RustAD - Rust Auto-Differentiation

A restrictive WIP beginnings of a library attempting to implement auto-differentiation in Rust.

Why would I use this over <insert library>? You wouldn't, not yet anyway. I'd say wait until support for ndarray is more comprehensive, then this becomes probably the most convenient Rust AutoDiff library.

It's all messy be warned.

Status

I'm thinking of transitioning this project to a binary where running cargo rust-ad performs auto-diff on any Rust code. This would allow support for ndarray, nalgebra and any library written in Rust code by performing auto-diff through all dependencies. This would allow a fully generalized conveniant approach to auto-diff producing high level code which can be optimized by the compiler.

This transition will occur when all support items are covered.

These are not ordered.

• Forward Auto-differentiation
• Reverse Auto-differentiation
• Numerical primitives (e.g. f32, u32 etc.) support*
• if, if else and else support
• for, while and loop support
• map and fold

*typeof (e.g. decltype) not being currently implemented in Rust makes support more difficult.

Application

Auto-differentiation is implemented via 2 attribute procedural macros, e.g.

fn multi_test() {
    let (f, (der_x, der_y)) = forward!(multi, 3f32, 5f32);
    assert_eq!(f, 15.4f32);
    assert_eq!(der_x, 8f32);
    assert_eq!(der_y, -0.08f32);

    /// f = x^2 + 2x + 2/y
    /// δx|y=5 = 2x + 2
    /// δy|x=3 = -2/y^2
    #[forward_autodiff]
    fn multi(x: f32, y: f32) -> f32 {
        let a = x.powi(2i32);
        let b = x * 2f32;
        let c = 2f32 / y;
        let f = a + b + c;
        return f;
    }
}

fn multi_test() {
    let (f, (der_x, der_y)) = reverse!(multi, (3f32, 5f32), (1f32));
    assert_eq!(f, 15.4f32);
    assert_eq!(der_x, 8f32);
    assert_eq!(der_y, -0.08f32);

    /// f = x^2 + 2x + 2/y
    /// δx|y=5 = 2x + 2
    /// δy|x=3 = -2/y^2
    #[reverse_autodiff]
    fn multi(x: f32, y: f32) -> f32 {
        let a = x.powi(2i32);
        let b = x * 2f32;
        let c = 2f32 / y;
        let f = a + b + c;
        return f;
    }
}