src/nmath/rbeta.c

/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 1995, 1996  Robert Gentleman and Ross Ihaka
 *  Copyright (C) 2000--2016 The R Core Team
 *  Copyright (C) 2001--2016 The R Foundation
 *
 *  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, a copy is available at
 *  https://www.R-project.org/Licenses/
 */

/* 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 "nmath.h"

#define expmax	(DBL_MAX_EXP * M_LN2)/* = log(DBL_MAX) */

double rbeta(double aa, double bb)
{
    if (ISNAN(aa) || ISNAN(bb) || aa < 0. || bb < 0.)
	ML_ERR_return_NAN;
    if (!R_FINITE(aa) && !R_FINITE(bb)) // a = b = Inf : all mass at 1/2
	return 0.5;
    if (aa == 0. && bb == 0.) // point mass 1/2 at each of {0,1} :
	return (unif_rand() < 0.5) ? 0. : 1.;
    // now, at least one of a, b is finite and positive
    if (!R_FINITE(aa) || bb == 0.)
    	return 1.0;
    if (!R_FINITE(bb) || aa == 0.)
    	return 0.0;

    double a, b, alpha;
    double r, s, t, u1, u2, v, w, y, z;
    int qsame;
    /* FIXME:  Keep Globals (properly) for threading */
    /* Uses these GLOBALS to save time when many rv's are generated : */
    static double beta, gamma, delta, k1, k2;
    static double olda = -1.0;
    static double oldb = -1.0;

    /* Test if we need new "initializing" */
    qsame = (olda == aa) && (oldb == bb);
    if (!qsame) { olda = aa; oldb = bb; }

    a = fmin2(aa, bb);
    b = fmax2(aa, bb); /* a <= b */
    alpha = a + b;

#define v_w_from__u1_bet(AA) 			\
	    v = beta * log(u1 / (1.0 - u1));	\
	    if (v <= expmax) {			\
		w = AA * exp(v);		\
		if(!R_FINITE(w)) w = DBL_MAX;	\
	    } else				\
		w = DBL_MAX


    if (a <= 1.0) {	/* --- Algorithm BC --- */

	/* changed notation, now also a <= b (was reversed) */

	if (!qsame) { /* initialize */
	    beta = 1.0 / a;
	    delta = 1.0 + b - a;
	    k1 = delta * (0.0138889 + 0.0416667 * a) / (b * beta - 0.777778);
	    k2 = 0.25 + (0.5 + 0.25 / delta) * a;
	}
	/* FIXME: "do { } while()", but not trivially because of "continue"s:*/
	for(;;) {
	    u1 = unif_rand();
	    u2 = unif_rand();
	    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) {
		    v_w_from__u1_bet(b);
		    break;
		}
		if (z >= k2)
		    continue;
	    }

	    v_w_from__u1_bet(b);

	    if (alpha * (log(alpha / (a + w)) + v) - 1.3862944 >= log(z))
		break;
	}
	return (aa == a) ? a / (a + w) : w / (a + w);

    }
    else {		/* Algorithm BB */

	if (!qsame) { /* initialize */
	    beta = sqrt((alpha - 2.0) / (2.0 * a * b - alpha));
	    gamma = a + 1.0 / beta;
	}
	do {
	    u1 = unif_rand();
	    u2 = unif_rand();

	    v_w_from__u1_bet(a);

	    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);

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