vector-space-0.8.3: Vector & affine spaces, linear maps, and derivatives

Stability experimental conal@conal.net, andygill@ku.edu None

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 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 (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 -> 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, Fractional s) => v -> v -> vSource

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