weibull_lcdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_WEIBULL_LCDF_HPP
#define STAN_MATH_PRIM_PROB_WEIBULL_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/log.hpp>
#include <stan/math/prim/fun/log1m.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/max_size.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_shape, typename T_scale,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_shape, T_scale>* = nullptr>
return_type_t<T_y, T_shape, T_scale> weibull_lcdf(const T_y& y,
                                                  const T_shape& alpha,
                                                  const T_scale& sigma) {
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_alpha_ref = ref_type_if_not_constant_t<T_shape>;
  using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
  static constexpr const char* function = "weibull_lcdf";
 
  T_y_ref y_ref = y;
  T_alpha_ref alpha_ref = alpha;
  T_sigma_ref sigma_ref = sigma;
 
  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) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
 
  check_nonnegative(function, "Random variable", y_val);
  check_positive_finite(function, "Shape parameter", alpha_val);
  check_positive_finite(function, "Scale parameter", sigma_val);
 
  if (size_zero(y, alpha, sigma)) {
    return 0.0;
  }
 
  auto ops_partials = make_partials_propagator(y_ref, alpha_ref, sigma_ref);
  if (any(value_of_rec(y_val) == 0)) {
    return ops_partials.build(stan::math::NEGATIVE_INFTY);
  }
 
  constexpr bool any_derivs = !is_constant_all<T_y, T_shape, T_scale>::value;
  const auto& log_y = to_ref_if<any_derivs>(log(y_val));
  const auto& log_sigma = to_ref_if<any_derivs>(log(sigma_val));
  const auto& log_y_div_sigma = to_ref_if<any_derivs>(log_y - log_sigma);
  const auto& log_pow_n = to_ref_if<any_derivs>(alpha_val * log_y_div_sigma);
  const auto& pow_n = to_ref_if<any_derivs>(exp(log_pow_n));
 
  if (any_derivs) {
    const auto& log_rep_deriv = to_ref(log_pow_n - log_diff_exp(pow_n, 0.0));
 
    if (!is_constant_all<T_y, T_scale>::value) {
      const auto& log_deriv_y_sigma = to_ref(log_rep_deriv + log(alpha_val));
      if (!is_constant_all<T_y>::value) {
        partials<0>(ops_partials) = exp(log_deriv_y_sigma - log_y);
      }
      if (!is_constant_all<T_scale>::value) {
        partials<2>(ops_partials) = -exp(log_deriv_y_sigma - log_sigma);
      }
    }
    if (!is_constant_all<T_shape>::value) {
      partials<1>(ops_partials) = exp(log_rep_deriv) * log_y_div_sigma;
    }
  }
  return ops_partials.build(sum(log1m_exp(-pow_n)));
}
 
}  // namespace math
}  // namespace stan
#endif