# gauss-quad

The `gauss-quad`

crate is a small library to calculate integrals of the type

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 | |

Simpson | |

GaussLegendre | |

GaussJacobi | |

GaussLaguerre | |

GaussHermite |

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));
```