Example #1
0
double PolyaGamma::rtigauss(double Z, RNG& r)
{
  Z = fabs(Z);
  double t = __TRUNC;
  double X = t + 1.0;
  if (__TRUNC_RECIP > Z) { // mu > t
    double alpha = 0.0;
    while (r.unif() > alpha) {
      // X = t + 1.0;
      // while (X > t)
      // 	X = 1.0 / r.gamma_rate(0.5, 0.5);
      // Slightly faster to use truncated normal.
      double E1 = r.expon_rate(1.0); double E2 = r.expon_rate(1.0);
      while ( E1*E1 > 2 * E2 / t) {
	E1 = r.expon_rate(1.0); E2 = r.expon_rate(1.0);
      }
      X = 1 + E1 * t;
      X = t / (X * X);
      alpha = exp(-0.5 * Z*Z * X);
    }
  }
  else {
    double mu = 1.0 / Z;
    while (X > t) {
      double Y = r.norm(1.0); Y *= Y;
      double half_mu = 0.5 * mu;
      double mu_Y    = mu  * Y;
      X = mu + half_mu * mu_Y - half_mu * sqrt(4 * mu_Y + mu_Y * mu_Y);
      if (r.unif() > mu / (mu + X))
	X = mu*mu / X;
    }
  }
  return X;
}
Example #2
0
double PolyaGamma::draw_like_devroye(double Z, RNG& r)
{
  // Change the parameter.
  Z = fabs(Z) * 0.5;

  // Now sample 0.25 * J^*(1, Z := Z/2).
  double fz = 0.125 * __PI*__PI + 0.5 * Z*Z;
  // ... Problems with large Z?  Try using q_over_p.
  // double p  = 0.5 * __PI * exp(-1.0 * fz * __TRUNC) / fz;
  // double q  = 2 * exp(-1.0 * Z) * pigauss(__TRUNC, Z);

  double X = 0.0;
  double S = 1.0;
  double Y = 0.0;
  // int iter = 0; If you want to keep track of iterations.

  while (true) {

    // if (r.unif() < p/(p+q))
    if ( r.unif() < mass_texpon(Z) )
      X = __TRUNC + r.expon_rate(1) / fz;
    else
      X = rtigauss(Z, r);

    S = a(0, X);
    Y = r.unif() * S;
    int n = 0;
    bool go = true;

    // Cap the number of iterations?
    while (go) {

      // Break infinite loop.  Put first so it always checks n==0.
      #ifdef USE_R
      if (n % 1000 == 0) R_CheckUserInterrupt();
      #endif

      ++n;
      if (n%2==1) {
	S = S - a(n, X);
	if ( Y<=S ) return 0.25 * X;
      }
      else {
	S = S + a(n, X);
	if ( Y>S ) go = false;
      }

    }
    // Need Y <= S in event that Y = S, e.g. when X = 0.

  }
} // draw_like_devroye