autodiff

An auto-differentiation library.

Currently supported features:

• Forward auto-differentiation

  • Single variable higher order differentiation

• Reverse auto-differentiation

To compute a derivative with respect to a variable using this library:

1. create a variable of type F, which implements the Float trait from the num-traits crate.

2. compute your function using this variable as the input.

3. request the derivative from this variable using the deriv method.

Disclaimer

This library is a work in progress and is not ready for production use.

Examples

The following example differentiates a 1D function defined by a closure.

    // Define a function `f(x) = e^{-0.5*x^2}`.
    let f = |x: F1| (-x * x / F1::cst(2.0)).exp();

    // Differentiate `f` at zero.
    println!("{}", diff(f, 0.0)); // prints `0`

To compute the gradient of a function, use the function grad as follows:

    // Define a function `f(x,y) = x*y^2`.
    let f = |x: &[F1]| x[0] * x[1] * x[1];

    // Differentiate `f` at `(1,2)`.
    let g = grad(f, &vec![1.0, 2.0]);
    println!("({}, {})", g[0], g[1]); // prints `(4, 4)`

Compute a specific derivative of a multi-variable function:

     // Define a function `f(x,y) = x*y^2`.
     let f = |v: &[F1]| v[0] * v[1] * v[1];
 
     // Differentiate `f` at `(1,2)` with respect to `x` (the first unknown) only.
     let v = vec![
         F1::var(1.0), // Create a variable.
         F1::cst(2.0), // Create a constant.
     ];
     println!("{}", f(&v).deriv()); // prints `4`

Compute higher order derivatives by nesting the generic parameter of F. For convenience we provide type aliases for the first 3 orders:

type F1 = F<f64>;
type F2 = F<F<f64>>;
type F3 = F<F<F<f64>>>;

To compute the third order derivative, we can use the F3 type as follows.

     // Define a function `f(x) = (x - 1)^3`.
     let f = |x: F3| (x - 1.0_f64).powi(3);
 
     // Compute the 3rd derivative of `f` at `x = 0`.
     println!("{}", f(F3::var(0.0)).deriv().deriv().deriv()); // prints `6`

License

This repository is licensed under either of

• Apache License, Version 2.0, (LICENSE-APACHE or https://www.apache.org/licenses/LICENSE-2.0)
• MIT License (LICENSE-MIT or https://opensource.org/licenses/MIT)

at your option.

Acknowledgements

This library started as a fork of rust-ad.