r2rs-nmath 0.1.1

Statistics programming for Rust based on R's nmath package
Documentation 
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// Translation of nmath's qwilcox
//
// Copyright (C) 2020 neek-sss
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <https://www.gnu.org/licenses/>.

use num_traits::Float;
use strafe_type::{FloatConstraint, LogProbability64, Natural64, Probability64, Real64};

use crate::{distribution::wilcox::cwilcox, func::choose, traits::DPQ};

/// The quantile function of the Wilcoxon distribution.
pub fn qwilcox<P: Into<Probability64>, N1: Into<Natural64>, N2: Into<Natural64>>(
    x: P,
    m: N1,
    n: N2,
    lower_tail: bool,
) -> Real64 {
    let x = x.into().unwrap();
    qwilcox_inner(x, m, n, lower_tail, false)
}

/// The quantile function of the Wilcoxon distribution.
pub fn log_qwilcox<LP: Into<LogProbability64>, N1: Into<Natural64>, N2: Into<Natural64>>(
    x: LP,
    m: N1,
    n: N2,
    lower_tail: bool,
) -> Real64 {
    let x = x.into().unwrap();
    qwilcox_inner(x, m, n, lower_tail, true)
}

fn qwilcox_inner<N1: Into<Natural64>, N2: Into<Natural64>>(
    mut x: f64,
    m: N1,
    n: N2,
    lower_tail: bool,
    log: bool,
) -> Real64 {
    let mut m = m.into().unwrap();
    let mut n = n.into().unwrap();

    let mut c = 0.0; /* lower_tail,non-log "p" */
    let mut p = 0.0;
    if !x.is_finite() || !m.is_finite() || !n.is_finite() {
        return f64::nan().into();
    }

    m = m.round();
    n = n.round();

    if x == f64::dt_0(lower_tail, log) {
        return 0.0.into();
    }
    if x == f64::dt_1(lower_tail, log) {
        return (m * n).into();
    }

    if log || !lower_tail {
        x = x.dt_qiv(lower_tail, log)
    }

    let mm = m;
    let nn = n;
    c = choose(m + n, n).into();
    p = 0.0;
    let mut q = 0;
    if x <= 0.5 {
        x = x - 10.0 * 2.2204460492503131e-16;
        loop {
            p += cwilcox(q, mm as usize, nn as usize) / c;
            if p >= x {
                break;
            }
            q += 1
        }
    } else {
        x = 1.0 - x + 10.0 * 2.2204460492503131e-16;
        loop {
            p += cwilcox(q, mm as usize, nn as usize) / c;
            if p > x {
                q = (m * n - q as f64) as i32;
                break;
            } else {
                q += 1
            }
        }
    }

    q.into()
}