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

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)

(^/) :: (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, AdditiveGroup (Scalar v)) => InnerSpace v where

Adds inner (dot) products.

Methods

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

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)

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.