Data.VectorSpace

Vector spaces. Fundep version. GHC-6.9 isn't quite up to the nicer version in Data.VectorSpace, which uses associated types.

Documentation

module Data.AdditiveGroup

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

Vector space v over a scalar field s. Extends AdditiveGroup with scalar multiplication.

Methods

(*^) :: s -> v -> v

Scale a vector

Instances

VectorSpace Double Double

VectorSpace Float Float

(RealFloat v, VectorSpace v s) => VectorSpace (Complex v) s

VectorSpace v s => VectorSpace (a -> v) s

(VectorSpace u s, VectorSpace v s) => VectorSpace (u, v) s

(HasTrie a, VectorSpace v s) => VectorSpace (:->: a v) s

(HasBasis a s, HasTrie (Basis a), 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

Vector divided by scalar

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

Vector multiplied by scalar

class VectorSpace v s => InnerSpace v s where

Adds inner (dot) products.

Methods

(<.>) :: v -> v -> s

Inner/dot product

Instances

InnerSpace Double Double

InnerSpace Float Float

(RealFloat v, InnerSpace v s, AdditiveGroup s) => InnerSpace (Complex v) s

(InnerSpace u s, InnerSpace v s, AdditiveGroup s) => InnerSpace (u, v) s

(InnerSpace u s, InnerSpace s s, VectorSpace s s, HasBasis a s, HasTrie (Basis a)) => InnerSpace (:> a u) (:> a s)

(InnerSpace u s, InnerSpace v s, InnerSpace w s, AdditiveGroup s) => InnerSpace (u, v, w) s

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

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

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

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

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

Length of a vector. See also magnitudeSq.

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

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