a) -> Vn Vec4D a
+make4d (w,x,y,z) = Vn (Vec4D w x y z)