Data.VectorSpace

Vector spaces

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

Documentation

module Data.AdditiveGroup

class AdditiveGroup v => VectorSpace v where

Vector space v.

Associated Types

type Scalar v :: *

Methods

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

Scale a vector

Instances

VectorSpace Double

VectorSpace Float

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

VectorSpace v => VectorSpace (Maybe v)

VectorSpace v => VectorSpace (a -> v)

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

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

(HasBasis a, HasTrie (Basis a), VectorSpace u, AdditiveGroup (Scalar u)) => VectorSpace (:> a u)

(s ~ Scalar u, s ~ Scalar v, s ~ Scalar w, VectorSpace u, VectorSpace v, VectorSpace w) => VectorSpace (u, v, w)

(s ~ Scalar u, s ~ Scalar v, s ~ Scalar w, s ~ Scalar x, VectorSpace u, VectorSpace v, VectorSpace w, VectorSpace x) => VectorSpace (u, v, w, x)

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

Vector divided by scalar

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

Vector multiplied by scalar

class VectorSpace v => InnerSpace v where

Adds inner (dot) products.

Methods

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

Inner/dot product

Instances

InnerSpace Double

InnerSpace Float

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

(InnerSpace a, AdditiveGroup (Scalar a)) => InnerSpace (Maybe a)

InnerSpace v => InnerSpace (a -> v)

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

(s ~ Scalar u, InnerSpace u, AdditiveGroup s, HasBasis a, HasTrie (Basis a)) => InnerSpace (:> a u)

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

(s ~ Scalar u, s ~ Scalar v, s ~ Scalar w, s ~ Scalar x, InnerSpace u, InnerSpace v, InnerSpace w, InnerSpace x, AdditiveGroup s) => InnerSpace (u, v, w, x)

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

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

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

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

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

Length of a vector. See also magnitudeSq.

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

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