Numeric.Vector

Vector is an alias to a DataFrame with order 1.

Type aliases

type Vector (t :: l) (n :: k) = DataFrame t '[n]

type Vec2f = Vector Float 2

type Vec3f = Vector Float 3

type Vec4f = Vector Float 4

type Vec2d = Vector Double 2

type Vec3d = Vector Double 3

type Vec4d = Vector Double 4

type Vec2i = Vector Int 2

type Vec3i = Vector Int 3

type Vec4i = Vector Int 4

type Vec2w = Vector Word 2

type Vec3w = Vector Word 3

type Vec4w = Vector Word 4

Common operations

(.*.) :: (Num t, Num (Vector t n), SubSpace t '[] '[n] '[n]) => Vector t n -> Vector t n -> Vector t n infixl 7

Scalar product -- sum of Vecs' components products, propagated into whole Vec

dot :: (Num t, Num (Vector t n), SubSpace t '[] '[n] '[n]) => Vector t n -> Vector t n -> Scalar t

Scalar product -- sum of Vecs' components products -- a scalar

(·) :: (Num t, Num (Vector t n), SubSpace t '[] '[n] '[n]) => Vector t n -> Vector t n -> Scalar t infixl 7

Dot product of two vectors

normL1 :: (Num t, SubSpace t '[] '[n] '[n]) => Vector t n -> Scalar t

Sum of absolute values

normL2 :: (Floating t, SubSpace t '[] '[n] '[n]) => Vector t n -> Scalar t

hypot function (square root of squares)

normLPInf :: (Ord t, Num t, SubSpace t '[] '[n] '[n]) => Vector t n -> Scalar t

Maximum of absolute values

normLNInf :: (Ord t, Num t, SubSpace t '[] '[n] '[n]) => Vector t n -> Scalar t

Minimum of absolute values

normLP :: (Floating t, SubSpace t '[] '[n] '[n]) => Int -> Vector t n -> Scalar t

Norm in Lp space

normalized :: (Floating t, Fractional (Vector t n), SubSpace t '[] '[n] '[n]) => Vector t n -> Vector t n

Normalize vector w.r.t. Euclidean metric (L2).

vec2 :: SubSpace t '[] '[2] '[2] => t -> t -> Vector t 2

Compose a 2D vector

vec3 :: SubSpace t '[] '[3] '[3] => t -> t -> t -> Vector t 3

Compose a 3D vector

vec4 :: SubSpace t '[] '[4] '[4] => t -> t -> t -> t -> Vector t 4

Compose a 4D vector

det2 :: (Num t, SubSpace t '[] '[2] '[2]) => Vector t 2 -> Vector t 2 -> Scalar t

Take a determinant of a matrix composed from two 2D vectors. Like a cross product in 2D.

cross :: (Num t, SubSpace t '[] '[3] '[3]) => Vector t 3 -> Vector t 3 -> Vector t 3

Cross product

(×) :: (Num t, SubSpace t '[] '[3] '[3]) => Vector t 3 -> Vector t 3 -> Vector t 3 infixl 7

Cross product for two vectors in 3D

unpackV2 :: SubSpace t '[] '[2] '[2] => Vector t 2 -> (t, t)

unpackV3 :: SubSpace t '[] '[3] '[3] => Vector t 3 -> (t, t, t)

unpackV4 :: SubSpace t '[] '[4] '[4] => Vector t 4 -> (t, t, t, t)