Library for vectors

Most people just use (Int,Int) or similar for a 2-vector. However, if you find yourself wanting to do lots of vector arithmetic, that becomes annoying quite quickly. Below is what I use; feel free to adapt it to your needs.

module Vector where

type Scalar = Double

class Vector v where
  vmap  :: (Scalar -> Scalar) -> v -> v
  vzip  :: (Scalar -> Scalar -> Scalar) -> v -> v -> v
  vfold :: (x -> Scalar -> x) -> x -> v -> x

vdot :: Vector v => v -> v -> Scalar
vdot v0 v1 = vfold (+) 0 $ vzip (*) v0 v1

vmag_sqr :: Vector v => v -> Scalar
vmag_sqr v = v `vdot` v

vmag :: Vector v => v -> Scalar
vmag = sqrt . vmag_sqr

vscale :: Vector v => Scalar -> v -> v
vscale s = vmap (s*)

vunit :: Vector v => v -> v
vunit v =
  if vmag v == 0
    then v
    else vscale (1 / vmag v) v


data Vector2 = Vector2 {v2x, v2y :: Scalar} deriving (Eq)

instance Show Vector2 where
  show (Vector2 x y) = "<" ++ (show x) ++ ", " ++ (show y) ++ ">"

instance Vector Vector2 where
  vmap  f   (Vector2 x y) = Vector2 (f x) (f y)
  vfold f i (Vector2 x y) = (i `f` x) `f` y
  vzip  f   (Vector2 x0 y0) (Vector2 x1 y1) = Vector2 (f x0 x1) (f y0 y1)

instance Num Vector2 where
  (+) = vzip (+)
  (-) = vzip (-)
  (*) = vzip (*)
  negate = vmap negate
  fromInteger s = Vector2 (fromInteger s) (fromInteger s)

instance Fractional Vector2 where
  (/) = vzip (/)
  fromDouble s = Vector2 s s


data Vector3 = Vector3 {v3x, v3y, v3z :: Scalar} deriving (Eq)

instance Show Vector3 where
  show (Vector3 x y z) = "<" ++ (show x) ++ ", " ++ (show y) ++ ", " ++ (show z) ++ ">"

instance Vector Vector3 where
  vmap  f   (Vector3 x y z) = Vector3 (f x) (f y) (f z)
  vfold f i (Vector3 x y z) = ((i `f` x) `f` y) `f` z
  vzip  f   (Vector3 x0 y0 z0) (Vector3 x1 y1 z1) = Vector3 (f x0 x1) (f y0 y1) (f z0 z1)

instance Num Vector3 where
  (+) = vzip (+)
  (-) = vzip (-)
  (*) = vzip (*)
  negate = vmap negate
  fromInteger s = Vector3 (fromInteger s) (fromInteger s) (fromInteger s)

instance Fractional Vector3 where
  (/) = vzip (/)
  fromDouble s = Vector3 s s s

v3cross (Vector3 x0 y0 z0) (Vector3 x1 y1 z1) = Vector3 (y0*z1 - y1*z0) (x0*z1 - x1*z0) (x0*y1 - x1*y0)

PS. If anybody knows a way to make every instance of Vector automatically become an instance of Num, etc., let me know!