r2rs-nmath 0.1.1

// Translation of nmath's qnbinom_mu
//
// 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, Real64};

use super::{log_pnbinom_mu, pnbinom_mu};
use crate::{
    distribution::{
        func::discrete_body,
        pois::{log_qpois, qpois},
    },
    traits::DPQ,
};

pub fn qnbinom_mu<PR: Into<Probability64>, PO1: Into<Positive64>, PO2: Into<Positive64>>(
    p: PR,
    size: PO1,
    mu: PO2,
    lower_tail: bool,
) -> Real64 {
    let p = p.into().unwrap();
    qnbinom_mu_inner(p, size, mu, lower_tail, false)
}

pub fn log_qnbinom_mu<LP: Into<LogProbability64>, PO1: Into<Positive64>, PO2: Into<Positive64>>(
    p: LP,
    size: PO1,
    mu: PO2,
    lower_tail: bool,
) -> Real64 {
    let p = p.into().unwrap();
    qnbinom_mu_inner(p, size, mu, lower_tail, true)
}

pub fn qnbinom_mu_inner<PO1: Into<Positive64>, PO2: Into<Positive64>>(
    p: f64,
    size: PO1,
    mu: PO2,
    lower_tail: bool,
    log: bool,
) -> Real64 {
    let size = size.into().unwrap();

    if size == f64::infinity() {
        return if log {
            log_qpois(p, mu, lower_tail)
        } else {
            qpois(p, mu, lower_tail)
        };
    }

    let mu = mu.into().unwrap();

    if mu == 0.0 || size == 0.0 {
        return 0.0.into();
    }

    if let Some(ret) = p.q_p01_boundaries(0.0, f64::infinity(), lower_tail, log) {
        return ret.into();
    }

    let Q = 1.0 + mu / size; // (size+mu)/size = 1 / prob
    let P = mu / size; // = (1 - prob) * Q = (1 - prob) / prob  =  Q - 1
    let sigma = (size * P * Q).sqrt();
    let gamma = (Q + P) / sigma;

    // R_DBG_printf("qnbinom_mu(p=%.12g, size=%.15g, mu=%g, l.t.=%d, log=%d):"
    //              " mu=%g, sigma=%g, gamma=%g;\n",
    //              p, size, mu, lower_tail, log_p, mu, sigma, gamma);

    let y = discrete_body(
        mu,
        sigma,
        gamma,
        p,
        None,
        lower_tail,
        log,
        &|p| pnbinom_mu(p, size, mu, lower_tail).unwrap(),
        &|p| log_pnbinom_mu(p, size, mu, lower_tail).unwrap(),
    );

    y.into()
}