## autodiff

An automatic differentiation library

### 11 releases

 0.2.2 Jul 23, 2020 Jul 21, 2020 May 20, 2020 Nov 7, 2019 Nov 10, 2018

#67 in Rust patterns

Used in 3 crates (2 directly)

MIT/Apache

44KB
1.5K SLoC

# 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`