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

123 points · mtantaoui · 1 days ago

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.

43 comments

zackangelo · 1 days ago

> Does the function oscillate over the region of integration? If it does, then make sure that the step size is chosen to be smaller than the wave length of the function.

Nyquist limit, but for numerical integration?

Show replies

antononcube · 1 days ago

I think the project should be called "NIntegrate".

BTW, that is not a serious suggestion; it is just that Wolfram Language (aka Mathematica) has both `Integrate` and `NIntegrate` for symbolic and numeric integration, respectively.

Show replies

JanisErdmanis · 1 days ago

It looks a bit sloppy to hardcode so many constants in a single file: `src/gauss_quadrature/legendre.rs`. Isn't it possible to generate them with the help of rust macros in the same way Julia uses metaprogramming?

Show replies

wjholden · 1 days ago

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?

Show replies

· 1 days ago

[deleted]