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 quadrature = QUADRATURE_RULE::init(n);

where QUADRATURE_RULE can currently be either:

GaussLegendre GaussHermite

Then to calculate the integral of a function can be calculated by calling

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 Hermite integrals

$\int_{-\infty}^\infty f(x) e^{-x^2} \mathrm{d}x$

no integral bounds should be passed and the call simplifies to let integral = quad.integrate(f(x));