Copyright	(c) Conal Elliott and Andy J Gill 2008
License	BSD3
Maintainer	conal@conal.net, andygill@ku.edu
Stability	experimental
Safe Haskell	Safe
Language	Haskell98

Data.VectorSpace

Description

Vector spaces

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

Synopsis

Documentation

module Data.AdditiveGroup

class AdditiveGroup v => VectorSpace v where #

Vector space v.

Minimal complete definition

(*^)

Associated Types

type Scalar v :: * #

Methods

(*^) :: Scalar v -> v -> v infixr 7 #

Scale a vector

Instances

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

(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v infixr 7 #

Vector divided by scalar

(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v infixl 7 #

Vector multiplied by scalar

class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where #

Adds inner (dot) products.

Minimal complete definition

(<.>)

Methods

(<.>) :: v -> v -> Scalar v infixr 7 #

Inner/dot product

Instances

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

lerp :: VectorSpace v => v -> v -> Scalar v -> v #

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

linearCombo :: VectorSpace v => [(v, Scalar v)] -> v #

Linear combination of vectors

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.