_Differentiation

Uncategorized

Protocols

• protocol Differentiable

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

Types

• struct AnyDerivative

  A type-erased derivative value.

• struct AnyDifferentiable

Globals

• 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, R>(of: @escaping (T, U) -> R) -> (T, U) -> R.TangentVector
• func derivative<T, U, V, R>(of: @escaping (T, U, V) -> R) -> (T, U, V) -> R.TangentVector
• func derivative<T, R>(of: @escaping (T) -> R) -> (T) -> 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, V, R>(of: @escaping (T, U, V) -> R) -> (T, U, V) -> (T.TangentVector, U.TangentVector, V.TangentVector)
• func gradient<T, U, R>(of: @escaping (T, U) -> R) -> (T, U) -> (T.TangentVector, U.TangentVector)
• func gradient<T, R>(of: @escaping (T) -> R) -> (T) -> T.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: @escaping (T, U, V) -> R) -> (value: R, derivative: R.TangentVector)
• func valueWithDerivative<T, U, R>(at: T, U, of: @escaping (T, U) -> R) -> (value: R, derivative: R.TangentVector)
• func valueWithDerivative<T, R>(at: T, of: @escaping (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.