vector-space-0.8.0: Vector & affine spaces, linear maps, and derivatives

Stability experimental conal@conal.net, andygill@ku.edu Safe-Infered

Data.VectorSpace

Description

Vector spaces

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

Synopsis

# Documentation

class AdditiveGroup v => VectorSpace v whereSource

Vector space `v`.

Associated Types

type Scalar v :: *Source

Methods

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

Scale a vector

Instances

 VectorSpace Double VectorSpace Float Integral a => VectorSpace (Ratio a) (RealFloat v, VectorSpace v) => VectorSpace (Complex v) VectorSpace v => VectorSpace (Maybe v) VectorSpace v => VectorSpace (a -> v) (VectorSpace u, ~ * s (Scalar u), VectorSpace v, ~ * s (Scalar v)) => VectorSpace (u, v) (HasTrie a, VectorSpace v) => VectorSpace (:->: a v) (HasTrie (Basis u), VectorSpace v) => VectorSpace (:-* u v) (HasBasis a, HasTrie (Basis a), VectorSpace u, AdditiveGroup (Scalar u)) => VectorSpace (:> a u) (VectorSpace u, ~ * s (Scalar u), VectorSpace v, ~ * s (Scalar v), VectorSpace w, ~ * s (Scalar w)) => VectorSpace (u, v, w) (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 -> vSource

Vector divided by scalar

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

Vector multiplied by scalar

class VectorSpace v => InnerSpace v whereSource

Methods

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

Inner/dot product

Instances

 InnerSpace Double InnerSpace Float Integral a => InnerSpace (Ratio a) (RealFloat v, InnerSpace v, ~ * s (Scalar v), AdditiveGroup s) => InnerSpace (Complex v) (InnerSpace a, AdditiveGroup (Scalar a)) => InnerSpace (Maybe a) InnerSpace v => InnerSpace (a -> v) (InnerSpace u, ~ * s (Scalar u), InnerSpace v, ~ * s (Scalar v), AdditiveGroup (Scalar v)) => InnerSpace (u, v) (InnerSpace u, ~ * s (Scalar u), AdditiveGroup s, HasBasis a, HasTrie (Basis a)) => InnerSpace (:> a u) (InnerSpace u, ~ * s (Scalar u), InnerSpace v, ~ * s (Scalar v), InnerSpace w, ~ * s (Scalar w), AdditiveGroup s) => InnerSpace (u, v, w) (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 -> vSource

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

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

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

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

Length of a vector. See also `magnitudeSq`.

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

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, Floating s) => v -> v -> vSource

`project u v` computes the projection of `v` onto `u`.