perplex_num 0.1.0

use std::{iter, vec};

use perplex_num::Perplex;
use plotters::{
    prelude::*,
    style::full_palette::{LIGHTBLUE, LIGHTGREEN, PURPLE},
};
type PerplexMap = Box<dyn Fn(&Perplex<f64>) -> Perplex<f64>>;

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let root =
        BitMapBackend::new("./examples/perplex_functions.jpg", (600, 600)).into_drawing_area();
    root.fill(&WHITE)?;
    let (t_min, t_max, x_min, x_max) = (-1, 3, -2, 2);

    let mut chart = ChartBuilder::on(&root)
        .caption(
            "Perplex Functions in the Right sector",
            ("sans-serif", 30).into_font(),
        )
        .margin(15)
        .x_label_area_size(50)
        .y_label_area_size(50)
        .build_cartesian_2d(t_min as f64..t_max as f64, x_min as f64..x_max as f64)?;

    let font = ("sans-serif", 20).into_font();
    chart
        .configure_mesh()
        .max_light_lines(2)
        .label_style(font.clone())
        .x_labels(3)
        .y_labels(3)
        .x_label_formatter(&|t| format!("t={:.0}", t))
        .y_label_formatter(&|x| format!("x={:.0}", x))
        .draw()?;
    let down_alpha = 0.1;
    let z = Perplex { t: 1.0, x: 0.5 };
    let d = z.squared_distance();
    let mut hyperbola_ru = Vec::new();
    let mut hyperbola_rd = Vec::new();
    (0..=100_000)
        .map(|i| d + i as f64 * (t_max as f64 - d) / 100_000.0)
        .for_each(|t| {
            let x = (t * t - d).sqrt();
            if x.is_finite() {
                hyperbola_ru.push(Perplex::new(t, x));
                hyperbola_rd.push(Perplex::new(t, -x));
            }
        });

    let functions: Vec<(&str, PerplexMap, &RGBColor)> = vec![
        (
            "inv",
            Box::new(|z: &Perplex<f64>| {
                z.try_inverse()
                    .expect("z is invertible since d is non-zero!")
            }),
            &RED,
        ),
        ("sinus", Box::new(|z: &Perplex<f64>| z.sin()), &LIGHTBLUE),
        ("sinh", Box::new(|z: &Perplex<f64>| z.sinh()), &PURPLE),
        ("exp", Box::new(|z: &Perplex<f64>| z.exp()), &GREEN),
        (
            "ln",
            Box::new(|z: &Perplex<f64>| z.ln().expect("The natural logarithm of z exists!")),
            &LIGHTGREEN,
        ),
        (
            "sqrt",
            Box::new(|z: &Perplex<f64>| z.sqrt().expect("Sqrt of a z in the Right sector exists!")),
            &MAGENTA,
        ),
    ];
    // Highlight the Right sector
    chart.draw_series(LineSeries::new(
        (t_min..=t_max).map(|x| (x as f64, x as f64)),
        &BLACK,
    ))?;
    chart.draw_series(LineSeries::new(
        (t_min..t_max).map(|x| (x as f64, -x as f64)),
        &BLACK,
    ))?;
    chart.draw_series(iter::once(Text::new(
        "Right-Sector",
        (0.1, 0.1),
        font.clone(),
    )))?;
    let bound_filter = |z: &Perplex<f64>| {
        t_min as f64 <= z.t && z.t <= t_max as f64 && x_min as f64 <= z.x && z.x <= x_max as f64
    };
    let bound_filter_ref = |z: &&Perplex<f64>| bound_filter(z);
    let perplex_coords = |z: &Perplex<f64>| (z.t, z.x);
    // Draw the hyperbola in the right section
    chart.draw_series(LineSeries::new(
        hyperbola_ru
            .iter()
            .filter(bound_filter_ref)
            .map(perplex_coords),
        &BLUE,
    ))?;
    chart.draw_series(iter::once(Text::new(
        format!("t²-x²={:.2}", d),
        (2.0 * d, 0.1),
        font.clone().color(&BLUE),
    )))?;
    chart.draw_series(LineSeries::new(
        hyperbola_rd
            .iter()
            .filter(bound_filter_ref)
            .map(perplex_coords),
        &BLUE.mix(down_alpha),
    ))?;
    // Plot the results of the functions
    for (label, f, color) in functions.iter() {
        let result_ru: Vec<Perplex<f64>> =
            hyperbola_ru.iter().map(f).filter(bound_filter).collect();
        let label_pos = perplex_coords(&result_ru[result_ru.len() / 2]);
        chart.draw_series(LineSeries::new(
            result_ru.iter().map(perplex_coords),
            *color,
        ))?;
        let result_rd: Vec<Perplex<f64>> =
            hyperbola_rd.iter().map(f).filter(bound_filter).collect();
        chart.draw_series(LineSeries::new(
            result_rd.iter().map(perplex_coords),
            color.mix(down_alpha),
        ))?;
        chart.draw_series(iter::once(Text::new(
            label.to_string(),
            (label_pos.0 + 0.15, label_pos.1 + 0.1),
            font.clone().color(color),
        )))?;
    }
    chart
        .configure_series_labels()
        .position(SeriesLabelPosition::LowerMiddle)
        .label_font(font.clone())
        .draw()?;
    Ok(())
}