Moduleswift-standard-library

Differentiation

import _Differentiation

Members

Functions

func derivative<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> R.TangentVector
func derivative<T, U, R>(at: T, U, of: (T, U) -> R) -> R.TangentVector
func derivative<T, R>(at: T, of: (T) -> R) -> R.TangentVector
func derivative<T, U, V, R>(of: (T, U, V) -> R) -> (T, U, V) -> R.TangentVector
func derivative<T, R>(of: (T) -> R) -> (T) -> R.TangentVector
func derivative<T, U, R>(of: (T, U) -> R) -> (T, U) -> R.TangentVector
func differential<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> (T.TangentVector, U.TangentVector, V.TangentVector) -> (R.TangentVector)
func differential<T, U, R>(at: T, U, of: (T, U) -> R) -> (T.TangentVector, U.TangentVector) -> R.TangentVector
func differential<T, R>(at: T, of: (T) -> R) -> (T.TangentVector) -> R.TangentVector
func gradient<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> (T.TangentVector, U.TangentVector, V.TangentVector)
func gradient<T, U, R>(at: T, U, of: (T, U) -> R) -> (T.TangentVector, U.TangentVector)
func gradient<T, R>(at: T, of: (T) -> R) -> T.TangentVector
func gradient<T, U, R>(of: (T, U) -> R) -> (T, U) -> (T.TangentVector, U.TangentVector)
func gradient<T, R>(of: (T) -> R) -> (T) -> T.TangentVector
func gradient<T, U, V, R>(of: (T, U, V) -> R) -> (T, U, V) -> (T.TangentVector, U.TangentVector, V.TangentVector)
func pullback<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> (R.TangentVector) -> (T.TangentVector, U.TangentVector, V.TangentVector)
func pullback<T, U, R>(at: T, U, of: (T, U) -> R) -> (R.TangentVector) -> (T.TangentVector, U.TangentVector)
func pullback<T, R>(at: T, of: (T) -> R) -> (R.TangentVector) -> T.TangentVector
func valueWithDerivative<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> (value: R, derivative: R.TangentVector)
func valueWithDerivative<T, U, R>(at: T, U, of: (T, U) -> R) -> (value: R, derivative: R.TangentVector)
func valueWithDerivative<T, R>(at: T, of: (T) -> R) -> (value: R, derivative: R.TangentVector)
func valueWithDifferential<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> (value: R, differential: (T.TangentVector, U.TangentVector, V.TangentVector) -> (R.TangentVector))
func valueWithDifferential<T, U, R>(at: T, U, of: (T, U) -> R) -> (value: R, differential: (T.TangentVector, U.TangentVector) -> R.TangentVector)
func valueWithDifferential<T, R>(at: T, of: (T) -> R) -> (value: R, differential: (T.TangentVector) -> R.TangentVector)
func valueWithGradient<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> (value: R, gradient: (T.TangentVector, U.TangentVector, V.TangentVector))
func valueWithGradient<T, U, R>(at: T, U, of: (T, U) -> R) -> (value: R, gradient: (T.TangentVector, U.TangentVector))
func valueWithGradient<T, R>(at: T, of: (T) -> R) -> (value: R, gradient: T.TangentVector)
func valueWithPullback<T, U, V, R>(at: T, U, V, of: (T, U, V) -> R) -> (value: R, pullback: (R.TangentVector) -> (T.TangentVector, U.TangentVector, V.TangentVector))
func valueWithPullback<T, U, R>(at: T, U, of: (T, U) -> R) -> (value: R, pullback: (R.TangentVector) -> (T.TangentVector, U.TangentVector))
func valueWithPullback<T, R>(at: T, of: (T) -> R) -> (value: R, pullback: (R.TangentVector) -> T.TangentVector)
func withoutDerivative<T>(at: T) -> T
Returns x like an identity function. When used in a context where x is being differentiated with respect to, this function will not produce any derivative at x.

Structures

struct AnyDerivative
A type-erased derivative value.
struct AnyDifferentiable

Protocols

protocol Differentiable
A type that mathematically represents a differentiable manifold whose tangent spaces are finite-dimensional.