public protocol EuclideanDifferentiable : Differentiable

A type that is differentiable in the Euclidean space. The type may represent a vector space, or consist of a vector space and some other non-differentiable component.

Mathematically, this represents a product manifold that consists of a differentiable vector space and some arbitrary manifold, where the tangent bundle of the entire product manifold is equal to the vector space component.

This abstraction is useful for representing common differentiable data structures that contain both differentiable vector properties and other stored properties that do not have a derivative, e.g.

struct Perceptron: @memberwise EuclideanDifferentiable {
    var weight: SIMD16<Float>
    var bias: Float
    @noDerivative var useBias: Bool
}

Note

Conform a type to EuclideanDifferentiable if it is differentiable only with respect to its vector space component and when its TangentVector is equal to its vector space component.
  • differentiableVectorView

    Default implementation

    The differentiable vector component of self.

    Default Implementation

    Declaration

    var differentiableVectorView: TangentVector { get }