r2rs-nmath 0.1.1

Statistics programming for Rust based on R's nmath package
Documentation 
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// Translation of nmath's qnbeta
//
// 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, Positive64, Probability64, Rational64, Real64,
};

use crate::{distribution::beta::pnbeta, traits::DPQ};

pub fn qnbeta<
    PR: Into<Probability64>,
    R1: Into<Rational64>,
    R2: Into<Rational64>,
    PO: Into<Positive64>,
>(
    p: PR,
    a: R1,
    b: R2,
    ncp: PO,
    lower_tail: bool,
) -> Real64 {
    let p = p.into().unwrap();
    qnbeta_inner(p, a, b, ncp, lower_tail, false)
}

pub fn log_qnbeta<
    LP: Into<LogProbability64>,
    R1: Into<Rational64>,
    R2: Into<Rational64>,
    P: Into<Positive64>,
>(
    p: LP,
    a: R1,
    b: R2,
    ncp: P,
    lower_tail: bool,
) -> Real64 {
    let p = p.into().unwrap();
    qnbeta_inner(p, a, b, ncp, lower_tail, true)
}

pub fn qnbeta_inner<R1: Into<Rational64>, R2: Into<Rational64>, P: Into<Positive64>>(
    mut p: f64,
    a: R1,
    b: R2,
    ncp: P,
    lower_tail: bool,
    log: bool,
) -> Real64 {
    let a = a.into().unwrap();
    let b = b.into().unwrap();
    let ncp = ncp.into().unwrap();

    static accu: f64 = 1e-15; /* must be > accu */
    static Eps: f64 = 1e-14;

    let mut ux = 0.0;
    let mut lx = 0.0;
    let mut nx = 0.0;
    let mut pp = 0.0;

    if !a.is_finite() {
        return f64::nan().into();
    }

    if let Some(ret) = p.q_p01_boundaries(0.0, 1.0, lower_tail, log) {
        return ret.into();
    }

    p = p.dt_qiv(lower_tail, log);

    /* Invert pnbeta(.) :
     * 1.0 finding an upper and lower bound */
    if p > 1.0 - 2.2204460492503131e-16f64 {
        return 1.0.into();
    }
    pp = (p * (1.0 + Eps)).min(1.0 - 2.2204460492503131e-16f64);
    ux = 0.5;
    while ux < 1.0 - 2.2204460492503131e-16f64 && pnbeta(ux, a, b, ncp, true).unwrap() < pp {
        ux = 0.5 * (1.0 + ux)
    }
    pp = p * (1.0 - Eps);
    lx = 0.5;
    while lx > 2.2250738585072014e-308 && pnbeta(lx, a, b, ncp, true).unwrap() > pp {
        lx *= 0.5
    }

    loop
    /* 2. interval (lx,ux)  halving : */
    {
        nx = 0.5 * (lx + ux);
        if pnbeta(nx, a, b, ncp, true).unwrap() > p {
            ux = nx
        } else {
            lx = nx
        }
        if !((ux - lx) / nx > accu) {
            break;
        }
    }

    return (0.5 * (ux + lx)).into();
}