text: #ifndef STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_PREC_LPDF_HPP
  #define STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_PREC_LPDF_HPP
  
  #include <stan/math/prim/mat/err/check_ldlt_factor.hpp>
  #include <stan/math/prim/mat/err/check_symmetric.hpp>
  #include <stan/math/prim/mat/fun/columns_dot_product.hpp>
  #include <stan/math/prim/mat/fun/columns_dot_self.hpp>
  #include <stan/math/prim/mat/fun/dot_product.hpp>
  #include <stan/math/prim/mat/fun/dot_self.hpp>
  #include <stan/math/prim/mat/fun/log_determinant_ldlt.hpp>
  #include <stan/math/prim/mat/fun/log.hpp>
  #include <stan/math/prim/mat/fun/log_determinant.hpp>
  #include <stan/math/prim/mat/fun/mdivide_left_spd.hpp>
  #include <stan/math/prim/mat/fun/mdivide_left_tri_low.hpp>
  #include <stan/math/prim/mat/fun/multiply.hpp>
  #include <stan/math/prim/mat/fun/subtract.hpp>
  #include <stan/math/prim/mat/fun/sum.hpp>
  #include <stan/math/prim/mat/fun/trace_quad_form.hpp>
  #include <stan/math/prim/mat/meta/vector_seq_view.hpp>
  #include <stan/math/prim/scal/err/check_size_match.hpp>
  #include <stan/math/prim/scal/err/check_finite.hpp>
  #include <stan/math/prim/scal/err/check_not_nan.hpp>
  #include <stan/math/prim/scal/err/check_positive.hpp>
  #include <stan/math/prim/scal/fun/constants.hpp>
  #include <stan/math/prim/scal/meta/max_size_mvt.hpp>
  #include <stan/math/prim/scal/meta/include_summand.hpp>
  #include <stan/math/prim/scal/meta/return_type.hpp>
  
  namespace stan {
  namespace math {
  
  template <bool propto, typename T_y, typename T_loc, typename T_covar>
  typename return_type<T_y, T_loc, T_covar>::type multi_normal_prec_lpdf(
      const T_y& y, const T_loc& mu, const T_covar& Sigma) {
    static const char* function = "multi_normal_prec_lpdf";
    typedef typename scalar_type<T_covar>::type T_covar_elem;
    typedef typename return_type<T_y, T_loc, T_covar>::type lp_type;
    lp_type lp(0.0);
  
    check_positive(function, "Precision matrix rows", Sigma.rows());
    check_symmetric(function, "Precision matrix", Sigma);
  
    LDLT_factor<T_covar_elem, Eigen::Dynamic, Eigen::Dynamic> ldlt_Sigma(Sigma);
    check_ldlt_factor(function, "LDLT_Factor of precision parameter", ldlt_Sigma);
  
    using Eigen::Matrix;
    using std::vector;
    vector_seq_view<T_y> y_vec(y);
    vector_seq_view<T_loc> mu_vec(mu);
    size_t size_vec = max_size_mvt(y, mu);
  
    int size_y = y_vec[0].size();
    int size_mu = mu_vec[0].size();
    if (size_vec > 1) {
      int size_y_old = size_y;
      int size_y_new;
      for (size_t i = 1, size_ = length_mvt(y); i < size_; i++) {
        int size_y_new = y_vec[i].size();
        check_size_match(function,
                         "Size of one of the vectors "
                         "of the random variable",
                         size_y_new,
                         "Size of another vector of "
                         "the random variable",
                         size_y_old);
        size_y_old = size_y_new;
      }
      int size_mu_old = size_mu;
      int size_mu_new;
      for (size_t i = 1, size_ = length_mvt(mu); i < size_; i++) {
        int size_mu_new = mu_vec[i].size();
        check_size_match(function,
                         "Size of one of the vectors "
                         "of the location variable",
                         size_mu_new,
                         "Size of another vector of "
                         "the location variable",
                         size_mu_old);
        size_mu_old = size_mu_new;
      }
      (void)size_y_old;
      (void)size_y_new;
      (void)size_mu_old;
      (void)size_mu_new;
    }
  
    check_size_match(function, "Size of random variable", size_y,
                     "size of location parameter", size_mu);
    check_size_match(function, "Size of random variable", size_y,
                     "rows of covariance parameter", Sigma.rows());
    check_size_match(function, "Size of random variable", size_y,
                     "columns of covariance parameter", Sigma.cols());
  
    for (size_t i = 0; i < size_vec; i++) {
      check_finite(function, "Location parameter", mu_vec[i]);
      check_not_nan(function, "Random variable", y_vec[i]);
    }
  
    if (size_y == 0)
      return lp;
  
    if (include_summand<propto, T_covar_elem>::value)
      lp += 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;
  
    if (include_summand<propto>::value)
      lp += NEG_LOG_SQRT_TWO_PI * size_y * size_vec;
  
    if (include_summand<propto, T_y, T_loc, T_covar_elem>::value) {
      lp_type sum_lp_vec(0.0);
      for (size_t i = 0; i < size_vec; i++) {
        Eigen::Matrix<typename return_type<T_y, T_loc>::type, Eigen::Dynamic, 1>
            y_minus_mu(size_y);
        for (int j = 0; j < size_y; j++)
          y_minus_mu(j) = y_vec[i](j) - mu_vec[i](j);
        sum_lp_vec += trace_quad_form(Sigma, y_minus_mu);
      }
      lp -= 0.5 * sum_lp_vec;
    }
    return lp;
  }
  
  template <typename T_y, typename T_loc, typename T_covar>
  inline typename return_type<T_y, T_loc, T_covar>::type multi_normal_prec_lpdf(
      const T_y& y, const T_loc& mu, const T_covar& Sigma) {
    return multi_normal_prec_lpdf<false>(y, mu, Sigma);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  