From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 3 Feb 2013 22:20:38 +0000 (-0500)
Subject: Add 2d/3d wrapper types for easy pattern matching.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=bd4568f6d35d814481d246f48b44ebc651f1534d;p=numerical-analysis.git

Add 2d/3d wrapper types for easy pattern matching.
Implement both safe and unsafe indexing.
---

diff --git a/src/FixedVector.hs b/src/FixedVector.hs
index 531c0fd..0a5312a 100644
--- a/src/FixedVector.hs
+++ b/src/FixedVector.hs
@@ -8,8 +8,7 @@ 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
 
@@ -18,7 +17,7 @@ import Normed
 newtype Vn a = Vn a
 
 
-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 +32,7 @@ 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 +50,14 @@ 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:
@@ -98,7 +97,7 @@ instance (Num a, Vector v a) => Num (Vn (v a)) where
 instance Functor Vn where
   fmap f (Vn v1) = Vn (f v1)
 
-instance (RealFloat a, Ord a, Vector v a) => Normed (Vn (v a)) where
+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 +135,7 @@ 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
 
 
@@ -149,13 +148,61 @@ 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
     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.
+--   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
+
+
+-- * 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
+-- 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
+
 
 -- | Convenience function for creating 2d vectors.
 --
@@ -164,12 +211,12 @@ 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 +226,9 @@ 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)