cauchy_lpdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_CAUCHY_LPDF_HPP
#define STAN_MATH_PRIM_PROB_CAUCHY_LPDF_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/constants.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/log1p.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 <bool propto, 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> cauchy_lpdf(const T_y& y,
                                                      const T_loc& mu,
                                                      const T_scale& sigma) {
  using T_partials_return = partials_return_t<T_y, T_loc, T_scale>;
  using std::log;
  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_sigma_ref = ref_type_if_not_constant_t<T_scale>;
  static constexpr const char* function = "cauchy_lpdf";
  check_consistent_sizes(function, "Random variable", y, "Location parameter",
                         mu, "Scale parameter", sigma);
  T_y_ref y_ref = y;
  T_mu_ref mu_ref = mu;
  T_sigma_ref sigma_ref = sigma;
 
  if (size_zero(y, mu, sigma)) {
    return 0.0;
  }
  if constexpr (!include_summand<propto, T_y, T_loc, T_scale>::value) {
    return 0.0;
  }
 
  T_partials_return logp(0.0);
  auto ops_partials = make_partials_propagator(y_ref, mu_ref, sigma_ref);
 
  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) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
  check_not_nan(function, "Random variable", y_val);
  check_finite(function, "Location parameter", mu_val);
  check_positive_finite(function, "Scale parameter", sigma_val);
 
  size_t N = max_size(y, mu, sigma);
 
  const auto& inv_sigma = to_ref_if<is_autodiff_v<T_scale>>(inv(sigma_val));
  const auto& y_minus_mu
      = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale>>(y_val - mu_val);
 
  logp -= sum(log1p(square(y_minus_mu * inv_sigma)));
  if constexpr (include_summand<propto>::value) {
    logp -= N * LOG_PI;
  }
  if constexpr (include_summand<propto, T_scale>::value) {
    logp -= sum(log(sigma_val)) * N / math::size(sigma);
  }
 
  if constexpr (is_any_autodiff_v<T_y, T_loc, T_scale>) {
    const auto& sigma_squared
        = to_ref_if<is_autodiff_v<T_scale>>(square(sigma_val));
    const auto& y_minus_mu_squared
        = to_ref_if<is_autodiff_v<T_scale>>(square(y_minus_mu));
    if constexpr (is_any_autodiff_v<T_y, T_loc>) {
      auto mu_deriv = to_ref_if<(is_autodiff_v<T_y> && is_autodiff_v<T_loc>)>(
          2 * y_minus_mu / (sigma_squared + y_minus_mu_squared));
      if constexpr (is_autodiff_v<T_y>) {
        if constexpr (is_vector<T_y>::value) {
          partials<0>(ops_partials) = -mu_deriv;
        } else {
          partials<0>(ops_partials)[0] = -sum(mu_deriv);
        }
      }
      if constexpr (is_autodiff_v<T_loc>) {
        partials<1>(ops_partials) = std::move(mu_deriv);
      }
    }
    if constexpr (is_autodiff_v<T_scale>) {
      partials<2>(ops_partials) = (y_minus_mu_squared - sigma_squared)
                                  * inv_sigma
                                  / (sigma_squared + y_minus_mu_squared);
    }
  }
  return ops_partials.build(logp);
}
 
template <typename T_y, typename T_loc, typename T_scale>
inline return_type_t<T_y, T_loc, T_scale> cauchy_lpdf(const T_y& y,
                                                      const T_loc& mu,
                                                      const T_scale& sigma) {
  return cauchy_lpdf<false>(y, mu, sigma);
}
 
}  // namespace math
}  // namespace stan
#endif