von_mises_rng.hpp

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#ifndef STAN_MATH_PRIM_PROB_VON_MISES_RNG_HPP
#define STAN_MATH_PRIM_PROB_VON_MISES_RNG_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/scalar_seq_view.hpp>
#include <boost/random/uniform_real_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename T_loc, typename T_conc, class RNG>
inline typename VectorBuilder<true, double, T_loc, T_conc>::type von_mises_rng(
    const T_loc& mu, const T_conc& kappa, RNG& rng) {
  using boost::variate_generator;
  using boost::random::uniform_real_distribution;
  using T_mu_ref = ref_type_t<T_loc>;
  using T_kappa_ref = ref_type_t<T_conc>;
  static constexpr const char* function = "von_mises_rng";
  check_consistent_sizes(function, "Location parameter", mu, "Scale parameter",
                         kappa);
  if (size_zero(mu, kappa)) {
    return {};
  }
  T_mu_ref mu_ref = mu;
  T_kappa_ref kappa_ref = kappa;
 
  check_finite(function, "Location parameter", mu_ref);
  check_nonnegative(function, "Scale parameter", kappa_ref);
  check_finite(function, "Scale parameter", kappa_ref);
 
  scalar_seq_view<T_mu_ref> mu_vec(mu_ref);
  scalar_seq_view<T_kappa_ref> kappa_vec(kappa_ref);
  size_t N = max_size(mu, kappa_ref);
  VectorBuilder<true, double, T_loc, T_conc> output(N);
 
  variate_generator<RNG&, uniform_real_distribution<> > uniform_rng(
      rng, uniform_real_distribution<>(0.0, 1.0));
 
  for (size_t n = 0; n < N; ++n) {
    // for kappa sufficiently close to zero, it reduces to a
    // circular uniform distribution centered at mu
    if (kappa_vec[n] < 1.4e-8) {
      output[n] = (uniform_rng() - 0.5) * TWO_PI
                  + std::fmod(std::fmod(mu_vec[n], TWO_PI) + TWO_PI, TWO_PI);
      continue;
    }
 
    double r = 1 + std::pow((1 + 4 * kappa_vec[n] * kappa_vec[n]), 0.5);
    double rho = 0.5 * (r - std::pow(2 * r, 0.5)) / kappa_vec[n];
    double s = 0.5 * (1 + rho * rho) / rho;
 
    bool done = false;
    double W;
    while (!done) {
      double Z = std::cos(pi() * uniform_rng());
      W = (1 + s * Z) / (s + Z);
      double Y = kappa_vec[n] * (s - W);
      double U2 = uniform_rng();
      done = Y * (2 - Y) - U2 > 0;
 
      if (!done) {
        done = std::log(Y / U2) + 1 - Y >= 0;
      }
    }
 
    double U3 = uniform_rng() - 0.5;
    double sign = ((U3 >= 0) - (U3 <= 0));
 
    //  it's really an fmod() with a positivity constraint
    output[n] = sign * std::acos(W)
                + std::fmod(std::fmod(mu_vec[n], TWO_PI) + TWO_PI, TWO_PI);
  }
 
  return output.data();
}
 
}  // namespace math
}  // namespace stan
#endif