#ifndef STAN_MATH_PRIM_MAT_PROB_MATRIX_NORMAL_PREC_LPDF_HPP
#define STAN_MATH_PRIM_MAT_PROB_MATRIX_NORMAL_PREC_LPDF_HPP

#include <stan/math/prim/mat/err/check_ldlt_factor.hpp>
#include <stan/math/prim/scal/err/check_size_match.hpp>
#include <stan/math/prim/mat/err/check_symmetric.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/mat/fun/log.hpp>
#include <stan/math/prim/mat/fun/log_determinant.hpp>
#include <stan/math/prim/mat/fun/log_determinant_ldlt.hpp>
#include <stan/math/prim/mat/fun/subtract.hpp>
#include <stan/math/prim/mat/fun/trace_quad_form.hpp>
#include <stan/math/prim/mat/fun/trace_gen_quad_form.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <string>

namespace stan {
  namespace math {
    /**
     * The log of the matrix normal density for the given y, mu, Sigma and D
     * where Sigma and D are given as precision matrices, not covariance matrices.
     *
     * @param y An mxn matrix.
     * @param Mu The mean matrix.
     * @param Sigma The mxm inverse covariance matrix (i.e., the precision matrix) of the
     * rows of y.
     * @param D The nxn inverse covariance matrix (i.e., the precision matrix) of the
     * columns of y.
     * @return The log of the matrix normal density.
     * @throw std::domain_error if Sigma or D are not square, not symmetric,
     * or not semi-positive definite.
     * @tparam T_y Type of scalar.
     * @tparam T_Mu Type of location.
     * @tparam T_Sigma Type of Sigma.
     * @tparam T_D Type of D.
     */
    template <bool propto,
              typename T_y, typename T_Mu, typename T_Sigma, typename T_D>
    typename boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type
    matrix_normal_prec_lpdf(const Eigen::Matrix
                           <T_y, Eigen::Dynamic, Eigen::Dynamic>& y,
                           const Eigen::Matrix
                           <T_Mu, Eigen::Dynamic, Eigen::Dynamic>& Mu,
                           const Eigen::Matrix
                           <T_Sigma, Eigen::Dynamic, Eigen::Dynamic>& Sigma,
                           const Eigen::Matrix
                           <T_D, Eigen::Dynamic, Eigen::Dynamic>& D) {
      static const std::string function = "matrix_normal_prec_lpdf";
      typename
        boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type lp(0.0);

      check_positive(function, "Sigma rows", Sigma.rows());
      check_finite(function, "Sigma", Sigma);
      check_symmetric(function, "Sigma", Sigma);

      LDLT_factor<T_Sigma, Eigen::Dynamic, Eigen::Dynamic> ldlt_Sigma(Sigma);
      check_ldlt_factor(function, "LDLT_Factor of Sigma", ldlt_Sigma);
      check_positive(function, "D rows", D.rows());
      check_finite(function, "D", D);
      check_symmetric(function, "Sigma", D);

      LDLT_factor<T_D, Eigen::Dynamic, Eigen::Dynamic> ldlt_D(D);
      check_ldlt_factor(function, "LDLT_Factor of D", ldlt_D);
      check_size_match(function,
                       "Rows of random variable", y.rows(),
                       "Rows of location parameter", Mu.rows());
      check_size_match(function,
                       "Columns of random variable", y.cols(),
                       "Columns of location parameter", Mu.cols());
      check_size_match(function,
                       "Rows of random variable", y.rows(),
                       "Rows of Sigma", Sigma.rows());
      check_size_match(function,
                       "Columns of random variable", y.cols(),
                       "Rows of D", D.rows());
      check_finite(function, "Location parameter", Mu);
      check_finite(function, "Random variable", y);

      if (include_summand<propto>::value)
        lp += NEG_LOG_SQRT_TWO_PI * y.cols() * y.rows();

      if (include_summand<propto, T_Sigma>::value) {
        lp += log_determinant_ldlt(ldlt_Sigma) * (0.5 * y.rows());
      }

      if (include_summand<propto, T_D>::value) {
        lp += log_determinant_ldlt(ldlt_D) * (0.5 * y.cols());
      }

      if (include_summand<propto, T_y, T_Mu, T_Sigma, T_D>::value) {
        lp -= 0.5 * trace_gen_quad_form(D, Sigma, subtract(y, Mu));
      }
      return lp;
    }

    template <typename T_y, typename T_Mu, typename T_Sigma, typename T_D>
    typename boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type
    matrix_normal_prec_lpdf(const Eigen::Matrix
                           <T_y, Eigen::Dynamic, Eigen::Dynamic>& y,
                           const Eigen::Matrix
                           <T_Mu, Eigen::Dynamic, Eigen::Dynamic>& Mu,
                           const Eigen::Matrix
                           <T_Sigma, Eigen::Dynamic, Eigen::Dynamic>& Sigma,
                           const Eigen::Matrix
                           <T_D, Eigen::Dynamic, Eigen::Dynamic>& D) {
      return matrix_normal_prec_lpdf<false>(y, Mu, Sigma, D);
    }

  }
}
#endif
