math

Numerical Integration

Here we integrate the Gaussian density, which integrates to 1:

\[ \int_{\mathbb{R}} \frac{1}{\sqrt{2 \pi}} e^{\left( -\frac{x^2}{2} \right)} dx = 1
\]

use std::{f64::consts::PI, time::Instant};
use RustQuant::math::*;

fn main() {
    // Define a function to integrate:
    // Standard Normal Distribution PDF
    fn f(x: f64) -> f64 {
        (2. * PI).sqrt().recip() * (-0.5 * x.powi(2)).exp()
    }

    // Integrate from -5 to 5.
    // This is: +/- 5 standard deviations from the mean.
    let integral = integrate(f, -5., 5.);

    // Standard Normal Distribution PDF has integral of 1.
    println!("Integral = {}", integral); // ~= 1.0
}