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:

| 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 | $\int_{-\infty}^\infty f(x)x^\alpha e^{-x} \mathrm{d}x$ | | 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));