Goal.Geometry.Map

The Map module provides tools for developing function space Manifolds. A map is a Manifold where the Points of the Manifold represent parametric functions between Manifolds. The defining feature of Maps is that they have a particular Domain and Codomain, which themselves are Manifolds.

Maps

class Manifold m => Map m where

Function Charts help track Charts on the Domain and Codomain. The first Chart corresponds to the Domains chart.

Associated Types

type Domain m :: *

type Codomain m :: *

Methods

domain :: m -> Domain m

codomain :: m -> Codomain m

Instances

(Manifold m, Manifold n) => Map (Tensor m n)

(Manifold m, Manifold n) => Map (Affine m n)

class Map m => Apply c d m where

Minimal complete definition

Nothing

Methods

(>.>) :: (Function c d :#: m) -> (c :#: Domain m) -> d :#: Codomain m infix 8

Map application.

(>$>) :: (Function c d :#: m) -> [c :#: Domain m] -> [d :#: Codomain m] infix 8

Map list application. May sometimes have a more efficient implementation than simply list-mapping (>.>).

Instances

(Manifold m, Manifold n) => Apply c d (Affine m n)

(Manifold m, Manifold n) => Apply c d (Tensor m n)

Map Charts

data Function c d

Constructors

Function c d