Stability	experimental
Maintainer	conal@conal.net, andygill@ku.edu
Safe Haskell	None

Data.VectorSpace

Description

Vector spaces

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

Synopsis

Documentation

Vector space v.

Associated Types

Methods

Scale a vector

Instances

VectorSpace Double
VectorSpace Float
VectorSpace Int
VectorSpace Integer
VectorSpace CSChar
VectorSpace CShort
VectorSpace CInt
VectorSpace CLong
VectorSpace CLLong
VectorSpace CFloat
VectorSpace CDouble
VectorSpace CIntMax
(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)

Vector divided by scalar

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

Vector multiplied by scalar

Adds inner (dot) products.

Methods

Inner/dot product

Instances

InnerSpace Double
InnerSpace Float
InnerSpace Int
InnerSpace Integer
InnerSpace CSChar
InnerSpace CShort
InnerSpace CInt
InnerSpace CLong
InnerSpace CLLong
InnerSpace CFloat
InnerSpace CDouble
InnerSpace CIntMax
(VectorSpace (Ratio a), AdditiveGroup (Scalar (Ratio a)), Integral a) => InnerSpace (Ratio a)
(VectorSpace (Complex v), AdditiveGroup (Scalar (Complex v)), RealFloat v, InnerSpace v) => InnerSpace (Complex v)
(VectorSpace (Maybe a), AdditiveGroup (Scalar (Maybe a)), InnerSpace a) => InnerSpace (Maybe a)
(VectorSpace (a -> v), AdditiveGroup (Scalar (a -> v)), InnerSpace v) => InnerSpace (a -> v)
(VectorSpace (u, v), AdditiveGroup (Scalar (u, v)), InnerSpace u, ~ * s (Scalar u), InnerSpace v, ~ * s (Scalar v)) => InnerSpace (u, v)
(VectorSpace (:> a u), AdditiveGroup (Scalar (:> a u)), InnerSpace u, ~ * s (Scalar u), AdditiveGroup s, HasBasis a, HasTrie (Basis a)) => InnerSpace (:> a u)
(VectorSpace (u, v, w), AdditiveGroup (Scalar (u, v, w)), InnerSpace u, ~ * s (Scalar u), InnerSpace v, ~ * s (Scalar v), InnerSpace w, ~ * s (Scalar w)) => InnerSpace (u, v, w)
(VectorSpace (u, v, w, x), AdditiveGroup (Scalar (u, v, w, x)), InnerSpace u, ~ * s (Scalar u), InnerSpace v, ~ * s (Scalar v), InnerSpace w, ~ * s (Scalar w), InnerSpace x, ~ * s (Scalar x)) => InnerSpace (u, v, w, x)

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

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

Length of a vector. See also magnitudeSq.

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

project u v computes the projection of v onto u.