The R Project SVN R

/*
 *  R : A Computer Language 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307 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 {
        ML_ERROR(ME_DOMAIN);
        return ML_NAN;
    }
    }
    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);
}