The R Project SVN R

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 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.
 *
 *  SYNOPSIS
 *
 *    #include "Mathlib.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.
 */

/* Factorial Table */
static double fact[10] =
{
    1.0,
    1.0,
    2.0,
    6.0,
    24.0,
    120.0,
    720.0,
    5040.0,
    40320.0,
    362880.0
};

#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 repeat for(;;)

#include "Mathlib.h"

double rpois(double mu)
{
    static double /* a0, a1, a2, a3, a4, a5, a6, a7, */ b1, b2;
    static double c, c0, c1, c2, c3, d, del, difmuk, e;
    static double fk, fx, fy, g, omega;
    static double p, p0, px, py, q, s, t, u, v, x, xx;
    static double pp[36];
    static int j, k, kflag, l, m;
    static int ipois;
    static double muprev = 0.0;
    static double muold = 0.0;

    if (mu != muprev) {
    if (mu >= 10.0) {
        /* case a. (recalculation of s,d,l */
        /* if mu has changed)  */
        /* the poisson probabilities pk */
        /* exceed the discrete normal */
        /* probabilities fk whenever k >= m(mu). */
        /* l=ifix(mu-1.1484) is an upper bound */
        /* to m(mu) for all mu >= 10. */
        muprev = mu;
        s = sqrt(mu);
        d = 6.0 * mu * mu;
        l = mu - 1.1484;
    } else {
        /* Case B. (start new table and */
        /* calculate p0 if necessary) */
        muprev = 0.0;
        if (mu != muold) {
        muold = mu;
        m = imax2(1, (int) mu);
        l = 0;
        p = exp(-mu);
        q = p;
        p0 = p;
        }
        repeat {
                /* Step U. uniform sample */
                /* for inversion method */
        u = sunif();
        ipois = 0;
        if (u <= p0)
            return (double)ipois;
                /* Step T. table comparison until */
                /* the end pp(l) of the pp-table of */
                /* cumulative poisson probabilities */
                /* (0.458=pp(9) for mu=10) */
        if (l != 0) {
            j = 1;
            if (u > 0.458)
            j = imin2(l, m);
            for (k = j; k <= l; k++)
            if (u <= pp[k])
                return (double)k;
            if (l == 35)
            continue;
        }
                /* Step C. creation of new poisson */
                /* probabilities p and their cumulatives */
                /* q=pp[k] */
        l = l + 1;
        for (k = l; k <= 35; k++) {
            p = p * mu / k;
            q = q + p;
            pp[k] = q;
            if (u <= q) {
            l = k;
            return (double)k;
            }
        }
        l = 35;
        }
    }
    }
    /* Step N. normal sample */
    /* snorm() for standard normal deviate */
    g = mu + s * snorm();
    if (g >= 0.0) {
    ipois = g;
    /* Step I. immediate acceptance */
    /* if ipois is large enough */
    if (ipois >= l)
        return (double)ipois;
    /* Step S. squeeze acceptance */
    /* sunif() for (0,1)-sample u */
    fk = ipois;
    difmuk = mu - fk;
    u = sunif();
    if (d * u >= difmuk * difmuk * difmuk)
        return (double)ipois;
    }
    /* Step P. preparations for steps Q and H. */
    /* (recalculations of parameters if necessary) */
    /* 0.3989423=(2*pi)**(-0.5) */
    /* 0.416667e-1=1./24. */
    /* 0.1428571=1./7. */
    /* The quantities b1, b2, c3, c2, c1, c0 are for the Hermite */
    /* approximations to the discrete normal probabilities fk. */
    /* c=.1069/mu guarantees majorization by the 'hat'-function. */
    if (mu != muold) {
    muold = mu;
    omega = 0.3989423 / s;
    b1 = 0.4166667e-1 / mu;
    b2 = 0.3 * b1 * b1;
    c3 = 0.1428571 * b1 * b2;
    c2 = b2 - 15. * c3;
    c1 = b1 - 6. * b2 + 45. * c3;
    c0 = 1. - b1 + 3. * b2 - 15. * c3;
    c = 0.1069 / mu;
    }
    if (g >= 0.0) {
    /* 'Subroutine' F is called (kflag=0 for correct return) */
    kflag = 0;
    goto L20;
    }
    repeat {
    /* Step E. Exponential Sample */
    /* sexp() for standard exponential deviate */
    /* e and sample t from the laplace 'hat' */
    /* (if t <= -0.6744 then pk < fk for all mu >= 10.) */
    e = sexp();
    u = sunif();
    u = u + u - 1.0;
    t = 1.8 + fsign(e, u);
    if (t > -0.6744) {
        ipois = mu + s * t;
        fk = ipois;
        difmuk = mu - fk;
        /* 'subroutine' f is called */
        /* (kflag=1 for correct return) */
        kflag = 1;
        /* Step f. 'subroutine' f. */
        /* calculation of px,py,fx,fy. */
        /* case ignpoi < 10 uses */
        /* factorials from table fact */
      L20:if (ipois < 10) {
          px = -mu;
          py = pow(mu, (double) ipois) / fact[ipois];
      } else {
                /* Case ipois >= 10 uses polynomial */
                /* approximation a0-a7 for accuracy */
                /* when advisable */
                /* 0.8333333e-1=1./12.0 */
                /* 0.3989423=(2*pi)**(-0.5) */
          del = 0.8333333e-1 / fk;
          del = del - 4.8 * del * 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
          px = fk * log(1.0 + v) - difmuk - del;
          py = 0.3989423 / sqrt(fk);
      }
        x = (0.5 - difmuk) / s;
        xx = x * x;
        fx = -0.5 * xx;
        fy = omega * (((c3 * xx + c2) * xx + c1) * xx + 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;
    }
    }
    return (double)ipois;
}