Goal.Geometry.Map

Definitions for working with manifolds of functions, a.k.a. function spaces.

Documentation

class (Manifold x, Manifold y, Manifold (f y x)) => Map c f y x where

A Manifold is a Map if it is a binary type-function of two Manifolds, and can transforms Points on the first Manifold into Points on the second Manifold.

Methods

(>.>) :: (c # f y x) -> (c #* x) -> c # y

Map application restricted.

(>$>) :: (c # f y x) -> [c #* x] -> [c # y]

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

Instances

(Manifold x, Manifold y) => Map c Tensor y x

Defined in Goal.Geometry.Map.Linear

Methods

(>.>) :: (c # Tensor y x) -> (c #* x) -> c # y

(>$>) :: (c # Tensor y x) -> [c #* x] -> [c # y]

(Translation z y, Map c f y x) => Map c (Affine f y) z x

Defined in Goal.Geometry.Map.Linear

Methods

(>.>) :: (c # Affine f y z x) -> (c #* x) -> c # z

(>$>) :: (c # Affine f y z x) -> [c #* x] -> [c # z]

Map c f z x => Map c (NeuralNetwork ('[] :: [(Type -> Type -> Type, Type)]) f) z x

Defined in Goal.Geometry.Map.NeuralNetwork

Methods

(>.>) :: (c # NeuralNetwork '[] f z x) -> (c #* x) -> c # z

(>$>) :: (c # NeuralNetwork '[] f z x) -> [c #* x] -> [c # z]

(Map c f z y, Map c (NeuralNetwork gys g) y x, Transition c (Dual c) y) => Map c (NeuralNetwork ('(g, y) ': gys) f) z x

Defined in Goal.Geometry.Map.NeuralNetwork

Methods

(>.>) :: (c # NeuralNetwork ('(g, y) ': gys) f z x) -> (c #* x) -> c # z

(>$>) :: (c # NeuralNetwork ('(g, y) ': gys) f z x) -> [c #* x] -> [c # z]

KnownConvolutional rd r c z x => Map a (Convolutional rd r c) z x

Defined in Goal.Geometry.Map.Linear.Convolutional

Methods

(>.>) :: (a # Convolutional rd r c z x) -> (a #* x) -> a # z

(>$>) :: (a # Convolutional rd r c z x) -> [a #* x] -> [a # z]