Add Rust version of Monte Carlo integration example

MonteCarloIntegration/Rust/Cargo.lock

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MonteCarloIntegration/Rust/Cargo.toml

+[package]
+name = "monte_carlo_integration"
+version = "0.1.0"
+authors = ["Thomas J. Kennedy <tkennedy@cs.odu.edu>"]
+edition = "2018"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+rand = "0.7"

MonteCarloIntegration/Rust/src/main.rs

+use rand::prelude::*;
+use std::env;
+
+struct Point(f64, f64);
+
+/// Generate a sequence of random x values and plug them into f(x).
+///
+/// Args:
+///     f: mathematical function
+///     lower_limit: 'a' the lower bound
+///     upper_bound: 'b' the upper bound
+///     n: number of points to generate
+///
+/// Yields:
+///     A sequence of points in the form (x, f(x))
+
+fn generate_random_points(f: fn(f64) -> f64,
+                          lower_limit: f64,
+                          upper_limit: f64,
+                          n: u64) -> Vec<Point> {
+
+    let d = rand::distributions::Uniform::new_inclusive(lower_limit, upper_limit);
+    let mut rng = thread_rng();
+
+    (0..n).map(|_| {
+        let x = rng.sample(d);
+        Point(x, f(x))
+    }).collect()
+}
+
+/// This main demonstrates the impact of the number of points on Monte Carlo
+/// integration
+fn main() {
+
+
+    let num_points = env::args().nth(1).unwrap().parse::<u64>(); // Unused in this version of main
+    let limit_a = env::args().nth(2).unwrap().parse::<f64>().unwrap();
+    let limit_b = env::args().nth(3).unwrap().parse::<f64>().unwrap();
+    let max_magnitude = env::args().nth(4).unwrap().parse::<u32>().unwrap();
+
+    let math_f = |x: f64| x.powf(2_f64);
+
+    println!("| {:^16} | {:^20} |", "# Points", "Est. f(x)");
+
+    let max_num_points: u64 = 2_u64.pow(max_magnitude);
+    let point_sequence = (generate_random_points(math_f, limit_a, limit_b, max_num_points));
+
+    for magnitude in 0..=max_magnitude {
+        let num_points = 2_u64.pow(magnitude);
+
+        let sum_of_f_of_x_values: f64 = point_sequence.iter()
+            .map(|point| point.1)
+            .take((num_points as usize))
+            .sum();
+
+        let integral_result = (limit_b - limit_a) /
+                              (num_points as f64) *
+                              sum_of_f_of_x_values;
+
+        println!("| {:>16} | {:^20.8} |", num_points, integral_result);
+    }
+}