vector-space-0.8.6: Vector & affine spaces, linear maps, and derivatives

Safe HaskellNone



Vector spaces

This version uses associated types instead of fundeps and requires ghc-6.10 or later



class AdditiveGroup v => VectorSpace v whereSource

Vector space v.

Associated Types

type Scalar v :: *Source


(*^) :: Scalar v -> v -> vSource

Scale a vector

(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> vSource

Vector divided by scalar

(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> vSource

Vector multiplied by scalar

class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v whereSource

Adds inner (dot) products.


(<.>) :: v -> v -> Scalar vSource

Inner/dot product

lerp :: VectorSpace v => v -> v -> Scalar v -> vSource

Linear interpolation between a (when t==0) and b (when t==1).

magnitudeSq :: (InnerSpace v, s ~ Scalar v) => v -> sSource

Square of the length of a vector. Sometimes useful for efficiency. See also magnitude.

magnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> sSource

Length of a vector. See also magnitudeSq.

normalized :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> vSource

Vector in same direction as given one but with length of one. If given the zero vector, then return it.

project :: (InnerSpace v, s ~ Scalar v, Fractional s) => v -> v -> vSource

project u v computes the projection of v onto u.