commit 80b72a2386726dab9bd6f2aa8bde40f4e3fab6e1
Author: jacekpoz <jacekpoz@cock.li>
Date:   Sun Nov 5 13:45:10 2023 +0100

    init

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diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..8ef97b2
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,8 @@
+[package]
+name = "zd1"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]
+plotters = "0.3.5"
+rand = "0.8.5"
diff --git 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<T> {
+    bounds: Range<T>,
+    function: Box<dyn Fn(T) -> T>,
+}
+
+struct Point {
+    x: f64,
+    y: f64,
+}
+
+fn rand_points(
+    n: u64,
+    x_range: &Range<f64>,
+    y_range: &Range<f64>,
+) -> Vec<Point> {
+    (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<Point>,
+    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>
+) -> 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>,
+) -> 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<f64>,
+    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::<f64>() / (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::<f64> {
+        bounds: (1.0..3.0),
+        function: Box::new(|x| x.powi(3)),
+    };
+    graph_function("0.png", 50, &i0, 20.0);
+
+    let i1 = Integral::<f64> {
+        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::<f64> {
+        bounds: (0.0..std::f64::consts::PI),
+        function: Box::new(|x| x.sin()),
+    };
+    graph_function("2.png", 50, &i2, 2.0);
+
+    let i3 = Integral::<f64> {
+        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::<f64> {
+        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);
+}