Binary Moduleswift 6.1.2_Differentiation
_Differentiation
import _DifferentiationModule information
- Declarations
- 92
- Symbols
- 145
import _Differentiationfunc derivative<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: (T, U, V) -> R) -> R.TangentVector where T : FloatingPoint, T : Differentiable, T == T.TangentVector, U : FloatingPoint, U : Differentiable, U == U.TangentVector, V : FloatingPoint, V : Differentiable, V == V.TangentVector, R : Differentiable func derivative<T, U, R>(at x: T, _ y: U, of f: (T, U) -> R) -> R.TangentVector where T : FloatingPoint, T : Differentiable, T == T.TangentVector, U : FloatingPoint, U : Differentiable, U == U.TangentVector, R : Differentiable func derivative<T, R>(at x: T, of f: (T) -> R) -> R.TangentVector where T : FloatingPoint, T : Differentiable, T == T.TangentVector, R : Differentiable func derivative<T, U, R>(of f: @escaping (T, U) -> R) -> (T, U) -> R.TangentVector where T : FloatingPoint, T : Differentiable, T == T.TangentVector, U : FloatingPoint, U : Differentiable, U == U.TangentVector, R : Differentiable func derivative<T, U, V, R>(of f: @escaping (T, U, V) -> R) -> (T, U, V) -> R.TangentVector where T : FloatingPoint, T : Differentiable, T == T.TangentVector, U : FloatingPoint, U : Differentiable, U == U.TangentVector, V : FloatingPoint, V : Differentiable, V == V.TangentVector, R : Differentiable func derivative<T, R>(of f: @escaping (T) -> R) -> (T) -> R.TangentVector where T : FloatingPoint, T : Differentiable, T == T.TangentVector, R : Differentiable func differential<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: (T, U, V) -> R) -> (T.TangentVector, U.TangentVector, V.TangentVector) -> R.TangentVector where T : Differentiable, U : Differentiable, V : Differentiable, R : Differentiable func differential<T, U, R>(at x: T, _ y: U, of f: (T, U) -> R) -> (T.TangentVector, U.TangentVector) -> R.TangentVector where T : Differentiable, U : Differentiable, R : Differentiable func differential<T, R>(at x: T, of f: (T) -> R) -> (T.TangentVector) -> R.TangentVector where T : Differentiable, R : Differentiable func gradient<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: (T, U, V) -> R) -> (T.TangentVector, U.TangentVector, V.TangentVector) where T : Differentiable, U : Differentiable, V : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func gradient<T, U, R>(at x: T, _ y: U, of f: (T, U) -> R) -> (T.TangentVector, U.TangentVector) where T : Differentiable, U : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func gradient<T, R>(at x: T, of f: (T) -> R) -> T.TangentVector where T : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func gradient<T, U, V, R>(of f: @escaping (T, U, V) -> R) -> (T, U, V) -> (T.TangentVector, U.TangentVector, V.TangentVector) where T : Differentiable, U : Differentiable, V : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func gradient<T, U, R>(of f: @escaping (T, U) -> R) -> (T, U) -> (T.TangentVector, U.TangentVector) where T : Differentiable, U : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func gradient<T, R>(of f: @escaping (T) -> R) -> (T) -> T.TangentVector where T : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func pullback<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: (T, U, V) -> R) -> (R.TangentVector) -> (T.TangentVector, U.TangentVector, V.TangentVector) where T : Differentiable, U : Differentiable, V : Differentiable, R : Differentiable func pullback<T, U, R>(at x: T, _ y: U, of f: (T, U) -> R) -> (R.TangentVector) -> (T.TangentVector, U.TangentVector) where T : Differentiable, U : Differentiable, R : Differentiable func pullback<T, R>(at x: T, of f: (T) -> R) -> (R.TangentVector) -> T.TangentVector where T : Differentiable, R : Differentiable func valueWithDerivative<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: @escaping (T, U, V) -> R) -> (value: R, derivative: R.TangentVector) where T : FloatingPoint, T : Differentiable, T == T.TangentVector, U : FloatingPoint, U : Differentiable, U == U.TangentVector, V : FloatingPoint, V : Differentiable, V == V.TangentVector, R : Differentiable func valueWithDerivative<T, U, R>(at x: T, _ y: U, of f: @escaping (T, U) -> R) -> (value: R, derivative: R.TangentVector) where T : FloatingPoint, T : Differentiable, T == T.TangentVector, U : FloatingPoint, U : Differentiable, U == U.TangentVector, R : Differentiable func valueWithDerivative<T, R>(at x: T, of f: @escaping (T) -> R) -> (value: R, derivative: R.TangentVector) where T : FloatingPoint, T : Differentiable, T == T.TangentVector, R : Differentiable func valueWithDifferential<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: (T, U, V) -> R) -> (value: R, differential: (T.TangentVector, U.TangentVector, V.TangentVector) -> R.TangentVector) where T : Differentiable, U : Differentiable, V : Differentiable, R : Differentiable func valueWithDifferential<T, U, R>(at x: T, _ y: U, of f: (T, U) -> R) -> (value: R, differential: (T.TangentVector, U.TangentVector) -> R.TangentVector) where T : Differentiable, U : Differentiable, R : Differentiable func valueWithDifferential<T, R>(at x: T, of f: (T) -> R) -> (value: R, differential: (T.TangentVector) -> R.TangentVector) where T : Differentiable, R : Differentiable func valueWithGradient<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: (T, U, V) -> R) -> (value: R, gradient: (T.TangentVector, U.TangentVector, V.TangentVector)) where T : Differentiable, U : Differentiable, V : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func valueWithGradient<T, U, R>(at x: T, _ y: U, of f: (T, U) -> R) -> (value: R, gradient: (T.TangentVector, U.TangentVector)) where T : Differentiable, U : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func valueWithGradient<T, R>(at x: T, of f: (T) -> R) -> (value: R, gradient: T.TangentVector) where T : Differentiable, R : FloatingPoint, R : Differentiable, R == R.TangentVector func valueWithPullback<T, U, V, R>(at x: T, _ y: U, _ z: V, of f: (T, U, V) -> R) -> (value: R, pullback: (R.TangentVector) -> (T.TangentVector, U.TangentVector, V.TangentVector)) where T : Differentiable, U : Differentiable, V : Differentiable, R : Differentiable func valueWithPullback<T, U, R>(at x: T, _ y: U, of f: (T, U) -> R) -> (value: R, pullback: (R.TangentVector) -> (T.TangentVector, U.TangentVector)) where T : Differentiable, U : Differentiable, R : Differentiable func valueWithPullback<T, R>(at x: T, of f: (T) -> R) -> (value: R, pullback: (R.TangentVector) -> T.TangentVector) where T : Differentiable, R : Differentiable func withoutDerivative<T>(at x: 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.
protocol DifferentiableA type that mathematically represents a differentiable manifold whose tangent spaces are finite-dimensional.
@frozen struct AnyDerivativeA type-erased derivative value.
struct AnyDifferentiableimport Cxximport Dispatchimport DispatchIntrospectionimport Distributedimport Foundationimport FoundationNetworkingimport FoundationXMLimport RegexBuilderimport Swiftimport XCTestimport _Concurrencyimport _RegexParserimport _StringProcessing