rbeta.cpp

/*
  Taken from R project 2.13.2

  Thorfinn@binf.ku.dk oct 07 2011

  This should proberly be implemented better using gsl or boost.

  we should cite the R project ....
 */

/* 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 <cstdlib>
#include <cstdlib>
#include <cmath>
#include <cstdio>
#include <cfloat>
#define expmax	(DBL_MAX_EXP * M_LN2)/* = log(DBL_MAX) */



double unif_rand() {
  return((double)rand() / (double)RAND_MAX);
}



double fmax2(double x, double y)
{
#ifdef IEEE_754
	if (ISNAN(x) || ISNAN(y))
		return x + y;
#endif
	return (x < y) ? y : x;
}

double fmin2(double x, double y)
{
#ifdef IEEE_754
	if (ISNAN(x) || ISNAN(y))
		return x + y;
#endif
	return (x < y) ? x : y;
}

double rbeta(double aa, double bb)
{
    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;

    if (aa <= 0. || bb <= 0. || (std::isinf(aa) && std::isinf(bb)))
//      fprintf(stderr,"Thorfinn write better error\n");

    if (std::isinf(aa))
    	return 1.0;

    if (std::isinf(bb))
    	return 0.0;


    /* 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(std::isinf(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);
    }
}