mtantaoui

Thanks! That’s awesome to hear—I’d love to see how your Raku numerical integration project turns out!

You can email me if you want to, I'll be happy to help.

for ]-inf, inf[ integrals, you can use Gauss Hermite method, just keep in mind to multiply your function with exp(x^2).

    use integrate::{
        gauss_quadrature::hermite::gauss_hermite_rule,
    };
    use statrs::distribution::{Continuous, Normal};

    fn dnorm(x: f64) -> f64 {
        Normal::new(0.0, 1.0).unwrap().pdf(x)* x.powi(2).exp()
    }

    fn main() {
        let n: usize = 170;
        let result = gauss_hermite_rule(dnorm, n);
        println!("Result: {:?}", result);
    }

I got Result: 1.0000000183827922.

this was mainly to use an Iteration free method in this paper: https://www.cfm.brown.edu/faculty/gk/APMA2560/Handouts/GL_qu...

this method is much faster and simpler.

Integrate is a fast, small, lightweight Rust library for performing numerical integration of real-valued functions. It is designed to integrate functions, providing a simple and efficient way to approximate definite integrals using various numerical methods.

Integrate supports a variety of numerical integration techniques: - Newton-Cotes methods:

  - Rectangle Rule.
  - Trapezoidal Rule.
  - Simpson's Rule.
  - Newton's 3/8 Rule.

- Gauss quadrature methods:

  - Gauss-Legendre.
  - Gauss-Laguerre.
  - Gauss-Hermite.
  - Gauss-Chebyshev First Kind.
  - Gauss-Chebyshev Second Kind.

- Adaptive Methods:

  - Adaptive Simpson's method

- Romberg’s method.