multi_gp_lpdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_MULTI_GP_LPDF_HPP
#define STAN_MATH_PRIM_PROB_MULTI_GP_LPDF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/log_determinant_ldlt.hpp>
#include <stan/math/prim/fun/sum.hpp>
#include <stan/math/prim/fun/trace_gen_inv_quad_form_ldlt.hpp>
#include <stan/math/prim/fun/constants.hpp>
 
namespace stan {
namespace math {
 
template <bool propto, typename T_y, typename T_covar, typename T_w,
          require_all_matrix_t<T_y, T_covar>* = nullptr,
          require_col_vector_t<T_w>* = nullptr>
return_type_t<T_y, T_covar, T_w> multi_gp_lpdf(const T_y& y,
                                               const T_covar& Sigma,
                                               const T_w& w) {
  using T_lp = return_type_t<T_y, T_covar, T_w>;
  static constexpr const char* function = "multi_gp_lpdf";
  check_size_match(function, "Size of random variable (rows y)", y.rows(),
                   "Size of kernel scales (w)", w.size());
  check_size_match(function, "Size of random variable", y.cols(),
                   "rows of covariance parameter", Sigma.rows());
  check_positive(function, "Kernel rows", Sigma.rows());
 
  const auto& Sigma_ref = to_ref(Sigma);
  const auto& w_ref = to_ref(w);
  const auto& y_t_ref = to_ref(y.transpose());
 
  check_finite(function, "Kernel", Sigma_ref);
  check_symmetric(function, "Kernel", Sigma_ref);
  check_positive_finite(function, "Kernel scales", w_ref);
  check_finite(function, "Random variable", y_t_ref);
 
  auto ldlt_Sigma = make_ldlt_factor(Sigma_ref);
  check_ldlt_factor(function, "LDLT_Factor of Sigma", ldlt_Sigma);
 
  T_lp lp(0.0);
 
  if (y.rows() == 0) {
    return lp;
  }
 
  if (include_summand<propto>::value) {
    lp += NEG_LOG_SQRT_TWO_PI * y.size();
  }
 
  if (include_summand<propto, T_covar>::value) {
    lp -= 0.5 * log_determinant_ldlt(ldlt_Sigma) * y.rows();
  }
 
  if (include_summand<propto, T_w>::value) {
    lp += (0.5 * y.cols()) * sum(log(w_ref));
  }
 
  if (include_summand<propto, T_y, T_w, T_covar>::value) {
    lp -= 0.5 * trace_gen_inv_quad_form_ldlt(w_ref, ldlt_Sigma, y_t_ref);
  }
 
  return lp;
}
 
template <typename T_y, typename T_covar, typename T_w>
inline return_type_t<T_y, T_covar, T_w> multi_gp_lpdf(const T_y& y,
                                                      const T_covar& Sigma,
                                                      const T_w& w) {
  return multi_gp_lpdf<false>(y, Sigma, w);
}
 
}  // namespace math
}  // namespace stan
#endif