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jacekpoz 2023-11-05 13:45:10 +01:00
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8
Cargo.toml Normal file
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@ -0,0 +1,8 @@
[package]
name = "zd1"
version = "0.1.0"
edition = "2021"
[dependencies]
plotters = "0.3.5"
rand = "0.8.5"

161
src/main.rs Normal file
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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);
}