bernoulli_logit_lpmf.hpp

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#ifndef STAN_MATH_PRIM_PROB_BERNOULLI_LOGIT_LPMF_HPP
#define STAN_MATH_PRIM_PROB_BERNOULLI_LOGIT_LPMF_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_value_array_or_scalar.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/log1p.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/promote_scalar.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/fun/value_of_rec.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <bool propto, typename T_n, typename T_prob,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_n, T_prob>* = nullptr>
inline return_type_t<T_prob> bernoulli_logit_lpmf(const T_n& n,
                                                  const T_prob& theta) {
  using T_partials_return = partials_return_t<T_n, T_prob>;
  using T_partials_array = Eigen::Array<T_partials_return, Eigen::Dynamic, 1>;
  using std::exp;
  using T_n_ref = ref_type_if_not_constant_t<T_n>;
  using T_theta_ref = ref_type_if_not_constant_t<T_prob>;
  static constexpr const char* function = "bernoulli_logit_lpmf";
  check_consistent_sizes(function, "Random variable", n,
                         "Probability parameter", theta);
  if (size_zero(n, theta)) {
    return 0.0;
  }
  T_n_ref n_ref = n;
  T_theta_ref theta_ref = theta;
  check_bounded(function, "n", n_ref, 0, 1);
 
  decltype(auto) theta_val = to_ref(as_value_column_array_or_scalar(theta_ref));
 
  check_not_nan(function, "Logit transformed probability parameter", theta_val);
  if constexpr (!include_summand<propto, T_prob>::value) {
    return 0.0;
  }
 
  const auto& n_col = as_column_vector_or_scalar(n_ref);
  const auto& n_double = value_of_rec(n_col);
 
  auto signs = to_ref_if<is_autodiff_v<T_prob>>(
      (2 * as_array_or_scalar(n_double) - 1));
  T_partials_array ntheta;
  if constexpr (is_vector<T_n>::value || is_vector<T_prob>::value) {
    ntheta = signs * theta_val;
  } else {
    T_partials_return ntheta_s = signs * theta_val;
    ntheta = T_partials_array::Constant(1, 1, ntheta_s);
  }
  T_partials_array exp_m_ntheta = exp(-ntheta);
  static constexpr double cutoff = 20.0;
  T_partials_return logp = sum(
      (ntheta > cutoff)
          .select(-exp_m_ntheta,
                  (ntheta < -cutoff).select(ntheta, -log1p(exp_m_ntheta))));
 
  auto ops_partials = make_partials_propagator(theta_ref);
  if constexpr (is_autodiff_v<T_prob>) {
    edge<0>(ops_partials).partials_
        = (ntheta > cutoff)
              .select(
                  -exp_m_ntheta,
                  (ntheta >= -cutoff)
                      .select(promote_scalar<T_partials_return>(
                                  signs * exp_m_ntheta / (exp_m_ntheta + 1)),
                              promote_scalar<T_partials_return>(signs)));
  }
  return ops_partials.build(logp);
}
 
template <typename T_n, typename T_prob>
inline return_type_t<T_prob> bernoulli_logit_lpmf(const T_n& n,
                                                  const T_prob& theta) {
  return bernoulli_logit_lpmf<false>(n, theta);
}
 
}  // namespace math
}  // namespace stan
#endif