text: #ifndef STAN_MATH_PRIM_MAT_PROB_MULTI_GP_CHOLESKY_LPDF_HPP
  #define STAN_MATH_PRIM_MAT_PROB_MULTI_GP_CHOLESKY_LPDF_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_positive.hpp>
  #include <stan/math/prim/scal/fun/constants.hpp>
  #include <stan/math/prim/scal/meta/include_summand.hpp>
  #include <stan/math/prim/mat/fun/dot_self.hpp>
  #include <stan/math/prim/mat/fun/log.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/row.hpp>
  #include <stan/math/prim/mat/fun/sum.hpp>
  
  namespace stan {
    namespace math {
      /**
       * The log of a multivariate Gaussian Process for the given y, w, and
       * a Cholesky factor L of the kernel matrix Sigma.
       * Sigma = LL', a square, semi-positive definite matrix.
       * y is a dxN matrix, where each column is a different observation and each
       * row is a different output dimension.  The Gaussian Process is assumed to
       * have a scaled kernel matrix with a different scale for each output dimension.
       * This distribution is equivalent to:
       *    for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*LL').
       *
       * @param y A dxN matrix
       * @param L The Cholesky decomposition of a kernel matrix
       * @param w A d-dimensional vector of positve inverse scale parameters for each output.
       * @return The log of the multivariate GP density.
       * @throw std::domain_error if Sigma is not square, not symmetric,
       * or not semi-positive definite.
       * @tparam T_y Type of scalar.
       * @tparam T_covar Type of kernel.
       * @tparam T_w Type of weight.
       */
      template <bool propto,
                typename T_y, typename T_covar, typename T_w>
      typename boost::math::tools::promote_args<T_y, T_covar, T_w>::type
      multi_gp_cholesky_lpdf(const Eigen::Matrix
                            <T_y, Eigen::Dynamic, Eigen::Dynamic>& y,
                            const Eigen::Matrix
                            <T_covar, Eigen::Dynamic, Eigen::Dynamic>& L,
                            const Eigen::Matrix<T_w, Eigen::Dynamic, 1>& w) {
        static const char* function("multi_gp_cholesky_lpdf");
        typedef
          typename boost::math::tools::promote_args<T_y, T_covar, T_w>::type T_lp;
        T_lp lp(0.0);
  
  
        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", L.rows());
        check_finite(function, "Kernel scales", w);
        check_positive(function, "Kernel scales", w);
        check_finite(function, "Random variable", y);
  
        if (y.rows() == 0)
          return lp;
  
        if (include_summand<propto>::value) {
          lp += NEG_LOG_SQRT_TWO_PI * y.rows() * y.cols();
        }
  
        if (include_summand<propto, T_covar>::value) {
          lp -= L.diagonal().array().log().sum() * y.rows();
        }
  
        if (include_summand<propto, T_w>::value) {
          lp += 0.5 * y.cols() * sum(log(w));
        }
  
        if (include_summand<propto, T_y, T_w, T_covar>::value) {
          T_lp sum_lp_vec(0.0);
          for (int i = 0; i < y.rows(); i++) {
            Eigen::Matrix<T_y, Eigen::Dynamic, 1> y_row(y.row(i));
            Eigen::Matrix<typename boost::math::tools::promote_args
                          <T_y, T_covar>::type,
                          Eigen::Dynamic, 1>
              half(mdivide_left_tri_low(L, y_row));
            sum_lp_vec += w(i) * dot_self(half);
          }
          lp -= 0.5*sum_lp_vec;
        }
  
        return lp;
      }
  
      template <typename T_y, typename T_covar, typename T_w>
      inline
      typename boost::math::tools::promote_args<T_y, T_covar, T_w>::type
      multi_gp_cholesky_lpdf(const Eigen::Matrix
                            <T_y, Eigen::Dynamic, Eigen::Dynamic>& y,
                            const Eigen::Matrix
                            <T_covar, Eigen::Dynamic, Eigen::Dynamic>& L,
                            const Eigen::Matrix<T_w, Eigen::Dynamic, 1>& w) {
        return multi_gp_cholesky_lpdf<false>(y, L, w);
      }
  
    }
  }
  #endif
  