vector-space-0.2.0: Vector & affine spaces, plus derivatives Source code Contents Index

Data.VectorSpace Stability experimental Maintainer conal@conal.net, andygill@ku.edu

Description

Vector spaces

Synopsis

module Data.AdditiveGroup class AdditiveGroup v => VectorSpace v s | v -> s where (*^) :: s -> v -> v (^/) :: (Fractional s, VectorSpace v s) => v -> s -> v (^*) :: VectorSpace v s => v -> s -> v class VectorSpace v s => InnerSpace v s where (<.>) :: v -> v -> s lerp :: (VectorSpace v s, Num s) => v -> v -> s -> v magnitudeSq :: InnerSpace v s => v -> s magnitude :: (InnerSpace v s, Floating s) => v -> s normalized :: (InnerSpace v s, Floating s) => v -> v

Documentation

module Data.AdditiveGroup

class AdditiveGroup v => VectorSpace v s | v -> s where Source

Vector space v over a scalar field s. Extends AdditiveGroup with scalar multiplication. Methods (*^) :: s -> v -> v Source Scale a vector Instances VectorSpace Double Double VectorSpace Float Float (RealFloat v, VectorSpace v s) => VectorSpace (Complex v) s VectorSpace u s => VectorSpace (Vector2 u) s VectorSpace u s => VectorSpace (Vector3 u) s (VectorSpace u s, VectorSpace v s) => VectorSpace ((,) u v) s (VectorSpace v s, LMapDom u s) => VectorSpace (u :-* v) s (LMapDom a s, VectorSpace u s) => VectorSpace (a :> u) s (LMapDom a s, VectorSpace u s, VectorSpace s s) => VectorSpace (a :> u) (a :> s) (VectorSpace u s, VectorSpace v s, VectorSpace w s) => VectorSpace ((,,) u v w) s

(^/) :: (Fractional s, VectorSpace v s) => v -> s -> v Source

Vector divided by scalar

(^*) :: VectorSpace v s => v -> s -> v Source

Vector multiplied by scalar

class VectorSpace v s => InnerSpace v s where Source

Adds inner (dot) products. Methods (<.>) :: v -> v -> s Source Inner/dot product Instances InnerSpace Double Double InnerSpace Float Float (RealFloat v, InnerSpace v s, VectorSpace s s') => InnerSpace (Complex v) s (InnerSpace u s, AdditiveGroup s) => InnerSpace (Vector2 u) s (InnerSpace u s, AdditiveGroup s) => InnerSpace (Vector3 u) s (InnerSpace u s, InnerSpace v s, VectorSpace s s') => InnerSpace ((,) u v) s (InnerSpace u s, InnerSpace s s', VectorSpace s s, LMapDom a s) => InnerSpace (a :> u) (a :> s) (InnerSpace u s, InnerSpace v s, InnerSpace w s, VectorSpace s s') => InnerSpace ((,,) u v w) s

lerp :: (VectorSpace v s, Num s) => v -> v -> s -> v Source

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

magnitudeSq :: InnerSpace v s => v -> s Source

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

magnitude :: (InnerSpace v s, Floating s) => v -> s Source

Length of a vector. See also magnitudeSq.

normalized :: (InnerSpace v s, Floating s) => v -> v Source

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

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