use crate::{model::*, opti::*, utils::*};

use nalgebra::{base::*, ComplexField};

pub trait Solver<T, S: Settings, M: Model<T, S, D>, const D: usize> {
	fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D>;
}

#[derive(Clone)]
pub struct ExplicitEulerSolver<T: Copy + ComplexField<RealField = T>> {
	pub dt: T,
}

impl<T: Copy + ComplexField<RealField = T>, S: Settings, M: Model<T, S, D>, const D: usize>
	Solver<T, S, M, D> for ExplicitEulerSolver<T>
{
	fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D> {
		model.f(x) * self.dt + x
	}
}

#[derive(Clone)]
pub struct ImplicitEulerSolver<T: Clone + ComplexField<RealField = T>> {
	pub dt: T,
	pub tol: T,
	pub niters: usize,
}

impl<
		T: Copy + ComplexField<RealField = T> + PartialOrd,
		S: Settings,
		M: Model<T, S, D>,
		const D: usize,
	> Solver<T, S, M, D> for ImplicitEulerSolver<T>
where
	Const<D>: ToTypenum + DimMin<Const<D>, Output = Const<D>>,
{
	fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D> {
		newton(model, x, self.dt, self.tol, self.niters)
	}
}