# Library for vectors

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Revision as of 14:10, 18 April 2007 by MathematicalOrchid (Talk | contribs)

(Int,Int)

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)

Vector

Num