The R Project SVN R

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000-2015 The R Core Team
 *  Copyright (C) 2005-2015 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
 *  http://www.r-project.org/Licenses/
 *
 *  SYNOPSIS
 *
 *    #include <Rmath.h>
 *    double rhyper(double NR, double NB, double n);
 *
 *  DESCRIPTION
 *
 *    Random variates from the hypergeometric distribution.
 *    Returns the number of white balls drawn when kk balls
 *    are drawn at random from an urn containing nn1 white
 *    and nn2 black balls.
 *
 *  REFERENCE
 *
 *    V. Kachitvichyanukul and B. Schmeiser (1985).
 *    ``Computer generation of hypergeometric random variates,''
 *    Journal of Statistical Computation and Simulation 22, 127-145.
 *
 *    The original algorithm had a bug -- R bug report PR#7314 --
 *    giving numbers slightly too small in case III h2pe
 *    where (m < 100 || ix <= 50) , see below.
 */

#include "nmath.h"
#include "dpq.h"

/* afc(i) :=  ln( i! )  [logarithm of the factorial i.
 *     If (i > 7), use Stirling's approximation, otherwise use table lookup.
*/

static double afc(int i)
{
    const static double al[9] =
    {
    0.0,
    0.0,/*ln(0!)=ln(1)*/
    0.0,/*ln(1!)=ln(1)*/
    0.69314718055994530941723212145817,/*ln(2) */
    1.79175946922805500081247735838070,/*ln(6) */
    3.17805383034794561964694160129705,/*ln(24)*/
    4.78749174278204599424770093452324,
    6.57925121201010099506017829290394,
    8.52516136106541430016553103634712
    /*, 10.60460290274525022841722740072165*/
    };
    double di, value;

    if (i < 0) {
      MATHLIB_WARNING(("rhyper.c: afc(i), i=%d < 0 -- SHOULD NOT HAPPEN!\n"),
              i);
      return -1;/* unreached (Wall) */
    } else if (i <= 7) {
    value = al[i + 1];
    } else {
    di = i;
    value = (di + 0.5) * log(di) - di + 0.08333333333333 / di
        - 0.00277777777777 / di / di / di + 0.9189385332;
    }
    return value;
}

double rhyper(double nn1in, double nn2in, double kkin)
{
    const static double deltal = 0.0078;
    const static double deltau = 0.0034;

    /* extern double afc(int); */

    int nn1, nn2, kk;
    int i, ix;
    Rboolean reject, setup1, setup2;

    double e, f, g, r, t, y;

    /* These should become 'thread_local globals' : */
    static int ks = -1, n1s = -1, n2s = -1;
    static int k, m, minjx, maxjx, n1, n2;
    static double tn;
    // II :
    static double w;
    // III:
    static double a, d, s, xl, xr, kl, kr, lamdl, lamdr, p1, p2, p3;

    /* check parameter validity */

    if(!R_FINITE(nn1in) || !R_FINITE(nn2in) || !R_FINITE(kkin))
    ML_ERR_return_NAN;

    // Disabling large (nn1, nn2, kk) { =^= rhyper (m,n,k) }:
    nn1 = (int) R_forceint(nn1in);
    nn2 = (int) R_forceint(nn2in);
    kk  = (int) R_forceint(kkin);

    if (nn1 < 0 || nn2 < 0 || kk < 0 || kk > nn1 + nn2)
    ML_ERR_return_NAN;

    /* if new parameter values, initialize */
    reject = TRUE;
    if (nn1 != n1s || nn2 != n2s) {
    setup1 = TRUE;  setup2 = TRUE;
    } else if (kk != ks) {
    setup1 = FALSE; setup2 = TRUE;
    } else {
    setup1 = FALSE; setup2 = FALSE;
    }
    if (setup1) {
    n1s = nn1;
    n2s = nn2;
    tn = nn1 + nn2;
    if (nn1 <= nn2) {
        n1 = nn1;
        n2 = nn2;
    } else {
        n1 = nn2;
        n2 = nn1;
    }
    }
    if (setup2) {
    ks = kk;
    if (kk + kk >= tn) {
        k = (int)(tn - kk);
    } else {
        k = kk;
    }
    }
    if (setup1 || setup2) {
    m = (int) ((k + 1.0) * (n1 + 1.0) / (tn + 2.0));
    minjx = imax2(0, k - n2);
    maxjx = imin2(n1, k);
    }
    /* generate random variate --- Three basic cases */

    if (minjx == maxjx) { /* I: degenerate distribution ---------------- */
    ix = maxjx;
    /* return ix;
       No, need to unmangle <TSL>*/
    /* return appropriate variate */

    if (kk + kk >= tn) {
      if (nn1 > nn2) {
        ix = kk - nn2 + ix;
      } else {
        ix = nn1 - ix;
      }
    } else {
      if (nn1 > nn2)
        ix = kk - ix;
    }
    return ix;

    } else if (m - minjx < 10) { // II: (Scaled) algorithm HIN (inverse transformation) ----
    const static double scale = 1e25; // scaling factor against (early) underflow
    const static double con = 57.5646273248511421;
                                          // 25*log(10) = log(scale) { <==> exp(con) == scale }
    if (setup1 || setup2) {
        double lw; // log(w);  w = exp(lw) * scale = exp(lw + log(scale)) = exp(lw + con)
        if (k < n2) {
        lw = afc(n2) + afc(n1 + n2 - k) - afc(n2 - k) - afc(n1 + n2);
        } else {
        lw = afc(n1) + afc(     k     ) - afc(k - n2) - afc(n1 + n2);
        }
        w = exp(lw + con);
    }
    double p, u;
      L10:
    p = w;
    ix = minjx;
    u = unif_rand() * scale;
    while (u > p) {
        u -= p;
        p *= ((double) n1 - ix) * (k - ix);
        ix++;
        p = p / ix / (n2 - k + ix);
        if (ix > maxjx)
        goto L10;
    }
    } else { /* III : H2PE Algorithm --------------------------------------- */

    double u,v;

    if (setup1 || setup2) {
        s = sqrt((tn - k) * k * n1 * n2 / (tn - 1) / tn / tn);

        /* remark: d is defined in reference without int. */
        /* the truncation centers the cell boundaries at 0.5 */

        d = (int) (1.5 * s) + .5;
        xl = m - d + .5;
        xr = m + d + .5;
        a = afc(m) + afc(n1 - m) + afc(k - m) + afc(n2 - k + m);
        kl = exp(a - afc((int) (xl)) - afc((int) (n1 - xl))
             - afc((int) (k - xl))
             - afc((int) (n2 - k + xl)));
        kr = exp(a - afc((int) (xr - 1))
             - afc((int) (n1 - xr + 1))
             - afc((int) (k - xr + 1))
             - afc((int) (n2 - k + xr - 1)));
        lamdl = -log(xl * (n2 - k + xl) / (n1 - xl + 1) / (k - xl + 1));
        lamdr = -log((n1 - xr + 1) * (k - xr + 1) / xr / (n2 - k + xr));
        p1 = d + d;
        p2 = p1 + kl / lamdl;
        p3 = p2 + kr / lamdr;
    }
      L30:
    u = unif_rand() * p3;
    v = unif_rand();
    if (u < p1) {       /* rectangular region */
        ix = (int) (xl + u);
    } else if (u <= p2) {   /* left tail */
        ix = (int) (xl + log(v) / lamdl);
        if (ix < minjx)
        goto L30;
        v = v * (u - p1) * lamdl;
    } else {        /* right tail */
        ix = (int) (xr - log(v) / lamdr);
        if (ix > maxjx)
        goto L30;
        v = v * (u - p2) * lamdr;
    }

    /* acceptance/rejection test */

    if (m < 100 || ix <= 50) {
        /* explicit evaluation */
        /* The original algorithm (and TOMS 668) have
           f = f * i * (n2 - k + i) / (n1 - i) / (k - i);
           in the (m > ix) case, but the definition of the
           recurrence relation on p134 shows that the +1 is
           needed. */
        f = 1.0;
        if (m < ix) {
        for (i = m + 1; i <= ix; i++)
            f = f * (n1 - i + 1) * (k - i + 1) / (n2 - k + i) / i;
        } else if (m > ix) {
        for (i = ix + 1; i <= m; i++)
            f = f * i * (n2 - k + i) / (n1 - i + 1) / (k - i + 1);
        }
        if (v <= f) {
        reject = FALSE;
        }
    } else {
        double de, dg, dr, ds, dt, gl, gu, nk, nm, ub;
        double xk, xm, xn, y1, ym, yn, yk, alv;
        /* squeeze using upper and lower bounds */
        y = ix;
        y1 = y + 1.0;
        ym = y - m;
        yn = n1 - y + 1.0;
        yk = k - y + 1.0;
        nk = n2 - k + y1;
        r = -ym / y1;
        s = ym / yn;
        t = ym / yk;
        e = -ym / nk;
        g = yn * yk / (y1 * nk) - 1.0;
        dg = 1.0;
        if (g < 0.0)
        dg = 1.0 + g;
        gu = g * (1.0 + g * (-0.5 + g / 3.0));
        gl = gu - .25 * (g * g * g * g) / dg;
        xm = m + 0.5;
        xn = n1 - m + 0.5;
        xk = k - m + 0.5;
        nm = n2 - k + xm;
        ub = y * gu - m * gl + deltau
        + xm * r * (1. + r * (-0.5 + r / 3.0))
        + xn * s * (1. + s * (-0.5 + s / 3.0))
        + xk * t * (1. + t * (-0.5 + t / 3.0))
        + nm * e * (1. + e * (-0.5 + e / 3.0));
        /* test against upper bound */
        alv = log(v);
        if (alv > ub) {
        reject = TRUE;
        } else {
                /* test against lower bound */
        dr = xm * (r * r * r * r);
        if (r < 0.0)
            dr /= (1.0 + r);
        ds = xn * (s * s * s * s);
        if (s < 0.0)
            ds /= (1.0 + s);
        dt = xk * (t * t * t * t);
        if (t < 0.0)
            dt /= (1.0 + t);
        de = nm * (e * e * e * e);
        if (e < 0.0)
            de /= (1.0 + e);
        if (alv < ub - 0.25 * (dr + ds + dt + de)
            + (y + m) * (gl - gu) - deltal) {
            reject = FALSE;
        }
        else {
            /* * Stirling's formula to machine accuracy
             */
            if (alv <= (a - afc(ix) - afc(n1 - ix)
                - afc(k - ix) - afc(n2 - k + ix))) {
            reject = FALSE;
            } else {
            reject = TRUE;
            }
        }
        }
    } // else
    if (reject)
        goto L30;
    }

    /* return appropriate variate */

    if (kk + kk >= tn) {
    if (nn1 > nn2) {
        ix = kk - nn2 + ix;
    } else {
        ix = nn1 - ix;
    }
    } else {
    if (nn1 > nn2)
        ix = kk - ix;
    }
    return ix;
}