module Linear.Vector
where
-import Data.List (intercalate)
import Data.Vector.Fixed (
Dim,
Fun(..),
N2,
N3,
N4,
+ S,
Vector(..),
construct,
+ fromList,
inspect,
toList,
)
length,
)
-import Normed
-
-- * Low-dimension vector wrappers.
--
-- 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
--
-- Examples:
--
--- >>> let v1 = Vec2D 1 2
+-- >>> let v1 = D2 1 2
-- >>> v1 ! 1
-- 2
--
--
-- Examples:
--
--- >>> let v1 = Vec3D 1 2 3
+-- >>> let v1 = D3 1 2 3
-- >>> 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)
+-- >>> 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