// Arguments: Doubles, Doubles, Doubles
#include <stan/math/prim/prob/lognormal_lpdf.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/square.hpp>

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

class AgradDistributionsLognormal : public AgradDistributionTest {
 public:
  void valid_values(vector<vector<double> >& parameters,
                    vector<double>& log_prob) {
    vector<double> param(3);

    param[0] = 1.2;  // y
    param[1] = 0.3;  // mu
    param[2] = 1.5;  // sigma
    parameters.push_back(param);
    log_prob.push_back(-1.509802579439102343528);  // expected log_prob

    param[0] = 12.0;  // y
    param[1] = 3.0;   // mu
    param[2] = 0.9;   // sigma
    parameters.push_back(param);
    log_prob.push_back(-3.462263160811773765602);  // 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(0.0);

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

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

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

  template <typename T_y, typename T_loc, typename T_scale, typename T3,
            typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale> log_prob(const T_y& y,
                                                    const T_loc& mu,
                                                    const T_scale& sigma,
                                                    const T3&, const T4&,
                                                    const T5&) {
    return stan::math::lognormal_lpdf(y, mu, sigma);
  }

  template <bool propto, typename T_y, typename T_loc, typename T_scale,
            typename T3, typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale> log_prob(const T_y& y,
                                                    const T_loc& mu,
                                                    const T_scale& sigma,
                                                    const T3&, const T4&,
                                                    const T5&) {
    return stan::math::lognormal_lpdf<propto>(y, mu, sigma);
  }

  template <typename T_y, typename T_loc, typename T_scale, typename T3,
            typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale> log_prob_function(
      const T_y& y, const T_loc& mu, const T_scale& sigma, const T3&, const T4&,
      const T5&) {
    using stan::math::NEG_LOG_SQRT_TWO_PI;
    using stan::math::pi;
    using stan::math::square;

    return NEG_LOG_SQRT_TWO_PI - log(sigma) - log(y)
           - square(log(y) - mu) / (2.0 * sigma * sigma);
  }
};

TEST(ProbDistributionsLognormal, Cumulative) {
  using stan::math::lognormal_cdf;
  EXPECT_FLOAT_EQ(0.4687341, lognormal_cdf(1.2, 0.3, 1.5));
  EXPECT_FLOAT_EQ(0.2835506, lognormal_cdf(12.0, 3.0, 0.9));

  double pos_inf = std::numeric_limits<double>::infinity();

  // ?? double neg_inf = -pos_inf;
  // ?? EXPECT_FLOAT_EQ(0.0, lognormal_cdf(neg_inf, 0.0, 1.0));

  EXPECT_FLOAT_EQ(0.0, lognormal_cdf(0.0, 0.0, 1.0));
  EXPECT_FLOAT_EQ(1.0, lognormal_cdf(pos_inf, 0.0, 1.0));
}
