# Library for vectors

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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 :: Vector v => v -> Scalar
vmag v = sqrt \$ vdot v v

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!