autodiff

An auto-differentiation library.

Currently supported features:

• [x] Forward auto-differentiation

• [ ] Reverse auto-differentiation

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

1. create a variable of type Num, 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.

``rust // Define a functionf(x) = e^{-0.5*x^2}`. let f = |x: Num| (-x * x / Num::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:

``rust // Define a functionf(x,y) = x*y^2`. let f = |x: &[Num]| 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:

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

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

```

License

This library is licensed under the Apache License, Version 2.0, (LICENSE or https://www.apache.org/licenses/LICENSE-2.0).

Acknowledgements

This library started as a fork of rust-ad.