The R Project SVN R

/*
 *  R : A Computer Langage for Statistical Data Analysis
 *  Copyright (C) 1995, 1996  Robert Gentleman and Ross Ihaka
 *
 *  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 2 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, write to the Free Software
 *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/* Reference:
 * R. C. H. Cheng (1978).
 * Generating beta variates with nonintegral shape parameters.
 * Communications of the ACM 21, 317-322.
 * (Algorithms BB and BC)
 */

#include "Mathlib.h"

static double expmax = 0.0;

#define repeat for(;;)

double rbeta(double aa, double bb)
{
    static double a, b, delta, r, s, t, u1, u2, v, w, y, z;
    static double alpha, beta, gamma, k1, k2;
    static double olda = -1.0;
    static double oldb = -1.0;
    int qsame;

    if (expmax == 0.0)
        expmax = log(DBL_MAX);

    qsame = (olda == aa) && (oldb == bb);

    if (!qsame)
        if (aa > 0.0 && bb > 0.0) {
            olda = aa;
            oldb = bb;
        } else {
            DOMAIN_ERROR;
        }
    if (fmin2(aa, bb) <= 1.0) { /* Algorithm BC */
        if (!qsame) {
            a = fmax2(aa, bb);
            b = fmin2(aa, bb);
            alpha = a + b;
            beta = 1.0 / b;
            delta = 1.0 + a - b;
            k1 = delta * (0.0138889 + 0.0416667 * b) /
                (a * beta - 0.777778);
            k2 = 0.25 + (0.5 + 0.25 / delta) * b;
        }
        repeat {
            u1 = sunif();
            u2 = sunif();
            if (u1 < 0.5) {
                y = u1 * u2;
                z = u1 * y;
                if (0.25 * u2 + z - y >= k1)
                    continue;
            } else {
                z = u1 * u1 * u2;
                if (z <= 0.25)
                    break;
                if (z >= k2)
                    continue;
            }
            v = beta * log(u1 / (1.0 - u1));
            if (v <= expmax)
                w = a * exp(v);
            else
                w = DBL_MAX;
            if (alpha * (log(alpha / (b + w)) + v) - 1.3862944
                >= log(z))
                goto deliver;
        }
        v = beta * log(u1 / (1.0 - u1));
        if (v <= expmax)
            w = a * exp(v);
        else
            w = DBL_MAX;
    } else {        /* Algorithm BB */
        if (!qsame) {
            a = fmin2(aa, bb);
            b = fmax2(aa, bb);
            alpha = a + b;
            beta = sqrt((alpha - 2.0) / (2.0 * a * b - alpha));
            gamma = a + 1.0 / beta;
        }
        do {
            u1 = sunif();
            u2 = sunif();
            v = beta * log(u1 / (1.0 - u1));
            if (v <= expmax)
                w = a * exp(v);
            else
                w = DBL_MAX;
            z = u1 * u1 * u2;
            r = gamma * v - 1.3862944;
            s = a + r - w;
            if (s + 2.609438 >= 5.0 * z)
                break;
            t = log(z);
            if (s > t)
                break;
        }
        while (r + alpha * log(alpha / (b + w)) < t);
    }

      deliver:
    return (aa != a) ? b / (b + w) : w / (b + w);
}