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::init(n);

where QUADRATURE_RULE can currently be set to calculate either:

| QUADRATURERULE | Integral | | --------------- | ---------------------------------------------------------- | | Midpoint | $$\inta^b f(x) \mathrm{d}x$$ | | Simpson | $$\inta^b f(x) \mathrm{d}x$$ | | GaussLegendre | $$\inta^b f(x) \mathrm{d}x$$ | | GaussJacobi | $$\inta^b f(x)(1-x)^\alpha (1+x)^\beta \mathrm{d}x$$ | | GaussLaguerre | $$\int{-\infty}^\infty f(x)x^\alpha e^{-x} \mathrm{d}x$$ | | 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::init(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));