#ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_HPP

#include <boost/random/chi_squared_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <stan/math/prim/scal/meta/operands_and_partials.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/constants.hpp>
#include <stan/math/prim/scal/fun/multiply_log.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/meta/length.hpp>
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/scalar_seq_view.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/return_type.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <cmath>
#include <limits>

namespace stan {
  namespace math {

    /**
     * Returns the inverse chi square cumulative distribution function for the
     * given variate and degrees of freedom. If given containers of matching 
     * sizes, returns the product 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 probability or product 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>
    typename return_type<T_y, T_dof>::type
    inv_chi_square_cdf(const T_y& y, const T_dof& nu) {
      typedef typename stan::partials_return_type<T_y, T_dof>::type
        T_partials_return;

      if (!(stan::length(y) && stan::length(nu)))
        return 1.0;

      static const char* function("inv_chi_square_cdf");

      using boost::math::tools::promote_args;
      using std::exp;

      T_partials_return P(1.0);

      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(0.0);

      using boost::math::tgamma;
      using std::exp;
      using std::pow;

      VectorBuilder<!is_constant_struct<T_dof>::value,
                    T_partials_return, T_dof> gamma_vec(stan::length(nu));
      VectorBuilder<!is_constant_struct<T_dof>::value,
                    T_partials_return, T_dof> digamma_vec(stan::length(nu));

      if (!is_constant_struct<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 *= Pn;

        if (!is_constant_struct<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_struct<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;
      }

      if (!is_constant_struct<T_y>::value) {
        for (size_t n = 0; n < stan::length(y); ++n)
          ops_partials.edge1_.partials_[n] *= P;
      }
      if (!is_constant_struct<T_dof>::value) {
        for (size_t n = 0; n < stan::length(nu); ++n)
          ops_partials.edge2_.partials_[n] *= P;
      }
      return ops_partials.build(P);
    }

  }
}
#endif
