scaled_inv_chi_square.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__SCALED_INV_CHI_SQUARE_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__SCALED_INV_CHI_SQUARE_HPP__

#include <stan/agrad.hpp>
#include <stan/math/error_handling.hpp>
#include <stan/math/special_functions.hpp>
#include <stan/meta/traits.hpp>
#include <stan/prob/constants.hpp>
#include <stan/prob/traits.hpp>

namespace stan {

  namespace prob {

    template <bool propto,
              typename T_y, typename T_dof, typename T_scale, 
              class Policy>
    typename return_type<T_y,T_dof,T_scale>::type
    scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s, 
                              const Policy&) {
      static const char* function 
        = "stan::prob::scaled_inv_chi_square_log(%1%)";
      
      using stan::math::check_finite;
      using stan::math::check_positive;
      using stan::math::check_not_nan;
      using stan::math::check_consistent_sizes;
      using stan::math::value_of;

      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(nu) 
            && stan::length(s)))
        return 0.0;

      typename return_type<T_y,T_dof,T_scale>::type logp(0.0);
      if (!check_not_nan(function, y, "Random variable", &logp, Policy()))
        return logp;
      if (!check_finite(function, nu, "Degrees of freedom parameter", &logp, Policy()))
        return logp;
      if (!check_positive(function, nu, "Degrees of freedom parameter", &logp, Policy()))
        return logp;
      if (!check_finite(function, s, "Scale parameter", &logp, Policy()))
        return logp;
      if (!check_positive(function, s, "Scale parameter", &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   y,nu,s,
                                   "Random variable","Degrees of freedom parameter","Scale parameter",
                                   &logp, Policy())))
        return logp;

      // check if no variables are involved and prop-to
      if (!include_summand<propto,T_y,T_dof,T_scale>::value)
        return 0.0;

      VectorView<const T_y> y_vec(y);
      VectorView<const T_dof> nu_vec(nu);
      VectorView<const T_scale> s_vec(s);
      size_t N = max_size(y, nu, s);

      for (size_t n = 0; n < N; n++) {
        if (value_of(y_vec[n]) <= 0)
          return LOG_ZERO;
      }

      using stan::math::multiply_log;
      using stan::math::square;
    
      for (size_t n = 0; n < N; n++) {
        if (include_summand<propto,T_dof>::value) {
          typename return_type<T_dof>::type half_nu = 0.5 * nu_vec[n];
          logp += multiply_log(half_nu,half_nu) - lgamma(half_nu);
        }
        if (include_summand<propto,T_dof,T_scale>::value)
          logp += nu_vec[n] * log(s_vec[n]);
        if (include_summand<propto,T_dof,T_y>::value)
          logp -= multiply_log(nu_vec[n]*0.5+1.0, y_vec[n]);
        if (include_summand<propto,T_dof,T_y,T_scale>::value)
          logp -= nu_vec[n] * 0.5 * square(s_vec[n]) / y_vec[n];
      }
      return logp;
    }

    template <bool propto,
              typename T_y, typename T_dof, typename T_scale>
    inline
    typename return_type<T_y,T_dof,T_scale>::type
    scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s) {
      return scaled_inv_chi_square_log<propto>(y,nu,s,
                                               stan::math::default_policy());
    }

    template <typename T_y, typename T_dof, typename T_scale, 
              class Policy>
    inline
    typename return_type<T_y,T_dof,T_scale>::type
    scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s, 
                              const Policy&) {
      return scaled_inv_chi_square_log<false>(y,nu,s,Policy());
    }

    template <typename T_y, typename T_dof, typename T_scale>
    inline
    typename return_type<T_y,T_dof,T_scale>::type
    scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s) {
      return scaled_inv_chi_square_log<false>(y,nu,s,
                                              stan::math::default_policy());
    }

  }
}

#endif