student_t_qf.hpp

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#ifndef STAN_MATH_PRIM_PROB_STUDENT_T_QF_HPP
#define STAN_MATH_PRIM_PROB_STUDENT_T_QF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/sqrt.hpp>
#include <stan/math/prim/fun/inv_inc_beta.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
 
namespace stan {
namespace math {
 
template <typename T_p, typename T_nu, typename T_mu, typename T_sigma,
          require_all_stan_scalar_t<T_p, T_nu, T_mu, T_sigma>* = nullptr,
          require_all_arithmetic_t<T_p, T_nu, T_mu, T_sigma>* = nullptr>
inline double student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,
                           const T_sigma& sigma) {
  static constexpr const char* function = "student_t_qf";
  check_nonnegative(function, "Degrees of freedom parameter", nu);
  check_positive(function, "Scale parameter", sigma);
  check_bounded(function, "Probability parameter", p, 0.0, 1.0);
 
  if (p == 0.0) {
    return NEGATIVE_INFTY;
  } else if (p == 1.0) {
    return INFTY;
  } else if (p == 0.5) {
    return mu;
  }
 
  const double p_val_flip = p < 0.5 ? p : 1.0 - p;
  const double p_sign = p < 0.5 ? -1.0 : 1.0;
  const auto ibeta_arg = inv_inc_beta(0.5 * nu, 0.5, 2 * p_val_flip);
 
  return mu + p_sign * sigma * sqrt(nu) * sqrt(-1.0 + 1.0 / ibeta_arg);
}
 
template <typename T_p, typename T_nu, typename T_mu, typename T_sigma,
          require_any_vector_t<T_p, T_nu, T_mu, T_sigma>* = nullptr>
inline auto student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,
                         const T_sigma& sigma) {
  using ret_scalar = return_type_t<T_p, T_nu, T_mu, T_sigma>;
  static constexpr const char* function = "student_t_qf";
  const size_t max_size_all = max_size(p, nu, mu, sigma);
  Eigen::Matrix<ret_scalar, -1, 1> result(max_size_all);
 
  decltype(auto) p_ref = to_ref(p);
  decltype(auto) nu_ref = to_ref(nu);
  decltype(auto) mu_ref = to_ref(mu);
  decltype(auto) sigma_ref = to_ref(sigma);
 
  scalar_seq_view<decltype(p_ref)> p_vec(p_ref);
  scalar_seq_view<decltype(nu_ref)> nu_vec(nu_ref);
  scalar_seq_view<decltype(mu_ref)> mu_vec(mu_ref);
  scalar_seq_view<decltype(sigma_ref)> sigma_vec(sigma_ref);
 
  for (size_t i = 0; i < max_size_all; ++i) {
    result[i] = student_t_qf(p_vec[i], nu_vec[i], mu_vec[i], sigma_vec[i]);
  }
 
  return result;
}
 
}  // namespace math
}  // namespace stan
 
#endif