yagi 0.1.3

Batteries-included DSP library
Documentation 
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use crate::error::{Error, Result};
use crate::math::bessel::lnbesselif;
use crate::math::marcumq1f;
use crate::random::crandnf;
use num_complex::Complex;

pub fn randricekf(k: f32, omega: f32) -> Result<f32> {
    // validate input
    if k < 0.0 {
        return Err(Error::Config("k must be non-negative".to_string()));
    } else if omega <= 0.0 {
        return Err(Error::Config("omega must be greater than zero".to_string()));
    }

    let s = ((omega * k) / (k + 1.0)).sqrt();
    let sig = (0.5 * omega / (k + 1.0)).sqrt();

    let x = crandnf();
    let y = Complex::new(x.re * sig + s, x.im * sig);

    Ok(y.norm())
}

/// Rice-K random number probability distribution function
///  f(x) = (x/sigma^2) exp{ -(x^2+s^2)/(2sigma^2) } I0( x s / sigma^2 )
/// where
///  s     = sqrt( omega*K/(K+1) )
///  sigma = sqrt(0.5 omega/(K+1))
/// and
///  K     = shape parameter
///  omega = spread parameter
///  I0    = modified Bessel function of the first kind
///  x >= 0
pub fn randricekf_pdf(x: f32, k: f32, omega: f32) -> Result<f32> {
    // validate input
    if k < 0.0 {
        return Err(Error::Config("k must be non-negative".to_string()));
    } else if omega <= 0.0 {
        return Err(Error::Config("omega must be greater than zero".to_string()));
    }

    if x < 0.0 {
        return Ok(0.0);
    }

    let s = ((omega * k) / (k + 1.0)).sqrt();
    let sig = (0.5 * omega / (k + 1.0)).sqrt();

    let t = x * x + s * s;
    let sig2 = sig * sig;

    // check high tail condition
    if (x * s / sig2) > 80.0 {
        return Ok(0.0);
    }

    let t0 = x.ln() - sig2.ln();
    let t1 = -t / (2.0 * sig2);
    let t2 = lnbesselif(0.0, x * s / sig2);

    Ok((t0 + t1 + t2).exp())
    // Ok((x / sig2) * (-t / (2.0 * sig2)).exp() * lnbesselif(0.0, x * s / sig2))
}

/// Rice-K random number cumulative distribution function
pub fn randricekf_cdf(x: f32, k: f32, omega: f32) -> Result<f32> {
    // validate input
    if k < 0.0 {
        return Err(Error::Config("k must be non-negative".to_string()));
    } else if omega <= 0.0 {
        return Err(Error::Config("omega must be greater than zero".to_string()));
    }

    if x <= 0.0 {
        return Ok(0.0);
    }

    let s = ((omega * k) / (k + 1.0)).sqrt();
    let sig = (0.5 * omega / (k + 1.0)).sqrt();

    // test arguments of Q1 function
    let alpha = s / sig;
    let beta = x / sig;

    if (alpha / beta) > 3.0 {
        return Ok(0.0);
    }
    if (beta / alpha) > 3.0 {
        return Ok(1.0);
    }

    let f = 1.0 - marcumq1f(alpha, beta);

    // check for precision error
    if f < 0.0 {
        Ok(0.0)
    } else if f > 1.0 {
        Ok(1.0)
    } else {
        Ok(f)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use test_macro::autotest_annotate;
    use approx::assert_relative_eq;

    #[test]
    #[autotest_annotate(autotest_randricekf)]
    fn test_randricekf() {
        const NUM_TRIALS: usize = 100_000;
        const TOL: f32 = 0.1;

        let k: f32 = 2.0;
        let omega: f32 = 1.0;

        let mut m1: f32 = 0.0;
        let mut m2: f32 = 0.0;

        for _ in 0..NUM_TRIALS {
            let x = randricekf(k, omega).unwrap();
            m1 += x;
            m2 += x * x;
        }

        m1 /= NUM_TRIALS as f32;
        m2 /= NUM_TRIALS as f32;

        // compute expected moments (closed-form solution)
        let m1_exp = 0.92749f32;
        let m2_exp = omega;

        println!("m1 = {:.6} (expected {:.6})", m1, m1_exp);
        println!("m2 = {:.6} (expected {:.6})", m2, m2_exp);

        assert_relative_eq!(m1, m1_exp, epsilon = TOL);
        assert_relative_eq!(m2, m2_exp, epsilon = TOL);
    }
}