#ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LPMF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LPMF_HPP

#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/meta/length.hpp>
#include <stan/math/prim/scal/meta/scalar_seq_view.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/return_type.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
#include <stan/math/prim/scal/fun/inc_beta.hpp>
#include <stan/math/prim/scal/meta/max_size.hpp>
#include <boost/math/special_functions/digamma.hpp>
#include <boost/random/negative_binomial_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>

namespace stan {
  namespace math {

    // NegBinomial(n|alpha, beta)  [alpha > 0;  beta > 0;  n >= 0]
    template <bool propto,
              typename T_n,
              typename T_shape, typename T_inv_scale>
    typename return_type<T_shape, T_inv_scale>::type
    neg_binomial_lpmf(const T_n& n,
                     const T_shape& alpha,
                     const T_inv_scale& beta) {
      typedef typename stan::partials_return_type<T_n, T_shape,
                                                  T_inv_scale>::type
        T_partials_return;

      static const char* function("neg_binomial_lpmf");

      if (!(stan::length(n)
            && stan::length(alpha)
            && stan::length(beta)))
        return 0.0;

      T_partials_return logp(0.0);
      check_nonnegative(function, "Failures variable", n);
      check_positive_finite(function, "Shape parameter", alpha);
      check_positive_finite(function, "Inverse scale parameter", beta);
      check_consistent_sizes(function,
                             "Failures variable", n,
                             "Shape parameter", alpha,
                             "Inverse scale parameter", beta);

      if (!include_summand<propto, T_shape, T_inv_scale>::value)
        return 0.0;

      using std::log;
      using std::log;

      scalar_seq_view<const T_n> n_vec(n);
      scalar_seq_view<const T_shape> alpha_vec(alpha);
      scalar_seq_view<const T_inv_scale> beta_vec(beta);
      size_t size = max_size(n, alpha, beta);

      OperandsAndPartials<T_shape, T_inv_scale>
        operands_and_partials(alpha, beta);

      size_t len_ab = max_size(alpha, beta);
      VectorBuilder<true, T_partials_return, T_shape, T_inv_scale>
        lambda(len_ab);
      for (size_t i = 0; i < len_ab; ++i)
        lambda[i] = value_of(alpha_vec[i]) / value_of(beta_vec[i]);

      VectorBuilder<true, T_partials_return, T_inv_scale>
        log1p_beta(length(beta));
      for (size_t i = 0; i < length(beta); ++i)
        log1p_beta[i] = log1p(value_of(beta_vec[i]));

      VectorBuilder<true, T_partials_return, T_inv_scale>
        log_beta_m_log1p_beta(length(beta));
      for (size_t i = 0; i < length(beta); ++i)
        log_beta_m_log1p_beta[i] = log(value_of(beta_vec[i])) - log1p_beta[i];

      VectorBuilder<true, T_partials_return, T_inv_scale, T_shape>
        alpha_times_log_beta_over_1p_beta(len_ab);
      for (size_t i = 0; i < len_ab; ++i)
        alpha_times_log_beta_over_1p_beta[i]
          = value_of(alpha_vec[i])
          * log(value_of(beta_vec[i])
                / (1.0 + value_of(beta_vec[i])));

      VectorBuilder<!is_constant_struct<T_shape>::value,
                    T_partials_return, T_shape>
        digamma_alpha(length(alpha));
      if (!is_constant_struct<T_shape>::value) {
        for (size_t i = 0; i < length(alpha); ++i)
          digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
      }

      VectorBuilder<!is_constant_struct<T_shape>::value,
                    T_partials_return, T_inv_scale> log_beta(length(beta));
      if (!is_constant_struct<T_shape>::value) {
        for (size_t i = 0; i < length(beta); ++i)
          log_beta[i] = log(value_of(beta_vec[i]));
      }

      VectorBuilder<!is_constant_struct<T_inv_scale>::value,
                    T_partials_return, T_shape, T_inv_scale>
        lambda_m_alpha_over_1p_beta(len_ab);
      if (!is_constant_struct<T_inv_scale>::value) {
        for (size_t i = 0; i < len_ab; ++i)
          lambda_m_alpha_over_1p_beta[i] =
            lambda[i]
            - (value_of(alpha_vec[i])
               / (1.0 + value_of(beta_vec[i])));
      }

      for (size_t i = 0; i < size; i++) {
        if (alpha_vec[i] > 1e10) {  // reduces numerically to Poisson
          if (include_summand<propto>::value)
            logp -= lgamma(n_vec[i] + 1.0);
          if (include_summand<propto, T_shape, T_inv_scale>::value)
            logp += multiply_log(n_vec[i], lambda[i]) - lambda[i];

          if (!is_constant_struct<T_shape>::value)
            operands_and_partials.d_x1[i]
              += n_vec[i] / value_of(alpha_vec[i])
              - 1.0 / value_of(beta_vec[i]);
          if (!is_constant_struct<T_inv_scale>::value)
            operands_and_partials.d_x2[i]
              += (lambda[i] - n_vec[i]) / value_of(beta_vec[i]);
        } else {  // standard density definition
          if (include_summand<propto, T_shape>::value)
            if (n_vec[i] != 0)
              logp += binomial_coefficient_log(n_vec[i]
                                               + value_of(alpha_vec[i])
                                               - 1.0,
                                               n_vec[i]);
          if (include_summand<propto, T_shape, T_inv_scale>::value)
            logp +=
              alpha_times_log_beta_over_1p_beta[i]
              - n_vec[i] * log1p_beta[i];

          if (!is_constant_struct<T_shape>::value)
            operands_and_partials.d_x1[i]
              += digamma(value_of(alpha_vec[i]) + n_vec[i])
              - digamma_alpha[i]
              + log_beta_m_log1p_beta[i];
          if (!is_constant_struct<T_inv_scale>::value)
            operands_and_partials.d_x2[i]
              += lambda_m_alpha_over_1p_beta[i]
              - n_vec[i]  / (value_of(beta_vec[i]) + 1.0);
        }
      }
      return operands_and_partials.value(logp);
    }

    template <typename T_n,
              typename T_shape, typename T_inv_scale>
    inline
    typename return_type<T_shape, T_inv_scale>::type
    neg_binomial_lpmf(const T_n& n,
                     const T_shape& alpha,
                     const T_inv_scale& beta) {
      return neg_binomial_lpmf<false>(n, alpha, beta);
    }

  }
}
#endif
