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

(AdditiveGroup (Ratio a), Integral a) => VectorSpace (Ratio a)

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

(AdditiveGroup (Maybe v), VectorSpace v) => VectorSpace (Maybe v)

(AdditiveGroup (a -> v), VectorSpace v) => VectorSpace (a -> v)

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

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

(AdditiveGroup (:-* u v), HasTrie (Basis u), VectorSpace v) => VectorSpace (:-* u v)

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

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

(AdditiveGroup (u, v, w, x), VectorSpace u, ~ * s (Scalar u), VectorSpace v, ~ * s (Scalar v), VectorSpace w, ~ * s (Scalar w), VectorSpace x, ~ * s (Scalar 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

(VectorSpace (Ratio a), Integral a) => InnerSpace (Ratio a)

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

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

(VectorSpace (a -> v), InnerSpace v) => InnerSpace (a -> v)

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

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

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

(VectorSpace (u, v, w, x), InnerSpace u, ~ * s (Scalar u), InnerSpace v, ~ * s (Scalar v), InnerSpace w, ~ * s (Scalar w), InnerSpace x, ~ * s (Scalar 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.

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

project u v computes the projection of v onto u.