// Arguments: Doubles, Doubles, Doubles, Doubles
#include <stan/math/prim/prob/exp_mod_normal_lpdf.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/erfc.hpp>
#include <stan/math/prim/fun/sqrt.hpp>

using stan::math::var;
using std::numeric_limits;
using std::vector;

class AgradDistributionExpModNormal : public AgradDistributionTest {
 public:
  void valid_values(vector<vector<double> >& parameters,
                    vector<double>& log_prob) {
    vector<double> param(4);

    param[0] = 0.0;  // y
    param[1] = 0.0;  // mu
    param[2] = 1.0;  // sigma
    param[3] = 1.0;  // lambda
    parameters.push_back(param);
    log_prob.push_back(
        -1.34102164500926350577078307323252902154767190882327);  // expected
                                                                 // log_prob

    param[0] = 1.0;  // y
    param[1] = 0.0;  // mu
    param[2] = 1.0;  // sigma
    param[3] = 1.0;  // lambda
    parameters.push_back(param);
    log_prob.push_back(-1.193147180559945397249);  // expected log_prob

    param[0] = -2.0;  // y
    param[1] = 0.0;   // mu
    param[2] = 1.0;   // sigma
    param[3] = 2.0;   // lambda
    parameters.push_back(param);
    log_prob.push_back(
        -3.66695430596734551844348822271447899701975756228145);  // expected
                                                                 // log_prob
  }

  void invalid_values(vector<size_t>& index, vector<double>& value) {
    // y

    // mu
    index.push_back(1U);
    value.push_back(-numeric_limits<double>::infinity());

    index.push_back(1U);
    value.push_back(numeric_limits<double>::infinity());

    // sigma
    index.push_back(2U);
    value.push_back(-numeric_limits<double>::infinity());

    index.push_back(2U);
    value.push_back(-1.0);

    index.push_back(2U);
    value.push_back(0.0);

    // lambda
    index.push_back(3U);
    value.push_back(-numeric_limits<double>::infinity());

    index.push_back(3U);
    value.push_back(-1.0);

    index.push_back(3U);
    value.push_back(0.0);

    index.push_back(3U);
    value.push_back(numeric_limits<double>::infinity());
  }

  template <typename T_y, typename T_loc, typename T_scale,
            typename T_inv_scale, typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale, T_inv_scale> log_prob(
      const T_y& y, const T_loc& mu, const T_scale& sigma,
      const T_inv_scale& lambda, const T4&, const T5&) {
    return stan::math::exp_mod_normal_lpdf(y, mu, sigma, lambda);
  }

  template <bool propto, typename T_y, typename T_loc, typename T_scale,
            typename T_inv_scale, typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale, T_inv_scale> log_prob(
      const T_y& y, const T_loc& mu, const T_scale& sigma,
      const T_inv_scale& lambda, const T4&, const T5&) {
    return stan::math::exp_mod_normal_lpdf<propto>(y, mu, sigma, lambda);
  }

  template <typename T_y, typename T_loc, typename T_scale,
            typename T_inv_scale, typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale, T_inv_scale> log_prob_function(
      const T_y& y, const T_loc& mu, const T_scale& sigma,
      const T_inv_scale& lambda, const T4&, const T5&) {
    return log(2) + log(lambda)
           + lambda * (mu + 0.5 * lambda * sigma * sigma - y)
           + log(erfc((mu + lambda * sigma * sigma - y) / (sqrt(2.0) * sigma)));
  }
};
