forward API

The forward package turns a function on dual numbers into its derivative at a point. It contains the two scalar forward-mode drivers, diff and value_and_diff, and re-exports Dual. The root package re-exports both functions, so most programs call them as @autodiff.diff and @autodiff.value_and_diff.

Source: src/forward/forward.mbt.

Importing

import {
  "Luna-Flow/autodiff/forward",
}

Drivers

value_and_diff

Evaluates f at x and returns the value together with the first derivative.

pub fn[T : @luna-generic.One] value_and_diff((@dual.Dual[T]) -> @dual.Dual[T], T) -> (T, T)

It calls f(Dual::variable(x)) once and returns (y.value(), y.tangent()). By the dual design, the pair is $(f(x), f'(x))$ when f is built from the operations of Dual[T] and treats every other input as a constant. The cost is one evaluation of f on dual numbers. f must not inspect the tangent of its argument; whatever f does is differentiated, including branches on value().

diff

Returns only the derivative $f'(x)$.

pub fn[T : @luna-generic.One] diff((@dual.Dual[T]) -> @dual.Dual[T], T) -> T

diff(f, x) is the second component of value_and_diff(f, x).

test "scalar drivers" {
  let (value, derivative) = @forward.value_and_diff(x => x * x * x, 2.0)
  assert_eq(value, 8.0)
  assert_eq(derivative, 12.0)
  assert_eq(@forward.diff(x => x.sin(), 0.0), 1.0)
}

Re-exported type

Dual

pub using @dual {type Dual} makes @forward.Dual the same type as @dual.Dual; see the dual API.

pub using @dual {type Dual}