Integrators

A Rust crate which provides a generic interface for numerical integrators. It includes implementations of this interface for integrators from the GSL and Cuba libraries.

GSL Wrappers

On Ubuntu-based systems, these wrappers should work with libgsl-dev. If you do not wish to use these wrappers, you can disable them by disabling the gsl feature. These algorithms can only integrate one dimensional integrals.

See the GSL docs here for a complete list of integration algorithms. Currently, only four wrappers are implemented:

1. QAG is a general, adaptive integration algorithm which should work for most well-behaved functions.
2. QNG is a similarly general, non-adaptive algorithm, which applies a series of fixed-order quadrature rules. This algorithm requires less overhead than QAG, and so may provide a performance boost for functions which are known to be easily integrable.
3. QAGS is an adaptive, general algorithm which can handle some kinds of singularities.
4. QAGP is the same algorithm as QAGS, but requires the user to provide a list of known locations of singularities.

I will add wrappers for more functions as I go.

Cuba Wrappers

Cuba is a suite of advanced multidimensional numerical integration algorithms, including both Monte Carlo and deterministic methods. See its documentation here for details and installation instructions. If you do not wish to use these wrappers, you can disable them by disabling the cuba feature.

Cuba has four algorithms: Vegas, Suave, Cuhre, and Divonne. Currently, wrappers are only implemented for the first three; the last has a number of extra arguments for finding singularities which I have not addressed yet.

Examples

This example will integrate a Gaussian over a given range with a GSL integrator. In reality, of course, you should probably find an erf() implementation to call instead, but this illustrates its use.

extern crate integrators;
use integrators::{Integrator, Real};

fn integrate_gaussian(from: f64, to: f64, sigma: f64, mean: f64) -> f64 {
    let normalization = (2f64 * ::std::f64::consts::PI).sqrt() * sigma;
    integrators::gsl::QAG::new(1000)
                      .with_range(from, to)
                      .integrate(|x: Real| {
                          (-((x - mean) / (2f64 * sigma)).powi(2)).exp()
                          / normalization
                          }, 1e-6, 1e-18)
                      .unwrap()
                      .value
}

fn main() {
    let ranges: &'static [(Real, Real)] = &[(-0.3, 0.0), (0.0, 1.5),
                                            (1.5, 3.2), (3.2, 5.9)];
    for &(a, b) in ranges.iter() {
        let integrated = integrate_gaussian(a, b, 1.0, 0.0);
        println!("range: {}, {}", a, b);
        println!("integrated: {}", integrated);
    }
}