The R Project SVN R

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000-2002 The R Development Core Team
 *
 *  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.
 *
 *  SYNOPSIS
 *
 *    #include <Rmath.h>
 *    double rgamma(double a, double scale);
 *
 *  DESCRIPTION
 *
 *    Random variates from the gamma distribution.
 *
 *  REFERENCES
 *
 *    [1] Shape parameter a >= 1.  Algorithm GD in:
 *
 *    Ahrens, J.H. and Dieter, U. (1982).
 *    Generating gamma variates by a modified
 *    rejection technique.
 *    Comm. ACM, 25, 47-54.
 *
 *
 *    [2] Shape parameter 0 < a < 1. Algorithm GS in:
 *
 *    Ahrens, J.H. and Dieter, U. (1974).
 *    Computer methods for sampling from gamma, beta,
 *    poisson and binomial distributions.
 *    Computing, 12, 223-246.
 *
 *    Input: a = parameter (mean) of the standard gamma distribution.
 *    Output: a variate from the gamma(a)-distribution
 */

#include "nmath.h"

#define repeat for(;;)

double rgamma(double a, double scale)
{
/* Constants : */
    const double sqrt32 = 5.656854;
    const double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */

    /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k))
     * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k)
     * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k)
     */
    const double q1 = 0.04166669;
    const double q2 = 0.02083148;
    const double q3 = 0.00801191;
    const double q4 = 0.00144121;
    const double q5 = -7.388e-5;
    const double q6 = 2.4511e-4;
    const double q7 = 2.424e-4;

    const double a1 = 0.3333333;
    const double a2 = -0.250003;
    const double a3 = 0.2000062;
    const double a4 = -0.1662921;
    const double a5 = 0.1423657;
    const double a6 = -0.1367177;
    const double a7 = 0.1233795;

    /* State variables [FIXME for threading!] :*/
    static double aa = 0.;
    static double aaa = 0.;
    static double s, s2, d;    /* no. 1 (step 1) */
    static double q0, b, si, c;/* no. 2 (step 4) */

    double e, p, q, r, t, u, v, w, x, ret_val;

    if (!R_FINITE(a) || !R_FINITE(scale))
    ML_ERR_return_NAN;

    if (a < 1.) { /* GS algorithm for parameters a < 1 */
    e = 1.0 + exp_m1 * a;
    repeat {
        p = e * unif_rand();
        if (p >= 1.0) {
        x = -log((e - p) / a);
        if (exp_rand() >= (1.0 - a) * log(x))
            break;
        } else {
        x = exp(log(p) / a);
        if (exp_rand() >= x)
            break;
        }
    }
    return scale * x;
    }

    /* --- a >= 1 : GD algorithm --- */

    /* Step 1: Recalculations of s2, s, d if a has changed */
    if (a != aa) {
    aa = a;
    s2 = a - 0.5;
    s = sqrt(s2);
    d = sqrt32 - s * 12.0;
    }
    /* Step 2: t = standard normal deviate,
               x = (s,1/2) -normal deviate. */

    /* immediate acceptance (i) */
    t = norm_rand();
    x = s + 0.5 * t;
    ret_val = x * x;
    if (t >= 0.0)
    return scale * ret_val;

    /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */
    u = unif_rand();
    if (d * u <= t * t * t)
    return scale * ret_val;

    /* Step 4: recalculations of q0, b, si, c if necessary */

    if (a != aaa) {
    aaa = a;
    r = 1.0 / a;
    q0 = ((((((q7 * r + q6) * r + q5) * r + q4) * r + q3) * r
           + q2) * r + q1) * r;

    /* Approximation depending on size of parameter a */
    /* The constants in the expressions for b, si and c */
    /* were established by numerical experiments */

    if (a <= 3.686) {
        b = 0.463 + s + 0.178 * s2;
        si = 1.235;
        c = 0.195 / s - 0.079 + 0.16 * s;
    } else if (a <= 13.022) {
        b = 1.654 + 0.0076 * s2;
        si = 1.68 / s + 0.275;
        c = 0.062 / s + 0.024;
    } else {
        b = 1.77;
        si = 0.75;
        c = 0.1515 / s;
    }
    }
    /* Step 5: no quotient test if x not positive */

    if (x > 0.0) {
    /* Step 6: calculation of v and quotient q */
    v = t / (s + s);
    if (fabs(v) <= 0.25)
        q = q0 + 0.5 * t * t * ((((((a7 * v + a6) * v + a5) * v + a4) * v
                      + a3) * v + a2) * v + a1) * v;
    else
        q = q0 - s * t + 0.25 * t * t + (s2 + s2) * log(1.0 + v);


    /* Step 7: quotient acceptance (q) */
    if (log(1.0 - u) <= q)
        return scale * ret_val;
    }

    repeat {
    /* Step 8: e = standard exponential deviate
     *  u =  0,1 -uniform deviate
     *  t = (b,si)-double exponential (laplace) sample */
    e = exp_rand();
    u = unif_rand();
    u = u + u - 1.0;
    if (u < 0.0)
        t = b - si * e;
    else
        t = b + si * e;
    /* Step  9:  rejection if t < tau(1) = -0.71874483771719 */
    if (t >= -0.71874483771719) {
        /* Step 10:  calculation of v and quotient q */
        v = t / (s + s);
        if (fabs(v) <= 0.25)
        q = q0 + 0.5 * t * t *
            ((((((a7 * v + a6) * v + a5) * v + a4) * v + a3) * v
              + a2) * v + a1) * v;
        else
        q = q0 - s * t + 0.25 * t * t + (s2 + s2) * log(1.0 + v);
        /* Step 11:  hat acceptance (h) */
        /* (if q not positive go to step 8) */
        if (q > 0.0) {
        w = expm1(q);
        /*  ^^^^^ original code had approximation with rel.err < 2e-7 */
        /* if t is rejected sample again at step 8 */
        if (c * fabs(u) <= w * exp(e - 0.5 * t * t))
            break;
        }
    }
    } /* repeat .. until  `t' is accepted */
    x = s + 0.5 * t;
    return scale * x * x;
}