gauss-quad
| Crates.io | gauss-quad |
| lib.rs | gauss-quad |
| version | 0.2.1 |
| source | src |
| created_at | 2019-08-13 18:00:59.602754 |
| updated_at | 2024-08-24 16:35:47.542393 |
| description | Library for applying Gaussian quadrature to integrate a function |
| homepage | |
| repository | https://github.com/domidre/gauss-quad |
| max_upload_size | |
| id | 156518 |
| size | 297,396 |
Domi (DomiDre)
documentation
README
gauss-quad
The gauss-quad crate is a small library to calculate integrals of the type
$$\int_a^b f(x) w(x) \mathrm{d}x$$
using Gaussian quadrature.
To use the crate, the desired quadrature rule has to be included in the program, e.g. for a Gauss-Legendre rule
use gauss_quad::GaussLegendre;
The general call structure is to first initialize the n-point quadrature rule setting the degree n via
let quad = QUADRATURE_RULE::new(n)?;
where QUADRATURE_RULE can currently be set to calculate either:
| QUADRATURE_RULE | Integral |
|---|---|
| Midpoint | $$\int_a^b f(x) \mathrm{d}x$$ |
| Simpson | $$\int_a^b f(x) \mathrm{d}x$$ |
| GaussLegendre | $$\int_a^b f(x) \mathrm{d}x$$ |
| GaussJacobi | $$\int_a^b f(x)(1-x)^\alpha (1+x)^\beta \mathrm{d}x$$ |
| GaussLaguerre | $$\int_{0}^\infty f(x)x^\alpha e^{-x} \mathrm{d}x$$ |
| GaussHermite | $$\int_{-\infty}^\infty f(x) e^{-x^2} \mathrm{d}x$$ |
For the quadrature rules that take an additional parameter, such as Gauss-Laguerre and Gauss-Jacobi, the parameters have to be added to the initialization, e.g.
let quad = GaussLaguerre::new(n, alpha)?;
Then to calculate the integral of a function call
let integral = quad.integrate(a, b, f(x));
where a and b (both f64) are the integral bounds and the f(x) the integrand (Fn(f64) -> f64). For example to integrate a parabola from 0..1 one can use a lambda expression as integrand and call:
let integral = quad.integrate(0.0, 1.0, |x| x*x);
If the integral is improper, as in the case of Gauss-Laguerre and Gauss-Hermite integrals, no integral bounds should be passed and the call simplifies to
let integral = quad.integrate(f(x));
Rules can be nested into double and higher integrals:
let double_integral = quad.integrate(a, b, |x| quad.integrate(c(x), d(x), |y| f(x, y)));
If the computation time for the evaluation of the integrand is large (>> 100µs), the rayon feature can be used to parallelize the computation on multiple cores (for low computation any gain is overshadowed by the overhead from parallelization)
let slow_integral = quad.par_integrate(a, b, |x| f(x));