loglogistic_cdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_LOGLOGISTIC_CDF_HPP
#define STAN_MATH_PRIM_PROB_LOGLOGISTIC_CDF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
#include <stan/math/prim/fun/lmultiply.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
#include <stan/math/prim/fun/promote_scalar.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename T_y, typename T_scale, typename T_shape,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_scale, T_shape>* = nullptr>
inline return_type_t<T_y, T_scale, T_shape> loglogistic_cdf(
    const T_y& y, const T_scale& alpha, const T_shape& beta) {
  using T_partials_return = partials_return_t<T_y, T_scale, T_shape>;
  using T_y_ref = ref_type_t<T_y>;
  using T_alpha_ref = ref_type_t<T_scale>;
  using T_beta_ref = ref_type_t<T_shape>;
  using std::pow;
  static constexpr const char* function = "loglogistic_cdf";
  check_consistent_sizes(function, "Random variable", y, "Scale parameter",
                         alpha, "Shape parameter", beta);
  T_y_ref y_ref = y;
  T_alpha_ref alpha_ref = alpha;
  T_beta_ref beta_ref = beta;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) alpha_val = to_ref(as_value_column_array_or_scalar(alpha_ref));
  decltype(auto) beta_val = to_ref(as_value_column_array_or_scalar(beta_ref));
 
  check_nonnegative(function, "Random variable", y_val);
  check_positive_finite(function, "Scale parameter", alpha_val);
  check_positive_finite(function, "Shape parameter", beta_val);
 
  if (size_zero(y, alpha, beta)) {
    return 1.0;
  }
 
  auto ops_partials = make_partials_propagator(y_ref, alpha_ref, beta_ref);
 
  if (sum(promote_scalar<int>(y_val == 0))) {
    return ops_partials.build(0.0);
  }
 
  const auto& alpha_div_y
      = to_ref_if<is_autodiff_v<T_shape>>(alpha_val / y_val);
  const auto& alpha_div_y_pow_beta
      = to_ref_if<is_any_autodiff_v<T_y, T_scale, T_shape>>(
          pow(alpha_div_y, beta_val));
  const auto& prod_all = to_ref_if<is_any_autodiff_v<T_y, T_scale, T_shape>>(
      1 / (1 + alpha_div_y_pow_beta));
 
  T_partials_return cdf = prod(prod_all);
 
  if constexpr (is_any_autodiff_v<T_y, T_scale, T_shape>) {
    const auto& prod_all_sq = to_ref_if<
        is_autodiff_v<
            T_y> + is_autodiff_v<T_scale> + is_autodiff_v<T_shape> >= 2>(
        square(prod_all));
    const auto& cdf_div_elt = to_ref_if<
        is_autodiff_v<
            T_y> + is_autodiff_v<T_scale> + is_autodiff_v<T_shape> >= 2>(
        cdf / prod_all);
    if constexpr (is_any_autodiff_v<T_y, T_scale>) {
      const auto& alpha_div_times_beta
          = to_ref_if<is_autodiff_v<T_y> + is_autodiff_v<T_scale> == 2>(
              alpha_div_y_pow_beta * beta_val);
      if constexpr (is_autodiff_v<T_y>) {
        const auto& y_deriv = alpha_div_times_beta / y_val * prod_all_sq;
        partials<0>(ops_partials) = y_deriv * cdf_div_elt;
      }
      if constexpr (is_autodiff_v<T_scale>) {
        const auto& alpha_deriv
            = -alpha_div_times_beta / alpha_val * prod_all_sq;
        partials<1>(ops_partials) = alpha_deriv * cdf_div_elt;
      }
    }
    if constexpr (is_autodiff_v<T_shape>) {
      const auto& beta_deriv
          = -lmultiply(alpha_div_y_pow_beta, alpha_div_y) * prod_all_sq;
      partials<2>(ops_partials) = beta_deriv * cdf_div_elt;
    }
  }
 
  return ops_partials.build(cdf);
}
 
}  // namespace math
}  // namespace stan
#endif