rmpfit

Very simple pure Rust implementation of the CMPFIT library: the Levenberg-Marquardt technique to solve the least-squares problem.

The code is mainly copied directly from CMPFIT almost without changing. The original CMPFIT tests (Linear (free parameters), Quad (free and fixed parameters), and Gaussian (free and fixed parameters) function) are reproduced and passed.

Just a few obvoius Rust-specific optimizations are done:

• Removing goto (fuf).
• Standart Rust Result as result.
• A few loops are zipped to help the compiler optimize the code (no performance tests are done anyway).
• Using trait MPFitter to call the user code.
• Using bool type if possible.

Advantages

• Pure Rust.
• No external dependencies (assert_approx_eq just for testing).
• Internal Jacobian calculations.

Disadvantages

• Sided, analitical or user provided derivates are not implemented.

Usage Example

A user should implement trait MPFitter for its struct:

use rmpfit::{MPFitter, MPResult, mpfit};

struct Linear {
    x: Vec<f64>,
    y: Vec<f64>,
    ye: Vec<f64>,
}

impl MPFitter for Linear {
    fn eval(&self, params: &[f64], deviates: &mut [f64]) -> MPResult<()> {
        for (((d, x), y), ye) in deviates
            .iter_mut()
            .zip(self.x.iter())
            .zip(self.y.iter())
            .zip(self.ye.iter())
        {
            let f = params[0] + params[1] * *x;
            *d = (*y - f) / *ye;
        }
        Ok(())
    }
    
    fn number_of_points(&self) -> usize {
        self.x.len()
    }
}

fn main() {
    let l = Linear {
        x: vec![
            -1.7237128E+00,
            1.8712276E+00,
            -9.6608055E-01,
            -2.8394297E-01,
            1.3416969E+00,
            1.3757038E+00,
            -1.3703436E+00,
            4.2581975E-02,
            -1.4970151E-01,
            8.2065094E-01,
        ],
        y: vec![
            1.9000429E-01,
            6.5807428E+00,
            1.4582725E+00,
            2.7270851E+00,
            5.5969253E+00,
            5.6249280E+00,
            0.787615,
            3.2599759E+00,
            2.9771762E+00,
            4.5936475E+00,
        ],
        ye: vec![0.07; 10],
    };
    // initializing input parameters
    let mut init = [1., 1.];
    let res = l.mpfit(&mut init, None, &Default::default()).unwrap();
    // actual 3.2
    assert_approx_eq!(init[0], 3.20996572);
    assert_approx_eq!(status.xerror[0], 0.02221018);
    // actual 1.78
    assert_approx_eq!(init[1], 1.77095420);
    assert_approx_eq!(status.xerror[1], 0.01893756);
}

then init will contain the refined parameters of the fitting function. If user function fails to calculate residuals, it should return MPError::Eval.