module Linear.Vector
where
-import Data.List (intercalate)
import Data.Vector.Fixed (
Dim,
- Fun(..),
N1,
- N2,
- N3,
N4,
+ N5,
+ S,
Vector(..),
- construct,
- inspect,
+ fromList,
toList,
)
import qualified Data.Vector.Fixed as V (
length,
)
+import Data.Vector.Fixed.Boxed
-import Normed
-
-
--- * 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 D1 a = D1 a
-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
-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
-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
-type instance Dim D4 = N4
-instance Vector D4 a where
- inspect (D4 w x y z) (Fun f) = f w x y z
- construct = Fun D4
+type Vec1 = Vec N1
+type Vec4 = Vec N4
+type Vec5 = Vec N5
-- | Unsafe indexing.
--
-- Examples:
--
--- >>> let v1 = Vec2D 1 2
+-- >>> import Data.Vector.Fixed (mk2)
+-- >>> let v1 = mk2 1 2 :: Vec2 Int
-- >>> v1 ! 1
-- 2
--
--
-- Examples:
--
--- >>> let v1 = Vec3D 1 2 3
+-- >>> import Data.Vector.Fixed (mk3)
+-- >>> let v1 = mk3 1 2 3 :: Vec3 Int
-- >>> v1 !? 2
-- Just 3
-- >>> v1 !? 3
| 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)
+-- >>> import Data.Vector.Fixed (mk3)
+-- >>> let b = mk3 1 2 3 :: Vec3 Int
+-- >>> delete b 1 :: Vec2 Int
+-- fromList [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