# gauss-quad 0.1.4

Library for applying Gaussian quadrature to integrate a function
gauss-quad-0.1.4 is not a library.

# 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));
``````