#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>
#include <string>

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 std::string 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
