Goal.Geometry.Vector

The Linear module provides the tools for treating a locally Euclidean patch of a manifold as a linear space.

Vector Spaces

(.>) :: Double -> (c # x) -> c # x infix 7

Scalar multiplication of points on a manifold.

(/>) :: Double -> (c # x) -> c # x infix 7

Scalar division of points on a manifold.

convexCombination :: Manifold x => Double -> (c # x) -> (c # x) -> c # x

Combination of two Points. Takes the first argument of the second argument, and (1-first argument) of the third argument.

Dual Spaces

class (Dual (Dual c) ~ c, Primal (Dual c)) => Primal c

Primal charts have a Dual coordinate system.

Associated Types

type Dual c :: Type

Instances

Primal Cartesian

Defined in Goal.Geometry.Vector

Associated Types

type Dual Cartesian

type (#*) c x = Point (Dual c) x infix 3

A Point on a Manifold in the Dual coordinates of c.

(<.>) :: (c # x) -> (c #* x) -> Double infix 7

<.> is the inner product between a dual pair of Points.

dotMap :: Manifold x => (c # x) -> [c #* x] -> [Double]

dotMap computes the inner product over a list of dual elements.