gumbel_cdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_GUMBEL_CDF_HPP
#define STAN_MATH_PRIM_PROB_GUMBEL_CDF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
#include <stan/math/prim/fun/as_array_or_scalar.hpp>
#include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/size.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/value_of.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename T_y, typename T_loc, typename T_scale,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_loc, T_scale>* = nullptr>
inline return_type_t<T_y, T_loc, T_scale> gumbel_cdf(const T_y& y,
                                                     const T_loc& mu,
                                                     const T_scale& beta) {
  using T_partials_return = partials_return_t<T_y, T_loc, T_scale>;
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
  using T_beta_ref = ref_type_if_not_constant_t<T_scale>;
  static constexpr const char* function = "gumbel_cdf";
  check_consistent_sizes(function, "Random variable", y, "Location parameter",
                         mu, "Scale parameter", beta);
  T_y_ref y_ref = y;
  T_mu_ref mu_ref = mu;
  T_beta_ref beta_ref = beta;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
  decltype(auto) beta_val = to_ref(as_value_column_array_or_scalar(beta_ref));
 
  check_not_nan(function, "Random variable", y_val);
  check_finite(function, "Location parameter", mu_val);
  check_positive(function, "Scale parameter", beta_val);
 
  if (size_zero(y, mu, beta)) {
    return 1.0;
  }
 
  auto ops_partials = make_partials_propagator(y_ref, mu_ref, beta_ref);
 
  const auto& scaled_diff = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale>>(
      (y_val - mu_val) / beta_val);
  const auto& exp_m_scaled_diff
      = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale>>(exp(-scaled_diff));
  const auto& cdf_n = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale>>(
      exp(-exp_m_scaled_diff));
 
  T_partials_return cdf(1.0);
  if constexpr (is_vector<T_y>::value || is_vector<T_loc>::value
                || is_vector<T_scale>::value) {
    cdf = cdf_n.prod();
  } else {
    cdf = cdf_n;
  }
 
  if constexpr (is_any_autodiff_v<T_y, T_loc, T_scale>) {
    const auto& rep_deriv_tmp = exp(-scaled_diff - exp_m_scaled_diff);
    const auto& rep_deriv = to_ref_if<
        is_autodiff_v<
            T_loc> + is_autodiff_v<T_scale> + is_autodiff_v<T_y> >= 2>(
        cdf * rep_deriv_tmp / (beta_val * cdf_n));
    if constexpr (is_autodiff_v<T_y>) {
      partials<0>(ops_partials) = rep_deriv;
    }
    if constexpr (is_autodiff_v<T_loc>) {
      partials<1>(ops_partials) = -rep_deriv;
    }
    if constexpr (is_autodiff_v<T_scale>) {
      partials<2>(ops_partials) = -rep_deriv * scaled_diff;
    }
  }
  return ops_partials.build(cdf);
}
 
}  // namespace math
}  // namespace stan
#endif