where
import Data.List (intercalate)
-import qualified Data.Vector.Fixed as V
+import Data.Vector.Fixed (
+ Dim,
+ Fun(..),
+ N1,
+ N2,
+ N3,
+ N4,
+ Vector(..),
+ (!),
+ construct,
+ inspect,
+ toList,
+ )
+import qualified Data.Vector.Fixed as V (
+ foldl,
+ length,
+ map,
+ replicate,
+ sum,
+ zipWith
+ )
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 Dim (Vn v) = Dim v
-instance (Show a, V.Vector v a) => Show (Vn (v a)) where
+instance (Vector v a) => Vector (Vn v) a where
+ -- | Fortunately, 'Fun' is an instance of 'Functor'. The
+ -- 'construct' defined on our contained type will return a
+ -- 'Fun', and we simply slap our constructor on top with fmap.
+ construct = fmap Vn construct
+
+ -- | Defer to the inspect defined on the contained type.
+ inspect (Vn v1) = inspect v1
+
+instance (Show a, 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
show (Vn v1) =
"(" ++ (intercalate "," element_strings) ++ ")"
where
- v1l = V.toList v1
+ v1l = toList v1
element_strings = Prelude.map show v1l
-- >>> v1 == v3
-- False
--
-instance (Eq a, V.Vector v a, V.Vector v Bool) => Eq (Vn (v a)) where
+instance (Eq a, Vector v a, 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, V.Vector v a) => Num (Vn (v a)) where
+instance (Num a, Vector v a) => Num (Vn v a) where
-- | Componentwise addition.
--
-- Examples:
--
-- 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)
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, V.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, 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.
-- >>> dot v1 v2
-- 32
--
-dot :: (Num a, V.Vector v a) => Vn (v a) -> Vn (v a) -> a
+dot :: (Num a, Vector v a) => Vn v a -> Vn v a -> a
dot (Vn v1) (Vn v2) = V.sum $ V.zipWith (*) v1 v2
-- >>> angle v1 v2 == pi/2.0
-- True
--
-angle :: (RealFloat a, V.Vector v a) => Vn (v a) -> Vn (v a) -> a
+angle :: (RealFloat a, Vector v a) => Vn v a -> Vn v a -> a
angle v1 v2 =
acos theta
where
theta = (v1 `dot` v2) / norms
norms = (norm v1) * (norm v2)
--- | 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.
--
-- >>> v1 !? 3
-- Nothing
--
-(!?) :: (V.Vector v a) => Vn (v a) -> Int -> Maybe a
-(!?) v1@(Vn v2) idx
- | idx < 0 || idx >= V.length v2 = Nothing
+(!?) :: (Vector v a) => v a -> Int -> Maybe a
+(!?) v1 idx
+ | idx < 0 || idx >= V.length v1 = 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.
+-- * Low-dimension vector wrappers.
--
--- Examples:
---
--- >>> fromList [1,2] :: Vn (Vec2D Int)
--- (1,2)
---
-fromList :: (V.Vector v a) => [a] -> Vn (v a)
-fromList xs = Vn $ V.fromList xs
-
--- * Two- and three-dimensional wrappers.
---
--- These two wrappers are instances of 'Vector', so they inherit all
--- of the userful instances defined above. But, they use fixed
+-- 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
+type instance Dim Vec2D = N2
+instance Vector Vec2D a where
+ inspect (Vec2D x y) (Fun f) = f x y
+ construct = 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
+type instance Dim Vec3D = N3
+instance Vector Vec3D a where
+ inspect (Vec3D x y z) (Fun f) = f x y z
+ construct = Fun Vec3D
+
+data Vec4D a = Vec4D a a a a
+type instance Dim Vec4D = N4
+instance Vector Vec4D a where
+ inspect (Vec4D w x y z) (Fun f) = f w x y z
+ construct = Fun Vec4D
-- | Convenience function for creating 2d vectors.
-- >>> (x,y)
-- (1,2)
--
-make2d :: forall a. (a,a) -> Vn (Vec2D a)
+make2d :: forall a. (a,a) -> Vn Vec2D a
make2d (x,y) = Vn (Vec2D x y)
-- >>> (x,y,z)
-- (1,2,3)
--
-make3d :: forall a. (a,a,a) -> Vn (Vec3D 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)
projects / numerical-analysis.git / blobdiff