LaTeX labels¶

use ironlab::prelude::*;

pub const TITLE: &str = "LaTeX labels";
pub const DESCRIPTION: &str = "The frequency response of a driven, damped oscillator, whose title, axis labels and \
     legend use LaTeX fractions, square roots, Greek letters, subscripts and units.";

pub fn figure() -> Figure {
    let natural_frequency = 10.0; // ω₀ in rad/s
    let omega = linspace(0.0, 25.0, 251);

    let mut fig = Figure::new()
        .size_mm(160.0, 100.0)
        .title(r"Resonance of a damped oscillator with $\omega_0 = 10\,\mathrm{rad\,s^{-1}}$");
    let mut ax = fig.axes(0, 0);
    // One curve per damping ratio ζ: the lighter the damping, the higher and sharper the resonance peak at ω = ω₀.
    for zeta in [0.1, 0.2, 0.5, 1.0] {
        let amplification: Vec<f64> = omega
            .iter()
            .map(|w| {
                let r = w / natural_frequency; // the frequency ratio ω / ω₀
                1.0 / ((1.0 - r * r).powi(2) + (2.0 * zeta * r).powi(2)).sqrt()
            })
            .collect();
        ax.plot(&omega, &amplification)
            .display_name(format!(r"$\zeta = {zeta}$"));
    }
    ax.title(r"$\frac{|X|}{X_\mathrm{st}} = \frac{1}{\sqrt{(1 - r^2)^2 + (2 \zeta r)^2}}$, where $r = \omega / \omega_0$")
        .xlabel(r"Angular frequency $\omega$ ($\mathrm{rad\,s^{-1}}$)")
        .ylabel(r"Amplification $|X| / X_\mathrm{st}$")
        .ylim(0.0, 6.0)
        .grid(true)
        .legend(LegendLocation::NorthEast);
    fig
}