Safe Haskell	Safe-Inferred
Language	Haskell2010

Algebra.VectorSpace

Synopsis

class VectorSpace v where
- (+.) :: v -> v -> v
- (-.) :: v -> v -> v
- (*.) :: Double -> v -> v
- (/.) :: v -> Double -> v
- zero :: v
- negateV :: v -> v
vsum :: VectorSpace a => [a] -> a

Documentation

class VectorSpace v where Source #

A generic vector space. Not only classic vectors like Vec2 form a vector space, but also concepts like Angles – anything that can be added, inverted, and multiplied with a scalar.

Vector spaces come with a number of laws that you can look up on Wikipedia. The short version is: each operation behaves like addition/multiplication on normal numbers.

Minimal complete definition

(+.), (*.), ((-.) | negateV), zero

Methods

(+.) :: v -> v -> v infixl 6 Source #

Vector addition

(-.) :: v -> v -> v infixl 6 Source #

Vector subtraction

(*.) :: Double -> v -> v infixl 7 Source #

Multiplication with a scalar

(/.) :: v -> Double -> v infixl 7 Source #

Division by a scalar

zero :: v Source #

Neutral element

negateV :: v -> v Source #

Inverse element

Instances

Instances details

VectorSpace Angle Source #
Instance details Defined in Geometry.Core Methods (+.) :: Angle -> Angle -> Angle Source # (-.) :: Angle -> Angle -> Angle Source # (*.) :: Double -> Angle -> Angle Source # (/.) :: Angle -> Double -> Angle Source # zero :: Angle Source # negateV :: Angle -> Angle Source #
VectorSpace Mat2 Source #
Instance details Defined in Geometry.Core Methods (+.) :: Mat2 -> Mat2 -> Mat2 Source # (-.) :: Mat2 -> Mat2 -> Mat2 Source # (*.) :: Double -> Mat2 -> Mat2 Source # (/.) :: Mat2 -> Double -> Mat2 Source # zero :: Mat2 Source # negateV :: Mat2 -> Mat2 Source #
VectorSpace Vec2 Source #
Instance details Defined in Geometry.Core Methods (+.) :: Vec2 -> Vec2 -> Vec2 Source # (-.) :: Vec2 -> Vec2 -> Vec2 Source # (*.) :: Double -> Vec2 -> Vec2 Source # (/.) :: Vec2 -> Double -> Vec2 Source # zero :: Vec2 Source # negateV :: Vec2 -> Vec2 Source #
VectorSpace PhaseSpace Source #
Instance details Defined in Physics Methods (+.) :: PhaseSpace -> PhaseSpace -> PhaseSpace Source # (-.) :: PhaseSpace -> PhaseSpace -> PhaseSpace Source # (*.) :: Double -> PhaseSpace -> PhaseSpace Source # (/.) :: PhaseSpace -> Double -> PhaseSpace Source # zero :: PhaseSpace Source # negateV :: PhaseSpace -> PhaseSpace Source #
VectorSpace Double Source #
Instance details Defined in Algebra.VectorSpace Methods (+.) :: Double -> Double -> Double Source # (-.) :: Double -> Double -> Double Source # (*.) :: Double -> Double -> Double Source # (/.) :: Double -> Double -> Double Source # zero :: Double Source # negateV :: Double -> Double Source #
VectorSpace a => VectorSpace (NBody a) Source #
Instance details Defined in Physics Methods (+.) :: NBody a -> NBody a -> NBody a Source # (-.) :: NBody a -> NBody a -> NBody a Source # (*.) :: Double -> NBody a -> NBody a Source # (/.) :: NBody a -> Double -> NBody a Source # zero :: NBody a Source # negateV :: NBody a -> NBody a Source #
VectorSpace b => VectorSpace (a -> b) Source #
Instance details Defined in Algebra.VectorSpace Methods (+.) :: (a -> b) -> (a -> b) -> a -> b Source # (-.) :: (a -> b) -> (a -> b) -> a -> b Source # (*.) :: Double -> (a -> b) -> a -> b Source # (/.) :: (a -> b) -> Double -> a -> b Source # zero :: a -> b Source # negateV :: (a -> b) -> a -> b Source #
(VectorSpace v1, VectorSpace v2) => VectorSpace (v1, v2) Source #
Instance details Defined in Algebra.VectorSpace Methods (+.) :: (v1, v2) -> (v1, v2) -> (v1, v2) Source # (-.) :: (v1, v2) -> (v1, v2) -> (v1, v2) Source # (*.) :: Double -> (v1, v2) -> (v1, v2) Source # (/.) :: (v1, v2) -> Double -> (v1, v2) Source # zero :: (v1, v2) Source # negateV :: (v1, v2) -> (v1, v2) Source #
(VectorSpace v1, VectorSpace v2, VectorSpace v3) => VectorSpace (v1, v2, v3) Source #
Instance details Defined in Algebra.VectorSpace Methods (+.) :: (v1, v2, v3) -> (v1, v2, v3) -> (v1, v2, v3) Source # (-.) :: (v1, v2, v3) -> (v1, v2, v3) -> (v1, v2, v3) Source # (*.) :: Double -> (v1, v2, v3) -> (v1, v2, v3) Source # (/.) :: (v1, v2, v3) -> Double -> (v1, v2, v3) Source # zero :: (v1, v2, v3) Source # negateV :: (v1, v2, v3) -> (v1, v2, v3) Source #
(VectorSpace v1, VectorSpace v2, VectorSpace v3, VectorSpace v4) => VectorSpace (v1, v2, v3, v4) Source #
Instance details Defined in Algebra.VectorSpace Methods (+.) :: (v1, v2, v3, v4) -> (v1, v2, v3, v4) -> (v1, v2, v3, v4) Source # (-.) :: (v1, v2, v3, v4) -> (v1, v2, v3, v4) -> (v1, v2, v3, v4) Source # (*.) :: Double -> (v1, v2, v3, v4) -> (v1, v2, v3, v4) Source # (/.) :: (v1, v2, v3, v4) -> Double -> (v1, v2, v3, v4) Source # zero :: (v1, v2, v3, v4) Source # negateV :: (v1, v2, v3, v4) -> (v1, v2, v3, v4) Source #
(VectorSpace v1, VectorSpace v2, VectorSpace v3, VectorSpace v4, VectorSpace v5) => VectorSpace (v1, v2, v3, v4, v5) Source #
Instance details Defined in Algebra.VectorSpace Methods (+.) :: (v1, v2, v3, v4, v5) -> (v1, v2, v3, v4, v5) -> (v1, v2, v3, v4, v5) Source # (-.) :: (v1, v2, v3, v4, v5) -> (v1, v2, v3, v4, v5) -> (v1, v2, v3, v4, v5) Source # (*.) :: Double -> (v1, v2, v3, v4, v5) -> (v1, v2, v3, v4, v5) Source # (/.) :: (v1, v2, v3, v4, v5) -> Double -> (v1, v2, v3, v4, v5) Source # zero :: (v1, v2, v3, v4, v5) Source # negateV :: (v1, v2, v3, v4, v5) -> (v1, v2, v3, v4, v5) Source #

vsum :: VectorSpace a => [a] -> a Source #