X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FLinear%2FVector.hs;h=ec6ebcbfba47722110a056e90fb2590f93c8ed7d;hb=e4c2b71137d47045670cba23d420ea10a9e827b5;hp=9774dcd40c8132413ddd541a2a65be8976a462e1;hpb=303c5e7bba583f08e59bc6c848be8e75c1155a3b;p=numerical-analysis.git

diff --git a/src/Linear/Vector.hs b/src/Linear/Vector.hs
index 9774dcd..ec6ebcb 100644
--- a/src/Linear/Vector.hs
+++ b/src/Linear/Vector.hs
@@ -7,7 +7,6 @@
 module Linear.Vector
 where
 
-import Data.List (intercalate)
 import Data.Vector.Fixed (
   Dim,
   Fun(..),
@@ -15,17 +14,22 @@ import Data.Vector.Fixed (
   N2,
   N3,
   N4,
+  N5,
+  S,
   Vector(..),
   construct,
+  fromList,
   inspect,
   toList,
   )
 import qualified Data.Vector.Fixed as V (
   length,
   )
+import Data.Vector.Fixed.Boxed
 
-import Normed
-
+type Vec1 = Vec N1
+type Vec4 = Vec N4
+type Vec5 = Vec N5
 
 -- * Low-dimension vector wrappers.
 --
@@ -34,25 +38,25 @@ import Normed
 -- constructors, so you can pattern match out the individual
 -- components.
 
-data D1 a = D1 a
+data D1 a = D1 a deriving (Show, Eq)
 type instance Dim D1 = N1
 instance Vector D1 a where
   inspect (D1 x) (Fun f) = f x
   construct = Fun D1
 
-data D2 a = D2 a a
+data D2 a = D2 a a deriving (Show, Eq)
 type instance Dim D2 = N2
 instance Vector D2 a where
   inspect (D2 x y) (Fun f) = f x y
   construct = Fun D2
 
-data D3 a = D3 a a a
+data D3 a = D3 a a a deriving (Show, Eq)
 type instance Dim D3 = N3
 instance Vector D3 a where
   inspect (D3 x y z) (Fun f) = f x y z
   construct = Fun D3
 
-data D4 a = D4 a a a a
+data D4 a = D4 a a a a deriving (Show, Eq)
 type instance Dim D4 = N4
 instance Vector D4 a where
   inspect (D4 w x y z) (Fun f) = f w x y z
@@ -63,7 +67,7 @@ instance Vector D4 a where
 --
 --   Examples:
 --
---   >>> let v1 = Vec2D 1 2
+--   >>> let v1 = D2 1 2
 --   >>> v1 ! 1
 --   2
 --
@@ -74,7 +78,7 @@ instance Vector D4 a where
 --
 --   Examples:
 --
---   >>> let v1 = Vec3D 1 2 3
+--   >>> let v1 = D3 1 2 3
 --   >>> v1 !? 2
 --   Just 3
 --   >>> v1 !? 3
@@ -86,52 +90,17 @@ instance Vector D4 a where
   | otherwise                     = Just $ v1 ! idx
 
 
-
-
---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.
-  --
-  --   Examples:
-  --
-  --   >>> let v1 = make3d (1,5,2)
-  --   >>> norm_infty v1
-  --   5
-  --
---  norm_infty (Vn v1) = realToFrac $ V.foldl max 0 v1
-
-  -- | Generic p-norms. The usual norm in R^n is (norm_p 2).
-  --
-  --   Examples:
-  --
-  --   >>> let v1 = make2d (3,4)
-  --   >>> norm_p 1 v1
-  --   7.0
-  --   >>> norm_p 2 v1
-  --   5.0
-  --
---  norm_p p (Vn v1) =
---    realToFrac $ root $ V.sum $ V.map (exponentiate . abs) v1
---    where
---      exponentiate = (** (fromIntegral p))
---      root = (** (recip (fromIntegral p)))
-
-
-
-
-
--- | Convenient constructor for 2D vectors.
+-- | Remove an element of the given vector.
 --
 --   Examples:
 --
---   >>> import Roots.Simple
---   >>> let h = 0.5 :: Double
---   >>> let g1 (Vn (Vec2D x y)) = 1.0 + h*exp(-(x^2))/(1.0 + y^2)
---   >>> let g2 (Vn (Vec2D x y)) = 0.5 + h*atan(x^2 + y^2)
---   >>> let g u = make2d ((g1 u), (g2 u))
---   >>> let u0 = make2d (1.0, 1.0)
---   >>> let eps = 1/(10^9)
---   >>> fixed_point g eps u0
---   (1.0728549599342185,1.0820591495686167)
+--   >>> let b = D3 1 2 3
+--   >>> delete b 1 :: D2 Int
+--   D2 1 3
 --
+delete :: (Vector v a, Vector w a, Dim v ~ S (Dim w)) => v a -> Int -> w a
+delete v1 idx =
+  fromList $ (lhalf ++ rhalf')
+  where
+    (lhalf, rhalf) = splitAt idx (toList v1)
+    rhalf' = tail rhalf