inv_chi_square_lpdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_INV_CHI_SQUARE_LPDF_HPP
#define STAN_MATH_PRIM_PROB_INV_CHI_SQUARE_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/digamma.hpp>
#include <stan/math/prim/fun/gamma_q.hpp>
#include <stan/math/prim/fun/lgamma.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/promote_scalar.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_dof,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_dof>* = nullptr>
inline return_type_t<T_y, T_dof> inv_chi_square_lpdf(const T_y& y,
                                                     const T_dof& nu) {
  using T_partials_return = partials_return_t<T_y, T_dof>;
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_nu_ref = ref_type_if_not_constant_t<T_dof>;
  static constexpr const char* function = "inv_chi_square_lpdf";
  check_consistent_sizes(function, "Random variable", y,
                         "Degrees of freedom parameter", nu);
 
  T_y_ref y_ref = y;
  T_nu_ref nu_ref = nu;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) nu_val = to_ref(as_value_column_array_or_scalar(nu_ref));
 
  check_positive_finite(function, "Degrees of freedom parameter", nu_val);
  check_not_nan(function, "Random variable", y_val);
 
  if (size_zero(y, nu)) {
    return 0;
  }
  if constexpr (!include_summand<propto, T_y, T_dof>::value) {
    return 0;
  }
 
  if (sum(promote_scalar<int>(y_val <= 0))) {
    return LOG_ZERO;
  }
 
  auto ops_partials = make_partials_propagator(y_ref, nu_ref);
 
  const auto& log_y = to_ref_if<is_autodiff_v<T_dof>>(log(y_val));
  const auto& half_nu = to_ref(0.5 * nu_val);
 
  size_t N = max_size(y, nu);
  T_partials_return logp = -sum((half_nu + 1.0) * log_y);
  if constexpr (include_summand<propto, T_dof>::value) {
    logp -= (sum(nu_val) * HALF_LOG_TWO + sum(lgamma(half_nu))) * N
            / math::size(nu);
  }
  if constexpr (include_summand<propto, T_y>::value) {
    const auto& inv_y = to_ref_if<is_autodiff_v<T_y>>(inv(y_val));
    logp -= 0.5 * sum(inv_y) * N / math::size(y);
    if constexpr (is_autodiff_v<T_y>) {
      partials<0>(ops_partials) = (0.5 * inv_y - half_nu - 1.0) * inv_y;
    }
  }
 
  if constexpr (is_autodiff_v<T_dof>) {
    edge<1>(ops_partials).partials_
        = -HALF_LOG_TWO - (digamma(half_nu) + log_y) * 0.5;
  }
  return ops_partials.build(logp);
}
 
template <typename T_y, typename T_dof>
inline return_type_t<T_y, T_dof> inv_chi_square_lpdf(const T_y& y,
                                                     const T_dof& nu) {
  return inv_chi_square_lpdf<false>(y, nu);
}
 
}  // namespace math
}  // namespace stan
#endif