rayleigh_lcdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_RAYLEIGH_LCDF_HPP
#define STAN_MATH_PRIM_PROB_RAYLEIGH_LCDF_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/log1m.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_scale,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_scale>* = nullptr>
inline return_type_t<T_y, T_scale> rayleigh_lcdf(const T_y& y,
                                                 const T_scale& sigma) {
  using T_partials_return = partials_return_t<T_y, T_scale>;
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
  static constexpr const char* function = "rayleigh_lcdf";
  check_consistent_sizes(function, "Random variable", y, "Scale parameter",
                         sigma);
 
  T_y_ref y_ref = y;
  T_sigma_ref sigma_ref = sigma;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
 
  check_nonnegative(function, "Random variable", y_val);
  check_positive(function, "Scale parameter", sigma_val);
 
  if (size_zero(y, sigma)) {
    return 0;
  }
 
  auto ops_partials = make_partials_propagator(y_ref, sigma_ref);
 
  const auto& inv_sigma = to_ref_if<is_autodiff_v<T_scale>>(inv(sigma_val));
  const auto& y_div_sigma_square = to_ref_if<is_any_autodiff_v<T_y, T_scale>>(
      y_val * inv_sigma * inv_sigma);
  const auto& exp_val = to_ref_if<is_any_autodiff_v<T_y, T_scale>>(
      exp(-0.5 * y_val * y_div_sigma_square));
 
  T_partials_return cdf_log = sum(log1m(exp_val));
 
  if constexpr (is_any_autodiff_v<T_y, T_scale>) {
    auto common_deriv = y_div_sigma_square * exp_val / (1 - exp_val);
    if constexpr (is_autodiff_v<T_scale>) {
      partials<1>(ops_partials) = -y_val * inv_sigma * common_deriv;
    }
    if constexpr (is_autodiff_v<T_y>) {
      partials<0>(ops_partials) = std::move(common_deriv);
    }
  }
 
  return ops_partials.build(cdf_log);
}
 
}  // namespace math
}  // namespace stan
#endif