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:
-- >>> 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
-
+(!?) :: (V.Vector v a) => v a -> Int -> Maybe a
+(!?) v1 idx
+ | idx < 0 || idx >= V.length v1 = Nothing
+ | otherwise = Just $ v1 V.! 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