text: #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LCDF_HPP
  #define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_LCDF_HPP
  
  #include <stan/math/prim/meta.hpp>
  #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
  #include <stan/math/prim/scal/err/check_nonnegative.hpp>
  #include <stan/math/prim/scal/err/check_not_nan.hpp>
  #include <stan/math/prim/scal/err/check_positive_finite.hpp>
  #include <stan/math/prim/scal/fun/size_zero.hpp>
  #include <stan/math/prim/scal/fun/constants.hpp>
  #include <stan/math/prim/scal/fun/value_of.hpp>
  #include <stan/math/prim/scal/fun/gamma_q.hpp>
  #include <stan/math/prim/scal/fun/digamma.hpp>
  #include <stan/math/prim/scal/fun/tgamma.hpp>
  #include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
  #include <cmath>
  #include <limits>
  
  namespace stan {
  namespace math {
  
  /**
   * Returns the inverse chi square log cumulative distribution function for
   * the given variate and degrees of freedom. If given containers of
   * matching sizes, returns the log sum of probabilities.
   *
   * @tparam T_y type of scalar parameter
   * @tparam T_dof type of degrees of freedom parameter
   * @param y scalar parameter
   * @param nu degrees of freedom parameter
   * @return log probability or log sum of probabilities
   * @throw std::domain_error if y is negative or nu is nonpositive
   * @throw std::invalid_argument if container sizes mismatch
   */
  template <typename T_y, typename T_dof>
  return_type_t<T_y, T_dof> inv_chi_square_lcdf(const T_y& y, const T_dof& nu) {
    using T_partials_return = partials_return_t<T_y, T_dof>;
  
    if (size_zero(y, nu)) {
      return 0.0;
    }
  
    static const char* function = "inv_chi_square_lcdf";
  
    T_partials_return P(0.0);
  
    check_positive_finite(function, "Degrees of freedom parameter", nu);
    check_not_nan(function, "Random variable", y);
    check_nonnegative(function, "Random variable", y);
    check_consistent_sizes(function, "Random variable", y,
                           "Degrees of freedom parameter", nu);
  
    scalar_seq_view<T_y> y_vec(y);
    scalar_seq_view<T_dof> nu_vec(nu);
    size_t N = max_size(y, nu);
  
    operands_and_partials<T_y, T_dof> ops_partials(y, nu);
  
    // Explicit return for extreme values
    // The gradients are technically ill-defined, but treated as zero
    for (size_t i = 0; i < stan::length(y); i++) {
      if (value_of(y_vec[i]) == 0) {
        return ops_partials.build(negative_infinity());
      }
    }
  
    using std::exp;
    using std::log;
    using std::pow;
  
    VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
        gamma_vec(stan::length(nu));
    VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
        digamma_vec(stan::length(nu));
  
    if (!is_constant_all<T_dof>::value) {
      for (size_t i = 0; i < stan::length(nu); i++) {
        const T_partials_return nu_dbl = value_of(nu_vec[i]);
        gamma_vec[i] = tgamma(0.5 * nu_dbl);
        digamma_vec[i] = digamma(0.5 * nu_dbl);
      }
    }
  
    for (size_t n = 0; n < N; n++) {
      // Explicit results for extreme values
      // The gradients are technically ill-defined, but treated as zero
      if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
        continue;
      }
  
      const T_partials_return y_dbl = value_of(y_vec[n]);
      const T_partials_return y_inv_dbl = 1.0 / y_dbl;
      const T_partials_return nu_dbl = value_of(nu_vec[n]);
  
      const T_partials_return Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
  
      P += log(Pn);
  
      if (!is_constant_all<T_y>::value) {
        ops_partials.edge1_.partials_[n]
            += 0.5 * y_inv_dbl * y_inv_dbl * exp(-0.5 * y_inv_dbl)
               * pow(0.5 * y_inv_dbl, 0.5 * nu_dbl - 1) / tgamma(0.5 * nu_dbl)
               / Pn;
      }
      if (!is_constant_all<T_dof>::value) {
        ops_partials.edge2_.partials_[n]
            += 0.5
               * grad_reg_inc_gamma(0.5 * nu_dbl, 0.5 * y_inv_dbl, gamma_vec[n],
                                    digamma_vec[n])
               / Pn;
      }
    }
    return ops_partials.build(P);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  