#ifndef STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_CHOLESKY_LPDF_HPP
#define STAN_MATH_PRIM_MAT_PROB_MULTI_NORMAL_CHOLESKY_LPDF_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.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/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/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>
#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <string>

namespace stan {
  namespace math {
    /**
     * The log of the multivariate normal density for the given y, mu, and
     * a Cholesky factor L of the variance matrix.
     * Sigma = LL', a square, semi-positive definite matrix.
     *
     *
     * @param y A scalar vector
     * @param mu The mean vector of the multivariate normal distribution.
     * @param L The Cholesky decomposition of a variance matrix
     * of the multivariate normal distribution
     * @return The log of the multivariate normal density.
     * @throw std::domain_error if LL' is not square, not symmetric,
     * or not semi-positive definite.
     * @tparam T_y Type of scalar.
     * @tparam T_loc Type of location.
     * @tparam T_covar Type of scale.
     */
    template <bool propto,
              typename T_y, typename T_loc, typename T_covar>
    typename return_type<T_y, T_loc, T_covar>::type
    multi_normal_cholesky_lpdf(const T_y& y,
                              const T_loc& mu,
                              const T_covar& L) {
      static const std::string function = "multi_normal_cholesky_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);


      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", L.rows());
      check_size_match(function,
                       "Size of random variable", size_y,
                       "columns of covariance parameter", L.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>::value)
        lp += NEG_LOG_SQRT_TWO_PI * size_y * size_vec;

      if (include_summand<propto, T_covar_elem>::value)
        lp -= L.diagonal().array().log().sum() * 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);
          Eigen::Matrix<typename return_type<T_y, T_loc, T_covar>::type,
                        Eigen::Dynamic, 1>
            half(mdivide_left_tri_low(L, y_minus_mu));
          // FIXME: this code does not compile. revert after fixing subtract()
          // Eigen::Matrix<typename
          //               boost::math::tools::promote_args<T_covar,
          //                 typename value_type<T_loc>::type,
          //                 typename value_type<T_y>::type>::type>::type,
          //               Eigen::Dynamic, 1>
          //   half(mdivide_left_tri_low(L, subtract(y, mu)));
          sum_lp_vec += dot_self(half);
        }
        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_cholesky_lpdf(const T_y& y, const T_loc& mu,
                               const T_covar& L) {
      return multi_normal_cholesky_lpdf<false>(y, mu, L);
    }

  }
}
#endif
