use mathru::{
    algebra::linear::vector::Vector,
    analysis::differential_equation::ordinary::{
        problem::Euler, solver::implicit::BDF, ImplicitInitialValueProblemBuilder,
    },
    vector,
};
use plotters::prelude::*;

fn main() {
    let x_start = 0.0f64;
    let x_end = 20.0f64;

    // Create an ODE instance
    let ode = Euler::default();

    let problem = ImplicitInitialValueProblemBuilder::new(&ode, 0.0f64, vector![1.0; 
                                                                                0.0; 
                                                                                0.9])
        .t_end(x_end)
        .build();

    let step_size: f64 = 0.0001;
    let solver: BDF<f64> = BDF::new(6, step_size);

    let (x, y): (Vec<f64>, Vec<Vector<f64>>) = solver.solve(&problem).unwrap();

    //Create chart
    let mut graph_x1: Vec<(f64, f64)> = Vec::with_capacity(x.len());
    let mut graph_x2: Vec<(f64, f64)> = Vec::with_capacity(x.len());
    let mut graph_x3: Vec<(f64, f64)> = Vec::with_capacity(x.len());

    for i in 0..y.len() {
        let x_i = x[i];

        graph_x1.push((x_i, y[i][0]));
        graph_x2.push((x_i, y[i][1]));
        graph_x3.push((x_i, y[i][2]));
    }

    let root_area = BitMapBackend::new("./figures/ode_bdf.png", (1200, 800)).into_drawing_area();
    root_area.fill(&WHITE).unwrap();

    let mut ctx = ChartBuilder::on(&root_area)
        .margin(20)
        .set_label_area_size(LabelAreaPosition::Left, 40)
        .set_label_area_size(LabelAreaPosition::Bottom, 40)
        .caption("ODE solved with BDF", ("Arial", 40))
        .build_cartesian_2d(x_start..x_end, -1.0f64..1.5f64)
        .unwrap();

    ctx.configure_mesh()
        .x_desc("Time t")
        .axis_desc_style(("sans-serif", 25).into_font())
        .draw()
        .unwrap();

    ctx.draw_series(LineSeries::new(graph_x1, &BLACK)).unwrap();

    ctx.draw_series(LineSeries::new(graph_x2, &RED)).unwrap();

    ctx.draw_series(LineSeries::new(graph_x3, &BLUE)).unwrap();
}