autodiff

The autodiff module can be used to differentiate scalar output functions of the form:

\[f : \mathbb{R}^n \rightarrow \mathbb{R} \]

Simple expressions are differentiated as follows:

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    // SIMPLE EXPRESSIONS
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    let g = Graph::new();

    let a = 1.;
    let b = 2.;
    let x = g.var(69.);
    let y = g.var(420.);

    // Define a function.
    let f = a + b + (x * y).exp();

    // Accumulate the gradient.
    let gradient = f.accumulate();

    println!("z = {}", f.value);
    println!("dz/dx = {}", gradient.wrt(&x));
    println!("dz/dy = {}", gradient.wrt(&y));
    println!("grad = {:?}", gradient.wrt(&[x, y]));

Block expressions are also supported:

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    // BLOCK EXPRESSIONS
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    let g = Graph::new();

    let x = g.var(69.);
    let y = g.var(420.);

    let block = {
        let z = x.sin() + y.tan();
        z.exp()
    };

    let grad = block.accumulate();

    println!("f = {}", block.value);
    println!("df/dx = {}", grad.wrt(&x));
    println!("df/dy = {}", grad.wrt(&y));
    println!("grad = {:?}", grad.wrt(&[x, y]));

Closures and functions are also supported:

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    // CLOSURES
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    let g = Graph::new();

    let x = g.var(1.);
    let y = g.var(2.);

    let closure = || (x * y).cosh() / (x.tanh() * y.sinh());

    let grad = closure().accumulate();

    println!("z = {}", closure().value);
    println!("dz/dx = {}", grad.wrt(&x));
    println!("dz/dy = {}", grad.wrt(&y));
    println!("grad = {:?}", grad.wrt(&[x, y]));

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    // PROPER FUNCTIONS.
    //
    // Note that you can also add many variables via vectors, slices, arrays, etc.
    // This is where the `autodiff` crate really shines, as it allows
    // you to differentiate functions of any number of variables and
    // computing gradients for large functions using AD rather than
    // finite-difference quotients is significantly faster and has no error.
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    // Function to differentiate:
    // f = x^(y + cos(1)) - atanh(z) / 2 + 1
    // at x = 3, y = 2, z = 1.
    #[rustfmt::skip]
    fn function<'v>(variables: &[Variable<'v>], constants: &[f64]) -> Variable<'v> {
        variables[0].powf(variables[1] + constants[0].cos()) - 
        variables[2].atanh() / constants[1] +
        constants[0]
    }

    // New graph.
    let graph = Graph::new();

    // Variables and constants.
    let variables = graph.vars(&[3.0, 2.0, 1.0]);
    let constants = [1., 2.];

    // Evaluate and differentiate the function.
    let result = function(&variables, &constants);
    let gradient = result.accumulate();

    // Print the graph length.
    println!("Graph length: {}", graph.len());
    println!("{:?}", gradient.wrt(&variables));

    // Print the graphviz output.
    // You can copy and paste this into your Graphviz viewer of choice.
    println!("{}", graphviz(&graph, &variables));