lkj_corr_lpdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_LKJ_CORR_LPDF_HPP
#define STAN_MATH_PRIM_PROB_LKJ_CORR_LPDF_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/lgamma.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/sum.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
 
namespace stan {
namespace math {
 
template <typename T_shape>
return_type_t<double, T_shape> do_lkj_constant(const T_shape& eta,
                                               const unsigned int& K) {
  // Lewandowski, Kurowicka, and Joe (2009) theorem 5
  return_type_t<double, T_shape> constant;
  const int Km1 = K - 1;
  using stan::math::lgamma;
  if (eta == 1.0) {
    // C++ integer division is appropriate in this block
    Eigen::VectorXd denominator(Km1 / 2);
    for (int k = 1; k <= denominator.rows(); k++) {
      denominator(k - 1) = lgamma(2.0 * k);
    }
    constant = -denominator.sum();
    if ((K % 2) == 1) {
      constant -= 0.25 * (K * K - 1) * LOG_PI - 0.25 * (Km1 * Km1) * LOG_TWO
                  - Km1 * lgamma(0.5 * (K + 1));
    } else {
      constant -= 0.25 * K * (K - 2) * LOG_PI
                  + 0.25 * (3 * K * K - 4 * K) * LOG_TWO + K * lgamma(0.5 * K)
                  - Km1 * lgamma(static_cast<double>(K));
    }
  } else {
    constant = Km1 * lgamma(eta + 0.5 * Km1);
    for (int k = 1; k <= Km1; k++) {
      constant -= 0.5 * k * LOG_PI + lgamma(eta + 0.5 * (Km1 - k));
    }
  }
  return constant;
}
 
// LKJ_Corr(y|eta) [ y correlation matrix (not covariance matrix)
//                  eta > 0; eta == 1 <-> uniform]
template <bool propto, typename T_y, typename T_shape>
return_type_t<T_y, T_shape> lkj_corr_lpdf(const T_y& y, const T_shape& eta) {
  static constexpr const char* function = "lkj_corr_lpdf";
 
  return_type_t<T_y, T_shape> lp(0.0);
  const auto& y_ref = to_ref(y);
  check_positive(function, "Shape parameter", eta);
  check_corr_matrix(function, "Correlation matrix", y_ref);
 
  const unsigned int K = y.rows();
  if (K == 0) {
    return 0.0;
  }
 
  if (include_summand<propto, T_shape>::value) {
    lp += do_lkj_constant(eta, K);
  }
 
  if (eta == 1.0 && is_constant_all<scalar_type<T_shape>>::value) {
    return lp;
  }
 
  if (!include_summand<propto, T_y, T_shape>::value) {
    return lp;
  }
 
  value_type_t<T_y> sum_values = sum(log(y_ref.ldlt().vectorD()));
  lp += (eta - 1.0) * sum_values;
  return lp;
}
 
template <typename T_y, typename T_shape>
inline return_type_t<T_y, T_shape> lkj_corr_lpdf(const T_y& y,
                                                 const T_shape& eta) {
  return lkj_corr_lpdf<false>(y, eta);
}
 
}  // namespace math
}  // namespace stan
#endif