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

module Data.AdditiveGroup
class AdditiveGroup v => VectorSpace v where
- type Scalar v :: *
(^/) :: (VectorSpace v, s ~ Scalar v, Fractional s) => v -> s -> v
(^*) :: (VectorSpace v, s ~ Scalar v) => v -> s -> v
class (VectorSpace v, AdditiveGroup (Scalar v)) => InnerSpace v where
lerp :: VectorSpace v => v -> v -> Scalar v -> v
linearCombo :: VectorSpace v => [(v, Scalar v)] -> v
magnitudeSq :: (InnerSpace v, s ~ Scalar v) => v -> s
magnitude :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> s
normalized :: (InnerSpace v, s ~ Scalar v, Floating s) => v -> v
project :: (InnerSpace v, s ~ Scalar v, Fractional s) => v -> v -> v

Documentation

module Data.AdditiveGroup

class AdditiveGroup v => VectorSpace v where Source #

Vector space v.

Associated Types

type Scalar v :: * Source #

Methods

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

Scale a vector

(*^) :: (Generic v, VectorSpace (VRep v), Scalar (VRep v) ~ Scalar v) => Scalar v -> v -> v infixr 7 Source #

Scale a vector

Instances

VectorSpace Double Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar Double :: * Source # Methods (*^) :: Scalar Double -> Double -> Double Source #
VectorSpace Float Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar Float :: * Source # Methods (*^) :: Scalar Float -> Float -> Float Source #
VectorSpace Int Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar Int :: * Source # Methods (*^) :: Scalar Int -> Int -> Int Source #
VectorSpace Integer Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar Integer :: * Source # Methods (*^) :: Scalar Integer -> Integer -> Integer Source #
VectorSpace CSChar Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CSChar :: * Source # Methods (*^) :: Scalar CSChar -> CSChar -> CSChar Source #
VectorSpace CShort Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CShort :: * Source # Methods (*^) :: Scalar CShort -> CShort -> CShort Source #
VectorSpace CInt Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CInt :: * Source # Methods (*^) :: Scalar CInt -> CInt -> CInt Source #
VectorSpace CLong Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CLong :: * Source # Methods (*^) :: Scalar CLong -> CLong -> CLong Source #
VectorSpace CLLong Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CLLong :: * Source # Methods (*^) :: Scalar CLLong -> CLLong -> CLLong Source #
VectorSpace CFloat Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CFloat :: * Source # Methods (*^) :: Scalar CFloat -> CFloat -> CFloat Source #
VectorSpace CDouble Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CDouble :: * Source # Methods (*^) :: Scalar CDouble -> CDouble -> CDouble Source #
VectorSpace CIntMax Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar CIntMax :: * Source # Methods (*^) :: Scalar CIntMax -> CIntMax -> CIntMax Source #
VectorSpace v => VectorSpace (Maybe v) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Maybe v) :: * Source # Methods (*^) :: Scalar (Maybe v) -> Maybe v -> Maybe v Source #
Integral a => VectorSpace (Ratio a) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Ratio a) :: * Source # Methods (*^) :: Scalar (Ratio a) -> Ratio a -> Ratio a Source #
(RealFloat v, VectorSpace v) => VectorSpace (Complex v) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Complex v) :: * Source # Methods (*^) :: Scalar (Complex v) -> Complex v -> Complex v Source #
VectorSpace v => VectorSpace (a -> v) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (a -> v) :: * Source # Methods (*^) :: Scalar (a -> v) -> (a -> v) -> a -> v Source #
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v) => VectorSpace (u, v) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (u, v) :: * Source # Methods (*^) :: Scalar (u, v) -> (u, v) -> (u, v) Source #
(HasTrie a, VectorSpace v) => VectorSpace (a :->: v) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (a :->: v) :: * Source # Methods (*^) :: Scalar (a :->: v) -> (a :->: v) -> a :->: v Source #
(HasTrie (Basis u), VectorSpace v) => VectorSpace (u :-* v) Source #
Instance details Defined in Data.LinearMap Associated Types type Scalar (u :-* v) :: * Source # Methods (^) :: Scalar (u :- v) -> (u :-* v) -> u :-* v Source #
(HasBasis a, HasTrie (Basis a), VectorSpace u) => VectorSpace (a :> u) Source #
Instance details Defined in Data.Maclaurin Associated Types type Scalar (a :> u) :: * Source # Methods (*^) :: Scalar (a :> u) -> (a :> u) -> a :> u Source #
VectorSpace a => VectorSpace (Rec0 a s) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (Rec0 a s) :: * Source # Methods (*^) :: Scalar (Rec0 a s) -> Rec0 a s -> Rec0 a s Source #
(VectorSpace u, s ~ Scalar u, VectorSpace v, s ~ Scalar v, VectorSpace w, s ~ Scalar w) => VectorSpace (u, v, w) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (u, v, w) :: * Source # Methods (*^) :: Scalar (u, v, w) -> (u, v, w) -> (u, v, w) Source #
(VectorSpace (f p), VectorSpace (g p), Scalar (f p) ~ Scalar (g p)) => VectorSpace ((f :*: g) p) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar ((f :: g) p) :: Source # Methods (^) :: Scalar ((f :: g) p) -> (f :: g) p -> (f :: g) p Source #
(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) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (u, v, w, x) :: * Source # Methods (*^) :: Scalar (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) Source #
VectorSpace (f p) => VectorSpace (M1 i c f p) Source #
Instance details Defined in Data.VectorSpace Associated Types type Scalar (M1 i c f p) :: * Source # Methods (*^) :: Scalar (M1 i c f p) -> M1 i c f p -> M1 i c f p Source #

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

Vector divided by scalar

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

Vector multiplied by scalar

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

Adds inner (dot) products.

Methods

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

Inner/dot product

(<.>) :: (Generic v, InnerSpace (VRep v), Scalar (VRep v) ~ Scalar v) => v -> v -> Scalar v infixr 7 Source #

Inner/dot product

Instances

InnerSpace Double Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Double -> Double -> Scalar Double Source #
InnerSpace Float Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Float -> Float -> Scalar Float Source #
InnerSpace Int Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Int -> Int -> Scalar Int Source #
InnerSpace Integer Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Integer -> Integer -> Scalar Integer Source #
InnerSpace CSChar Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CSChar -> CSChar -> Scalar CSChar Source #
InnerSpace CShort Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CShort -> CShort -> Scalar CShort Source #
InnerSpace CInt Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CInt -> CInt -> Scalar CInt Source #
InnerSpace CLong Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CLong -> CLong -> Scalar CLong Source #
InnerSpace CLLong Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CLLong -> CLLong -> Scalar CLLong Source #
InnerSpace CFloat Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CFloat -> CFloat -> Scalar CFloat Source #
InnerSpace CDouble Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CDouble -> CDouble -> Scalar CDouble Source #
InnerSpace CIntMax Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: CIntMax -> CIntMax -> Scalar CIntMax Source #
InnerSpace a => InnerSpace (Maybe a) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Maybe a -> Maybe a -> Scalar (Maybe a) Source #
Integral a => InnerSpace (Ratio a) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Ratio a -> Ratio a -> Scalar (Ratio a) Source #
(RealFloat v, InnerSpace v) => InnerSpace (Complex v) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Complex v -> Complex v -> Scalar (Complex v) Source #
InnerSpace v => InnerSpace (a -> v) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: (a -> v) -> (a -> v) -> Scalar (a -> v) Source #
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v) => InnerSpace (u, v) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: (u, v) -> (u, v) -> Scalar (u, v) Source #
(InnerSpace u, s ~ Scalar u, AdditiveGroup s, HasBasis a, HasTrie (Basis a)) => InnerSpace (a :> u) Source #
Instance details Defined in Data.Maclaurin Methods (<.>) :: (a :> u) -> (a :> u) -> Scalar (a :> u) Source #
InnerSpace a => InnerSpace (Rec0 a s) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: Rec0 a s -> Rec0 a s -> Scalar (Rec0 a s) Source #
(InnerSpace u, s ~ Scalar u, InnerSpace v, s ~ Scalar v, InnerSpace w, s ~ Scalar w) => InnerSpace (u, v, w) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: (u, v, w) -> (u, v, w) -> Scalar (u, v, w) Source #
(InnerSpace (f p), InnerSpace (g p), Scalar (f p) ~ Scalar (g p), Num (Scalar (f p))) => InnerSpace ((f :*: g) p) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: (f :: g) p -> (f :: g) p -> Scalar ((f :*: g) p) Source #
(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) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: (u, v, w, x) -> (u, v, w, x) -> Scalar (u, v, w, x) Source #
InnerSpace (f p) => InnerSpace (M1 i c f p) Source #
Instance details Defined in Data.VectorSpace Methods (<.>) :: M1 i c f p -> M1 i c f p -> Scalar (M1 i c f p) Source #

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

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

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

Linear combination of vectors

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

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

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

Length of a vector. See also magnitudeSq.

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

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 Source #

project u v computes the projection of v onto u.