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a/src/main.rs b/src/main.rs new file mode 100644 index 0000000..0e8ea5d --- /dev/null +++ b/src/main.rs @@ -0,0 +1,161 @@ +use std::{ops::Range, iter}; + +use plotters::prelude::*; +use rand::Rng; + +struct Integral { + bounds: Range, + function: Box T>, +} + +struct Point { + x: f64, + y: f64, +} + +fn rand_points( + n: u64, + x_range: &Range, + y_range: &Range, +) -> Vec { + (0..n) + .map(|_| Point { + x: rand::thread_rng().gen_range(x_range.clone()), + y: rand::thread_rng().gen_range(y_range.clone()), + }) + .collect() +} + +fn points_under_graph( + points: &Vec, + function: &impl Fn(f64) -> f64, +) -> u64 { + points.iter() + .map(|point| point.y <= function(point.x)) + .map(|bool| if bool { 1 } else { 0 }) + .sum() +} + +fn get_sup( + integral: &Integral +) -> f64 { + let multiplier = 1_000f64; + let b = &integral.bounds; + let f = &integral.function; + + let mut sup = f(b.start); + + for i in + (((b.start * multiplier) as i64)..((b.end * multiplier) as i64)) + .map(|x| (x as f64) / multiplier) + { + if f(i) > sup { + sup = f(i); + } + } + + sup +} + +fn monte_carlo( + amount_of_points: u64, + integral: &Integral, +) -> f64 { + let m = get_sup(integral); + + let points = rand_points(amount_of_points, &integral.bounds, &(0.0..m)); + + let c = points_under_graph(&points, &integral.function); + + let average = (c as f64 / amount_of_points as f64) * ((integral.bounds.end - integral.bounds.start) * m); + + average +} + +fn graph_function( + output_path: &str, + iterations: u64, + integral: &Integral, + integral_value: f64, +) { + let root_drawing_area = BitMapBackend::new(output_path, (1920, 1080)) + .into_drawing_area(); + + root_drawing_area.fill(&WHITE).unwrap(); + + let quarter = integral_value / 4.0; + + let mut chart = ChartBuilder::on(&root_drawing_area) + .x_label_area_size(20) + .y_label_area_size(60) + .build_cartesian_2d( + 0f64..5050f64, + (integral_value - quarter)..integral_value + quarter, + ) + .unwrap(); + + chart.configure_mesh() + .x_labels(10) + .y_labels(10) + .draw() + .unwrap(); + + for n in (50..=5000).step_by(50) { + let mut results = vec![]; + + for _ in 0..iterations { + results.push(monte_carlo(n, &integral)); + } + + let average = results.iter().sum::() / (iterations as f64); + + chart.draw_series(PointSeries::<_, _, Circle<_, _>, _>::new( + results.iter().map(|x| (n as f64, *x)), + 2, + BLUE.filled(), + )).unwrap(); + + chart.draw_series(PointSeries::<_, _, Circle<_, _>, _>::new( + iter::once(average).map(|x| (n as f64, x)), + 5, + RED.filled(), + )).unwrap(); + + chart.draw_series(LineSeries::new( + vec![(0.0, integral_value), (5050.0, integral_value)], + GREEN.stroke_width(3), + )).unwrap(); + } +} + +fn main() { + let i0 = Integral:: { + bounds: (1.0..3.0), + function: Box::new(|x| x.powi(3)), + }; + graph_function("0.png", 50, &i0, 20.0); + + let i1 = Integral:: { + bounds: (0.0..8.0), + function: Box::new(|x| x.powf(1.0 / 3.0)), + }; + graph_function("1.png", 50, &i1, 12.0); + + let i2 = Integral:: { + bounds: (0.0..std::f64::consts::PI), + function: Box::new(|x| x.sin()), + }; + graph_function("2.png", 50, &i2, 2.0); + + let i3 = Integral:: { + bounds: (0.0..1.0), + function: Box::new(|x| 4.0 * x * (1.0 - x).powi(3)), + }; + graph_function("3.png", 50, &i3, 0.2); + + let i_pi = Integral:: { + bounds: (0.0..1.0), + function: Box::new(|x| 1.0 / (1.0 - (x * x)).sqrt()), + }; + graph_function("pi.png", 50, &i_pi, std::f64::consts::PI / 2.0); +}