I have a lot of one-off code where I've defined these myself. Is it possible to e.g. define vectors in R^2 and R^3, and write the p-norm functions only once?
Yes. it's possible.
{-# LANGUAGE TypeFamilies #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} import Data.Vector.Fixed as V import Data.Vector.Fixed.Internal -- ^^^ Needed for Fun /will be reexported from Data.Vector.Fixed import Data.Vector.Fixed.Unboxed
First we need to define data types and instances. It's possible to use vectors from library
data Vec2D a = Vec2D a a
type instance Dim Vec2D = S (S Z)
instance Vector Vec2D a where inspect (Vec2D x y) (Fun f) = f x y construct = Fun Vec2D
data Vec3D a = Vec3D a a a
type instance Dim Vec3D = S (S (S Z))
instance Vector Vec3D a where inspect (Vec3D x y z) (Fun f) = f x y z construct = Fun Vec3D
Now we can define generic p-norm. Maybe you had something different in mind but still it's function which will work with any vector of fixed length.
pNorm :: (Vector v a, Floating a) => a -> v a -> a pNorm p = (** recip p) . V.sum . V.map ((** p) . abs)
We will get folloiwng in GHCi: *Main> pNorm 1 $ Vec2D 1 2 :: Double 3.0 *Main> pNorm 1 $ Vec3D 1 2 3 :: Double 6.0 It's possible to avoid defining data types and use generic vectors from library. Vec2 is synonym to Data.Vector.Fixed.Unboxed.Vec (S (S Z)) *Main> pNorm 2 (vec $ con |> 1 |> 2 :: Vec2 Double) 2.23606797749979 At the moment their construction is a bit cumbersome so used replicate to illustrate other vector sizes. *Main> pNorm 1 (V.replicate 1 :: Vec2 Double) 2.0 *Main> pNorm 1 (V.replicate 1 :: Vec (S (S (S Z))) Double) 3.0 *Main> pNorm 1 (V.replicate 1 :: Vec (S (S (S (S Z)))) Double) 4.0