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

(github.com)
126 points mtantaoui | 2 comments | 19 Nov 24 12:41 UTC | HN request time: 0.447s | 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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JanisErdmanis ◴[19 Nov 24 14:42 UTC] No.42183942[source]▶
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?
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ok123456 ◴[19 Nov 24 15:18 UTC] No.42184353[source]▶
Gaussian quadrature points are typically solved numerically. There's a good chance these ultimately came from a table.

Additionally, compile time floating-point evaluation is limited. When I looked around recently, I didn't see a rust equivalent of gcem; any kind of transcendental function evaluation (which finding Gaussian quadrature points absolutely would require) would not allow compile-time evaluation.

replies(2): >>42185264 #>>42186782 #
AlotOfReading ◴[19 Nov 24 16:29 UTC] No.42185264[source]▶
Support for float const fns was merged just a couple months ago and hasn't been officially announced yet.
replies(2): >>42185347 #>>42185528 #
1. ok123456 ◴[19 Nov 24 16:37 UTC] No.42185347[source]▶
IIRC, that only supports elementary arithmetic operations. Useful but not general.
replies(1): >>42185534 #
2. AlotOfReading ◴[19 Nov 24 16:54 UTC] No.42185534[source]▶
It's relatively straightforward to build transcendental functions out of the basic operations and the stdlib support will eventually get there, but rust's float story is still a work in progress. They're trying to do things more properly and document semantics better than C and C++ have.