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literal 0 HcmV?d00001 diff --git a/src/3hist.py b/src/3hist.py new file mode 100755 index 0000000..ca2bbda --- /dev/null +++ b/src/3hist.py @@ -0,0 +1,17 @@ +#!/usr/bin/env python + +import json +import matplotlib.pyplot as plt + +with open(f"./results/3", "r") as file: + data = json.load(file) + + for key, values in data.items(): + n, bins, _ = plt.hist(values, bins = 20, range = [0, 1], density = True) + plt.title(f"n = {key}") + plt.xlabel("Wartość") + plt.ylabel("Gęstość") + bin_centers = (bins[1:] + bins[:-1]) * 0.5 + plt.plot(bin_centers, n, color = "green", linestyle = "-", linewidth = 2) + + plt.show() diff --git a/src/main.rs b/src/main.rs new file mode 100644 index 0000000..fc28ce4 --- /dev/null +++ b/src/main.rs @@ -0,0 +1,225 @@ +use std::{collections::HashMap, path::PathBuf}; +use std::fs; + +use plotters::{backend::BitMapBackend, chart::ChartBuilder, drawing::IntoDrawingArea, element::Circle, series::PointSeries, style::{Color, BLUE, WHITE}}; +use probability::prelude::*; +use rand::{thread_rng, Rng}; +use rand_mt::Mt64; +use lcg_rand::rand::LCG; + +fn zad1(path: &PathBuf) { + let p = 0.5; + + let mut output = String::new(); + let top_row = &format!("| {:<5} | {:<18} | {:<8} | {:<11} | {:<11} | {:<18} | {:<18} |\n", + "n", "a markov", "b markov", "a chebyshev", "b chebyshev", "a exact value", "b exact value" + ); + + let mut border = "=".repeat(top_row.len() - 1); + border.push('\n'); + + output.push_str(&border); + output.push_str(&top_row); + for n in [100., 1000., 10000.] { + let dist = Binomial::new(n as usize, p); + + // E(X) + let ex = n * p; + // var(X) + let varx = n * p * (1. - p); + // 6/5 * E(X) + let a = 1.2 * ex; + + let a_exact = 1.0 - ((0..(a as usize)) + .map(|k| dist.mass(k)) + .sum::()); + + // P(X >= 6/5*E(X)) + let a_markov = ex / a; + + // P(|X-E(X)| >= 6/5*E(X) - E(X)) + let a = 0.2 * ex; + let a_chebyshev = varx / (a*a); + + // 1/10 * E(X) + let b: f64 = 0.1 * ex; + + // P(|X - E(X)| >= 1/10*E(X)) + // P(X - E(X) >= 1/10*E(X) ∨ P(X - E(X) <= -1/10*E(X)) + // P(X >= 11/10*E(X) ∨ P(X <= 9/10*E(X)) + // P(X <= 9/10*E(X) ∨ P(X >= 11/10*E(X)) + // P(X <= 9/10*E(X)) + P(X >= 11/10*E(X)) + // oba są sobie równe, bo bin ma peak w E(X) + // czyli możemy + // 2 * P(X <= 9/10*E(X)) + let b_exact = dist.distribution(0.9 * ex) * 2.0; + + // P(|X-E(X)| >= 1/10*E(X)) + let b_chebyshev = varx / (b * b); + + let b_markov = (ex / (1.1 * ex)) * 2.0; + + output.push_str( + format!("| {:<5} | {:<18} | {:<8} | {:<11} | {:<11} | {:<18} | {:<18} |\n", + n, a_markov, b_markov, a_chebyshev, b_chebyshev, a_exact, b_exact + ).as_str() + ); + } + + output.push_str(&border); + + let _ = fs::write(path, output); +} + +fn zad2(path: &PathBuf) { + let k = 10000000; + let mut sums = vec![0; k]; + let mut rng = thread_rng(); + + for n in [5, 10, 15, 20, 25, 30, 100] { + let intervals = ((-n + 1)..(n + 1)) + .map(|n| (-n, -n + 1)) + .collect::>(); + + for i in 0..k { + sums[i] = (0..n) + .map(|_| ((rng.gen_range(0..=1) as f64 - 0.5) * 2.0) as i32) + .sum(); + } + + let counts = intervals.iter() + .map(|interval| + sums.iter() + .map(|sum| (*sum <= interval.1) as i32) + .sum::() + ) + .collect::>(); + + let xs = intervals.iter() + .map(|i| i.1 as f64) + .collect::>(); + + // SAFETY: we can assume it's not empty + let x_max = *xs.iter().max_by(|a, b| a.total_cmp(b)).unwrap(); + + // SAFETY: we can assume it's not empty + let max_count = *counts.iter().max().unwrap() as f64; + + let ys = counts.iter() + .map(|count| *count as f64 / max_count) + .collect::>(); + + // SAFETY: we can assume it's not empty + let y_max = *ys.iter().max_by(|a, b| a.total_cmp(b)).unwrap(); + + let mut n_path = path.clone(); + n_path.push(format!("{n}.png")); + + let root_drawing_area = BitMapBackend::new(&n_path, (1920, 1080)) + .into_drawing_area(); + + root_drawing_area.fill(&WHITE).unwrap(); + + let mut chart = ChartBuilder::on(&root_drawing_area) + .x_label_area_size(20) + .y_label_area_size(60) + .build_cartesian_2d( + -x_max..x_max, + 0f64..y_max, + ) + .unwrap(); + + chart.configure_mesh() + .x_labels(10) + .y_labels(10) + .draw() + .unwrap(); + + chart.draw_series(PointSeries::<_, _, Circle<_, _>, _>::new( + xs.iter() + .enumerate() + .map(|(i, x)| (*x as f64, ys[i] as f64)), + 2, + BLUE.filled(), + )).unwrap(); + + sums.clear(); + sums = vec![0; k]; + } +} + +fn random_walk(n: i32) -> i32 { + + let mut rng = thread_rng(); + + let mut position = 0; + let mut last_position = position; + let mut ret = 0; + + for _ in 0..n { + let direction = ((rng.gen_range(0..=1) as f64 - 0.5) * 2.0) as i32; + position += direction; + + if position > 0 || last_position > 0 { + ret += 1; + } + + last_position = position; + } + + ret +} + +fn zad3(path: &PathBuf) { + let k = 5000; + + let mut results = HashMap::new(); + + for n in [100, 1000, 10000] { + let mut pn = vec![0.0; k]; + + for i in 0..k { + pn[i] = random_walk(n) as f64 / n as f64; + } + results.insert(n, pn); + } + + let _ = fs::write(path, serde_json::to_string(&results).unwrap()); +} + +fn zad4(path: &PathBuf) { + let n = 10000000; + + let mut lcg_path = path.clone(); + lcg_path.push("lcg"); + + let mut output = String::new(); + + let mut lcg = LCG::from_seed(2137u64); + + for _ in 0..n { + output.push_str((lcg.next() % 2).to_string().as_str()); + } + + let _ = fs::write(lcg_path, output.clone()); + + output.clear(); + + let mut mt_path = path.clone(); + mt_path.push("mt"); + + let mut mt = Mt64::new(7312u64); + + for _ in 0..n { + output.push_str((mt.gen::() % 2).to_string().as_str()); + } + + let _ = fs::write(mt_path, output); +} + +fn main() { + zad1(&PathBuf::from("results/1")); + zad2(&PathBuf::from("results/2")); + zad3(&PathBuf::from("results/3")); + zad4(&PathBuf::from("results/4")); +} diff --git a/src/normal.py b/src/normal.py new file mode 100755 index 0000000..a6bdbd0 --- /dev/null +++ b/src/normal.py @@ -0,0 +1,16 @@ +#!/usr/bin/env python + +import matplotlib.pyplot as plt +import numpy as np +import scipy.stats as stats +import math + +mu = 0 + +for n in [5, 10, 15, 20, 25, 30, 100]: + variance = n + sigma = math.sqrt(variance) + x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100) + plt.title(f"n = {n}") + plt.plot(x, stats.norm.cdf(x, mu, sigma)) + plt.show()