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Show HN: Rust library for numerical integration of real-valued functions

(github.com)
123 points mtantaoui | 1 comments | 19 Nov 24 12:41 UTC | HN request time: 0.209s | source

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.
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wjholden ◴[19 Nov 24 14:49 UTC] No.42184001[source]▶
I was always amazed that R can do:

  > integrate(dnorm, -Inf, +Inf)
  1 with absolute error < 9.4e-05
Can we do the same in this library?
replies(4): >>42184765 #>>42184870 #>>42185462 #>>42185618 #
1. legobmw99 ◴[19 Nov 24 15:57 UTC] No.42184870[source]▶
It seems like it is lacking the functionality R's integrate has for handling infinite boundaries, but I suppose you could implement that yourself on the outside.

For what it's worth,

    use integrate::adaptive_quadrature::simpson::adaptive_simpson_method;
    use statrs::distribution::{Continuous, Normal};

    fn dnorm(x: f64) -> f64 {
        Normal::new(0.0, 1.0).unwrap().pdf(x)
    }
    
    fn main() {
        let result = adaptive_simpson_method(dnorm, -100.0, 100.0, 1e-2, 1e-8);
        println!("Result: {:?}", result);
    }
prints Result: Ok(1.000000000053865)

It does seem to be a usability hazard that the function being integrated is defined as a fn, rather than a Fn, as you can't pass closures that capture variables, requiring the weird dnorm definition