The R Project SVN R

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000-2001 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 rpois(double lambda)
 *
 *  DESCRIPTION
 *
 *    Random variates from the Poisson distribution.
 *
 *  REFERENCE
 *
 *    Ahrens, J.H. and Dieter, U. (1982).
 *    Computer generation of Poisson deviates
 *    from modified normal distributions.
 *    ACM Trans. Math. Software 8, 163-179.
 */

#define a0  -0.5
#define a1   0.3333333
#define a2  -0.2500068
#define a3   0.2000118
#define a4  -0.1661269
#define a5   0.1421878
#define a6  -0.1384794
#define a7   0.1250060

#define one_7   0.1428571428571428571
#define one_12  0.0833333333333333333
#define one_24  0.0416666666666666667

#define repeat for(;;)

#include "nmath.h"

double rpois(double mu)
{
    /* Factorial Table (0:9)! */
    const static double fact[10] =
    {
    1., 1., 2., 6., 24., 120., 720., 5040., 40320., 362880.
    };

    /* These are static --- persistent between calls for same mu : */
    static int l, m;

    static double b1, b2, c, c0, c1, c2, c3;
    static double pp[36], p0, p, q, s, d, omega;
    static double big_l;/* integer "w/o overflow" */
    static double muprev = 0., muprev2 = 0.;/*, muold    = 0.*/

    /* Local Vars  [initialize some for -Wall]: */
    double del, difmuk= 0., E= 0., fk= 0., fx, fy, g, px, py, t, u= 0., v, x;
    double pois = -1.;
    int k, kflag, big_mu, new_big_mu = FALSE;

    if (!R_FINITE(mu))
    ML_ERR_return_NAN;

    if (mu <= 0.)
    return 0.;

    big_mu = mu >= 10.;
    if(big_mu)
    new_big_mu = FALSE;

    if (!(big_mu && mu == muprev)) {/* maybe compute new persistent par.s */

    if (big_mu) {
        new_big_mu = TRUE;
        /* Case A. (recalculation of s,d,l  because mu has changed):
         * The poisson probabilities pk exceed the discrete normal
         * probabilities fk whenever k >= m(mu).
         */
        muprev = mu;
        s = sqrt(mu);
        d = 6. * mu * mu;
        big_l = floor(mu - 1.1484);
        /* = an upper bound to m(mu) for all mu >= 10.*/
    }
    else { /* Small mu ( < 10) -- not using normal approx. */

        /* Case B. (start new table and calculate p0 if necessary) */

        /*muprev = 0.;-* such that next time, mu != muprev ..*/
        if (mu != muprev) {
        muprev = mu;
        m = imax2(1, (int) mu);
        l = 0; /* pp[] is already ok up to pp[l] */
        q = p0 = p = exp(-mu);
        }

        repeat {
        /* Step U. uniform sample for inversion method */
        u = unif_rand();
        if (u <= p0)
            return 0.;

        /* Step T. table comparison until the end pp[l] of the
           pp-table of cumulative poisson probabilities
           (0.458 > ~= pp[9](= 0.45792971447) for mu=10 ) */
        if (l != 0) {
            for (k = (u <= 0.458) ? 1 : imin2(l, m);  k <= l; k++)
            if (u <= pp[k])
                return (double)k;
            if (l == 35) /* u > pp[35] */
            continue;
        }
        /* Step C. creation of new poisson
           probabilities p[l..] and their cumulatives q =: pp[k] */
        l++;
        for (k = l; k <= 35; k++) {
            p *= mu / k;
            q += p;
            pp[k] = q;
            if (u <= q) {
            l = k;
            return (double)k;
            }
        }
        l = 35;
        } /* end(repeat) */
    }/* mu < 10 */

    } /* end {initialize persistent vars} */

/* Only if mu >= 10 : ----------------------- */

    /* Step N. normal sample */
    g = mu + s * norm_rand();/* norm_rand() ~ N(0,1), standard normal */

    if (g >= 0.) {
    pois = floor(g);
    /* Step I. immediate acceptance if pois is large enough */
    if (pois >= big_l)
        return pois;
    /* Step S. squeeze acceptance */
    fk = pois;
    difmuk = mu - fk;
    u = unif_rand(); /* ~ U(0,1) - sample */
    if (d * u >= difmuk * difmuk * difmuk)
        return pois;
    }

    /* Step P. preparations for steps Q and H.
       (recalculations of parameters if necessary) */

    if (new_big_mu || mu != muprev2) {
        /* Careful! muprev2 is not always == muprev
       because one might have exited in step I or S
       */
        muprev2 = mu;
    omega = M_1_SQRT_2PI / s;
    /* The quantities b1, b2, c3, c2, c1, c0 are for the Hermite
     * approximations to the discrete normal probabilities fk. */

    b1 = one_24 / mu;
    b2 = 0.3 * b1 * b1;
    c3 = one_7 * b1 * b2;
    c2 = b2 - 15. * c3;
    c1 = b1 - 6. * b2 + 45. * c3;
    c0 = 1. - b1 + 3. * b2 - 15. * c3;
    c = 0.1069 / mu; /* guarantees majorization by the 'hat'-function. */
    }

    if (g >= 0.) {
    /* 'Subroutine' F is called (kflag=0 for correct return) */
    kflag = 0;
    goto Step_F;
    }


    repeat {
    /* Step E. Exponential Sample */

    E = exp_rand(); /* ~ Exp(1) (standard exponential) */

    /*  sample t from the laplace 'hat'
        (if t <= -0.6744 then pk < fk for all mu >= 10.) */
    u = 2 * unif_rand() - 1.;
    t = 1.8 + fsign(E, u);
    if (t > -0.6744) {
        pois = floor(mu + s * t);
        fk = pois;
        difmuk = mu - fk;

        /* 'subroutine' F is called (kflag=1 for correct return) */
        kflag = 1;

      Step_F: /* 'subroutine' F : calculation of px,py,fx,fy. */

        if (pois < 10) { /* use factorials from table fact[] */
        px = -mu;
        py = pow(mu, pois) / fact[(int)pois];
        }
        else {
        /* Case pois >= 10 uses polynomial approximation
           a0-a7 for accuracy when advisable */
        del = one_12 / fk;
        del = del * (1. - 4.8 * del * del);
        v = difmuk / fk;
        if (fabs(v) <= 0.25)
            px = fk * v * v * (((((((a7 * v + a6) * v + a5) * v + a4) *
                      v + a3) * v + a2) * v + a1) * v + a0)
            - del;
        else /* |v| > 1/4 */
            px = fk * log(1. + v) - difmuk - del;
        py = M_1_SQRT_2PI / sqrt(fk);
        }
        x = (0.5 - difmuk) / s;
        x *= x;/* x^2 */
        fx = -0.5 * x;
        fy = omega * (((c3 * x + c2) * x + c1) * x + c0);
        if (kflag > 0) {
        /* Step H. Hat acceptance (E is repeated on rejection) */
        if (c * fabs(u) <= py * exp(px + E) - fy * exp(fx + E))
            break;
        } else
        /* Step Q. Quotient acceptance (rare case) */
        if (fy - u * fy <= py * exp(px - fx))
            break;
    }/* t > -.67.. */
    }
    return pois;
}