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123 points mtantaoui | 1 comments | 19 Nov 24 12:41 UTC | HN request time: 0.212s | 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]▶

>>42182784 (OP) #

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. mtantaoui ◴[19 Nov 24 17:01 UTC] No.42185618[source]▶

>>42184001 #

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.

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