#ifndef STAN_MATH_PRIM_MAT_PROB_DIRICHLET_LPMF_HPP
#define STAN_MATH_PRIM_MAT_PROB_DIRICHLET_LPMF_HPP

#include <boost/math/special_functions/gamma.hpp>
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <stan/math/prim/mat/err/check_simplex.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_positive.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>

namespace stan {
  namespace math {

    /**
     * The log of the Dirichlet density for the given theta and
     * a vector of prior sample sizes, alpha.
     * Each element of alpha must be greater than 0.
     * Each element of theta must be greater than or 0.
     * Theta sums to 1.
     *
     * \f{eqnarray*}{
     \theta &\sim& \mbox{\sf{Dirichlet}} (\alpha_1, \ldots, \alpha_k) \\
     \log (p (\theta \, |\, \alpha_1, \ldots, \alpha_k) ) &=& \log \left( \frac{\Gamma(\alpha_1 + \cdots + \alpha_k)}{\Gamma(\alpha_1) \cdots \Gamma(\alpha_k)}
     \theta_1^{\alpha_1 - 1} \cdots \theta_k^{\alpha_k - 1} \right) \\
     &=& \log (\Gamma(\alpha_1 + \cdots + \alpha_k)) - \log(\Gamma(\alpha_1)) - \cdots - \log(\Gamma(\alpha_k)) +
     (\alpha_1 - 1) \log (\theta_1) + \cdots + (\alpha_k - 1) \log (\theta_k)
     \f}
     *
     * @param theta A scalar vector.
     * @param alpha Prior sample sizes.
     * @return The log of the Dirichlet density.
     * @throw std::domain_error if any element of alpha is less than
     * or equal to 0.
     * @throw std::domain_error if any element of theta is less than 0.
     * @throw std::domain_error if the sum of theta is not 1.
     * @tparam T_prob Type of scalar.
     * @tparam T_prior_sample_size Type of prior sample sizes.
     */
    template <bool propto,
              typename T_prob, typename T_prior_sample_size>
    typename boost::math::tools::promote_args<T_prob, T_prior_sample_size>::type
    dirichlet_lpmf(const Eigen::Matrix<T_prob, Eigen::Dynamic, 1>& theta,
                  const Eigen::Matrix
                  <T_prior_sample_size, Eigen::Dynamic, 1>& alpha) {
      static const char* function("dirichlet_lpmf");
      using boost::math::lgamma;
      using boost::math::tools::promote_args;

      typename promote_args<T_prob, T_prior_sample_size>::type lp(0.0);
      check_consistent_sizes(function,
                             "probabilities", theta,
                             "prior sample sizes", alpha);
      check_positive(function, "prior sample sizes", alpha);
      check_simplex(function, "probabilities", theta);

      if (include_summand<propto, T_prior_sample_size>::value) {
        lp += lgamma(alpha.sum());
        for (int k = 0; k < alpha.rows(); ++k)
          lp -= lgamma(alpha[k]);
      }
      if (include_summand<propto, T_prob, T_prior_sample_size>::value) {
        for (int k = 0; k < theta.rows(); ++k)
          lp += multiply_log(alpha[k]-1, theta[k]);
      }
      return lp;
    }

    template <typename T_prob, typename T_prior_sample_size>
    inline
    typename boost::math::tools::promote_args<T_prob, T_prior_sample_size>::type
    dirichlet_lpmf(const Eigen::Matrix<T_prob, Eigen::Dynamic, 1>& theta,
                  const Eigen::Matrix
                  <T_prior_sample_size, Eigen::Dynamic, 1>& alpha) {
      return dirichlet_lpmf<false>(theta, alpha);
    }

  }
}
#endif
