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swift-mirror/stdlib/public/Differentiation/DifferentialOperators.swift
Richard Wei 57d228b39e [AutoDiff upstream] Add differential operators and some utilities. 
* Add all [differential operators](https://github.com/apple/swift/blob/master/docs/DifferentiableProgramming.md#list-of-differential-operators).
* Add `withoutDerivative(at:)`, used for efficiently stopping the derivative propagation at a value and causing the derivative at the value to be zero.
* Add utility `differentiableFunction(from:)`, used for creating a `@differentiable` function from an original function and a derivative function.

Mostly work done by @marcrasi and @dan-zheng.
Partially resolves TF-843.

TODO:
* Add `AnyDerivative`.
* Add `Array.differentiableMap(_:)` and `differentiableReduce(_:_:)`.
2020-03-30 14:15:35 -07:00

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//===--- DifferentialOperators.swift --------------------------*- swift -*-===//
//
// This source file is part of the Swift.org open source project
//
// Copyright (c) 2014 - 2019 Apple Inc. and the Swift project authors
// Licensed under Apache License v2.0 with Runtime Library Exception
//
// See https://swift.org/LICENSE.txt for license information
// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
//
//===----------------------------------------------------------------------===//
//
// APIs for computing derivatives of functions.
//
//===----------------------------------------------------------------------===//
import Swift
// Transpose
@inlinable
public func transpose<T, R>(
of body: @escaping @differentiable(linear) (T) -> R
) -> @differentiable(linear) (R) -> T {
let original = body as (T) -> R
let transpose = { x in Builtin.applyTranspose_arity1(body, x) }
return Builtin.linearFunction_arity1(transpose, original)
}
// Value with differential
@inlinable
public func valueWithDifferential<T, R>(
at x: T, in f: @differentiable (T) -> R
) -> (value: R, differential: (T.TangentVector) -> R.TangentVector) {
return Builtin.applyDerivative_jvp(f, x)
}
@inlinable
public func valueWithDifferential<T, U, R>(
at x: T, _ y: U, in f: @differentiable (T, U) -> R
) -> (value: R,
differential: (T.TangentVector, U.TangentVector) -> R.TangentVector) {
return Builtin.applyDerivative_jvp_arity2(f, x, y)
}
@inlinable
public func valueWithDifferential<T, U, V, R>(
at x: T, _ y: U, _ z: V, in f: @differentiable (T, U, V) -> R
) -> (value: R,
differential: (T.TangentVector, U.TangentVector, V.TangentVector)
-> (R.TangentVector)) {
return Builtin.applyDerivative_jvp_arity3(f, x, y, z)
}
// Value with pullback
@inlinable
public func valueWithPullback<T, R>(
at x: T, in f: @differentiable (T) -> R
) -> (value: R, pullback: (R.TangentVector) -> T.TangentVector) {
return Builtin.applyDerivative_vjp(f, x)
}
@inlinable
public func valueWithPullback<T, U, R>(
at x: T, _ y: U, in f: @differentiable (T, U) -> R
) -> (value: R,
pullback: (R.TangentVector) -> (T.TangentVector, U.TangentVector)) {
return Builtin.applyDerivative_vjp_arity2(f, x, y)
}
@inlinable
public func valueWithPullback<T, U, V, R>(
at x: T, _ y: U, _ z: V, in f: @differentiable (T, U, V) -> R
) -> (value: R,
pullback: (R.TangentVector)
-> (T.TangentVector, U.TangentVector, V.TangentVector)) {
return Builtin.applyDerivative_vjp_arity3(f, x, y, z)
}
// Differential
@inlinable
public func differential<T, R>(
at x: T, in f: @differentiable (T) -> R
) -> (T.TangentVector) -> R.TangentVector {
return valueWithDifferential(at: x, in: f).1
}
@inlinable
public func differential<T, U, R>(
at x: T, _ y: U, in f: @differentiable (T, U) -> R
) -> (T.TangentVector, U.TangentVector) -> R.TangentVector {
return valueWithDifferential(at: x, y, in: f).1
}
@inlinable
public func differential<T, U, V, R>(
at x: T, _ y: U, _ z: V, in f: @differentiable (T, U, V) -> R
) -> (T.TangentVector, U.TangentVector, V.TangentVector) -> (R.TangentVector) {
return valueWithDifferential(at: x, y, z, in: f).1
}
// Pullback
@inlinable
public func pullback<T, R>(
at x: T, in f: @differentiable (T) -> R
) -> (R.TangentVector) -> T.TangentVector {
return Builtin.applyDerivative_vjp(f, x).1
}
@inlinable
public func pullback<T, U, R>(
at x: T, _ y: U, in f: @differentiable (T, U) -> R
) -> (R.TangentVector) -> (T.TangentVector, U.TangentVector) {
return Builtin.applyDerivative_vjp_arity2(f, x, y).1
}
@inlinable
public func pullback<T, U, V, R>(
at x: T, _ y: U, _ z: V, in f: @differentiable (T, U, V) -> R
) -> (R.TangentVector)
-> (T.TangentVector, U.TangentVector, V.TangentVector) {
return Builtin.applyDerivative_vjp_arity3(f, x, y, z).1
}
// Derivative
@inlinable
public func derivative<T: FloatingPoint, R>(
at x: T, in f: @differentiable (T) -> R
) -> R.TangentVector
where T.TangentVector == T {
return differential(at: x, in: f)(T(1))
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, R>(
at x: T, _ y: U, in f: @differentiable (T, U) -> R
) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U {
return differential(at: x, y, in: f)(T(1), U(1))
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, V: FloatingPoint, R>(
at x: T, _ y: U, _ z: V, in f: @differentiable (T, U, V) -> R
) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U,
V.TangentVector == V {
return differential(at: x, y, z, in: f)(T(1), U(1), V(1))
}
// Gradient
@inlinable
public func gradient<T, R>(
at x: T, in f: @differentiable (T) -> R
) -> T.TangentVector
where R : FloatingPoint, R.TangentVector == R {
return pullback(at: x, in: f)(R(1))
}
@inlinable
public func gradient<T, U, R>(
at x: T, _ y: U, in f: @differentiable (T, U) -> R
) -> (T.TangentVector, U.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return pullback(at: x, y, in: f)(R(1))
}
@inlinable
public func gradient<T, U, V, R>(
at x: T, _ y: U, _ z: V, in f: @differentiable (T, U, V) -> R
) -> (T.TangentVector, U.TangentVector, V.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return pullback(at: x, y, z, in: f)(R(1))
}
// Value with derivative
@inlinable
public func valueWithDerivative<T: FloatingPoint, R>(
at x: T, in f: @escaping @differentiable (T) -> R
) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T {
let (y, differential) = valueWithDifferential(at: x, in: f)
return (y, differential(T(1)))
}
@inlinable
public func valueWithDerivative<T: FloatingPoint, U: FloatingPoint, R>(
at x: T, _ y: U, in f: @escaping @differentiable (T, U) -> R
) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T,
U.TangentVector == U {
let (y, differential) = valueWithDifferential(at: x, y, in: f)
return (y, differential(T(1), U(1)))
}
@inlinable
public func valueWithDerivative<
T: FloatingPoint, U: FloatingPoint, V: FloatingPoint, R>(
at x: T, _ y: U, _ z: V, in f: @escaping @differentiable (T, U, V) -> R
) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T,
U.TangentVector == U,
V.TangentVector == V {
let (y, differential) = valueWithDifferential(at: x, y, z, in: f)
return (y, differential(T(1), U(1), V(1)))
}
// Value with gradient
@inlinable
public func valueWithGradient<T, R>(
at x: T, in f: @differentiable (T) -> R
) -> (value: R, gradient: T.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
let (y, pullback) = valueWithPullback(at: x, in: f)
return (y, pullback(R(1)))
}
@inlinable
public func valueWithGradient<T, U, R>(
at x: T, _ y: U, in f: @differentiable (T, U) -> R
) -> (value: R, gradient: (T.TangentVector, U.TangentVector))
where R : FloatingPoint, R.TangentVector == R {
let (y, pullback) = valueWithPullback(at: x, y, in: f)
return (y, pullback(R(1)))
}
@inlinable
public func valueWithGradient<T, U, V, R>(
at x: T, _ y: U, _ z: V, in f: @differentiable (T, U, V) -> R
) -> (value: R,
gradient: (T.TangentVector, U.TangentVector, V.TangentVector))
where R : FloatingPoint, R.TangentVector == R {
let (y, pullback) = valueWithPullback(at: x, y, z, in: f)
return (y, pullback(R(1)))
}
// Derivative (curried)
@inlinable
public func derivative<T: FloatingPoint, R>(
of f: @escaping @differentiable (T) -> R
) -> (T) -> R.TangentVector
where T.TangentVector == T {
return { x in derivative(at: x, in: f) }
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, R>(
of f: @escaping @differentiable (T, U) -> R
) -> (T, U) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U {
return { (x, y) in derivative(at: x, y, in: f) }
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, V: FloatingPoint, R>(
of f: @escaping @differentiable (T, U, V) -> R
) -> (T, U, V) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U,
V.TangentVector == V {
return { (x, y, z) in derivative(at: x, y, z, in: f) }
}
// Gradient (curried)
@inlinable
public func gradient<T, R>(
of f: @escaping @differentiable (T) -> R
) -> (T) -> T.TangentVector
where R : FloatingPoint, R.TangentVector == R {
return { x in gradient(at: x, in: f) }
}
@inlinable
public func gradient<T, U, R>(
of f: @escaping @differentiable (T, U) -> R
) -> (T, U) -> (T.TangentVector, U.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return { x, y in gradient(at: x, y, in: f) }
}
@inlinable
public func gradient<T, U, V, R>(
of f: @escaping @differentiable (T, U, V) -> R
) -> (T, U, V) -> (T.TangentVector, U.TangentVector, V.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return { x, y, z in gradient(at: x, y, z, in: f) }
}
// Value with derivative (curried)
@inlinable
public func valueWithDerivative<T: FloatingPoint, R>(
of f: @escaping @differentiable (T) -> R
) -> (T) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T {
return { x in valueWithDerivative(at: x, in: f) }
}
@inlinable
public func valueWithDerivative<T: FloatingPoint, U: FloatingPoint, R>(
of f: @escaping @differentiable (T, U) -> R
) -> (T, U) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T,
U.TangentVector == U {
return { (x, y) in valueWithDerivative(at: x, y, in: f) }
}
@inlinable
public func valueWithDerivative<
T: FloatingPoint, U: FloatingPoint, V: FloatingPoint, R>(
of f: @escaping @differentiable (T, U, V) -> R
) -> (T, U, V) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T,
U.TangentVector == U,
V.TangentVector == V {
return { (x, y, z) in valueWithDerivative(at: x, y, z, in: f) }
}
// Value with gradient (curried)
@inlinable
public func valueWithGradient<T, R>(
of f: @escaping @differentiable (T) -> R
) -> (T) -> (value: R, gradient: T.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return { x in valueWithGradient(at: x, in: f) }
}
@inlinable
public func valueWithGradient<T, U, R>(
of f: @escaping @differentiable (T, U) -> R
) -> (T, U) -> (value: R, gradient: (T.TangentVector, U.TangentVector))
where R : FloatingPoint, R.TangentVector == R {
return { x, y in valueWithGradient(at: x, y, in: f) }
}
@inlinable
public func valueWithGradient<T, U, V, R>(
of f: @escaping @differentiable (T, U, V) -> R
) -> (T, U, V)
-> (value: R,
gradient: (T.TangentVector, U.TangentVector, V.TangentVector))
where R : FloatingPoint, R.TangentVector == R {
return { x, y, z in valueWithGradient(at: x, y, z, in: f) }
}
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