How to pass data to a solver ?

[avhz]

If I want to minimise a squared error (or similar) between a function and some data, how do I pass the data to the cost function ?

[stefan-k]

You can do this via your problem definition:

struct MyProblem {
    data: MyData,
}

impl CostFunction for MyProblem {
    type Param = Vec<f64>;
    type Output = f64;

    fn cost(&self, p: &Self::Param) -> Result<Self::Output, Error> {
        Ok(my_cost_function(p, self.data))
    }
}

[avhz]

Is it possible to have a model defined by a struct that contains the parameters, and then solve for those parameters against some exogenous data ?

Something like:

struct MyModel {
    a: f64,
    b: f64,
}

impl MyModel {
    fn my_line(&self, x: f64) -> f64 {
        self.a * x + self.b
    }

    fn my_cost(&self, x: f64, y: f64) -> f64 {
        (self.my_line(x) - y).powi(2)
    }
}

const SOME_X_DATA: [f64; 9] = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0];
const SOME_Y_DATA: [f64; 9] = [0.0, 1.0, 2.0, 4.0, 7.0, 9.0, 5.0, 3.0, 7.0];

I would expect a result of: Y ~= 0.75 * X + 0.4722

So, I want to get:

MyModel { 
    a: 0.75, 
    b: 0.4722 
}

Thanks for any advice you can give ! Cheers!

[stefan-k]

Do you mean such that type Param = MyModel in the CostFunction trait impl? Yes, this is possible, but it will require you to implement several math related types on MyModel (which of those traits depends on the solver you want to use). I would suggest modelling your problem based on Vec<f64> or the equivalent ndarray/nalgebra types and then implement the conversion from Vec<f64> to MyModel:

struct MyProblem {}

impl CostFunction for MyProblem {
    type Param = Vec<f64>;
    type Output = f64;

    fn cost(&self, p: &Self::Param) -> Result<Self::Output, Error> {
        let cost = (0..9).iter().map(|i| (p[0] * SOME_X_DATA[i] + p[1] - SOME_Y_DATA[i]).powi(2)).sum();
        Ok(cost)
    }
}

// Then run optimization, obtain final solution `res`
// ...

let final_params = MyModel { a: res[0], b: res[1] }; // Of course  you can also implement `From<Vec<f64>>` for `MyModel` 

Then a = res[0] and b = res[1] where res is the final solution.

[avhz]

This is super helpful, thank you !

[avhz]

Hi, taking a look at this again after a while.

If the additional data/arguments are not const as I gave previously, how can they be passed to the solver?

e.g. scipy.optimize.root(fun, x0, args=(), ...) has the args argument for this purpose. How can I achieve this if the only input to cost is the parameter vector ?

[stefan-k]

Does the data change during an optimization run?

[avhz]

No, just extra arguments to the function.

[stefan-k]

You can add those arguments as fields to your problem struct and set them when creating an instance of your problem. Then you have them available in your cost function.