inv_chi_square.hpp

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#ifndef __STAN__PROB__DIST__UNI__CONTINUOUS__INV_CHI_SQUARE_HPP__
#define __STAN__PROB__DIST__UNI__CONTINUOUS__INV_CHI_SQUARE_HPP__

#include <boost/random/chi_squared_distribution.hpp>
#include <boost/random/variate_generator.hpp>

#include <stan/agrad.hpp>
#include <stan/math/error_handling.hpp>
#include <stan/math/functions/value_of.hpp>
#include <stan/meta/traits.hpp>
#include <stan/prob/constants.hpp>
#include <stan/prob/traits.hpp>
#include <stan/prob/internal_math.hpp>

namespace stan {

  namespace prob {

    template <bool propto,
              typename T_y, typename T_dof, 
              class Policy>
    typename return_type<T_y,T_dof>::type
    inv_chi_square_log(const T_y& y, const T_dof& nu, 
                       const Policy&) {
      static const char* function = "stan::prob::inv_chi_square_log(%1%)";

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

      using stan::math::check_finite;      
      using stan::math::check_positive;
      using stan::math::check_not_nan;
      using stan::math::value_of;
      using stan::math::check_consistent_sizes;

      double logp(0.0);
      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_not_nan(function, y, "Random variable", &logp, Policy()))
        return logp;

      if (!(check_consistent_sizes(function,
                                   y,nu,
                                   "Random variable","Degrees of freedom parameter",
                                   &logp, Policy())))
        return logp;

       
      // set up template expressions wrapping scalars into vector views
      VectorView<const T_y> y_vec(y);
      VectorView<const T_dof> nu_vec(nu);
      size_t N = max_size(y, nu);
      
      for (size_t n = 0; n < length(y); n++) 
        if (value_of(y_vec[n]) <= 0)
          return LOG_ZERO;

      using boost::math::digamma;
      using boost::math::lgamma;
      using stan::math::multiply_log;

      DoubleVectorView<include_summand<propto,T_y,T_dof>::value,
        is_vector<T_y>::value> log_y(length(y));
      for (size_t i = 0; i < length(y); i++)
        if (include_summand<propto,T_y,T_dof>::value)
          log_y[i] = log(value_of(y_vec[i]));

      DoubleVectorView<include_summand<propto,T_y>::value,
        is_vector<T_y>::value> inv_y(length(y));
      for (size_t i = 0; i < length(y); i++)
        if (include_summand<propto,T_y>::value)
          inv_y[i] = 1.0 / value_of(y_vec[i]);

      DoubleVectorView<include_summand<propto,T_dof>::value,
        is_vector<T_dof>::value> lgamma_half_nu(length(nu));
      DoubleVectorView<!is_constant_struct<T_dof>::value,
        is_vector<T_dof>::value> digamma_half_nu_over_two(length(nu));
      for (size_t i = 0; i < length(nu); i++) {
        double half_nu = 0.5 * value_of(nu_vec[i]);
        if (include_summand<propto,T_dof>::value)
          lgamma_half_nu[i] = lgamma(half_nu);
        if (!is_constant_struct<T_dof>::value)
          digamma_half_nu_over_two[i] = digamma(half_nu) * 0.5;
      }

      agrad::OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
      for (size_t n = 0; n < N; n++) {
        const double nu_dbl = value_of(nu_vec[n]);
        const double half_nu = 0.5 * nu_dbl;
  
        if (include_summand<propto,T_dof>::value)
          logp += nu_dbl * NEG_LOG_TWO_OVER_TWO - lgamma_half_nu[n];
        if (include_summand<propto,T_y,T_dof>::value)
          logp -= (half_nu+1.0) * log_y[n];
        if (include_summand<propto,T_y>::value)
          logp -= 0.5 * inv_y[n];

        if (!is_constant_struct<T_y>::value) {
          operands_and_partials.d_x1[n] 
            += -(half_nu+1.0) * inv_y[n] + 0.5 * inv_y[n] * inv_y[n];
        }
        if (!is_constant_struct<T_dof>::value) {
          operands_and_partials.d_x2[n]
            += NEG_LOG_TWO_OVER_TWO - digamma_half_nu_over_two[n] - 0.5*log_y[n];
        }
      }
      return operands_and_partials.to_var(logp);
    }

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

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

    template <typename T_y, typename T_dof>
    inline
    typename return_type<T_y,T_dof>::type
    inv_chi_square_log(const T_y& y, const T_dof& nu) {
      return inv_chi_square_log<false>(y,nu,stan::math::default_policy());
    }
      
    template <typename T_y, typename T_dof, class Policy>
    typename return_type<T_y,T_dof>::type
    inv_chi_square_cdf(const T_y& y, const T_dof& nu, const Policy&) {
          
      // Size checks
      if ( !( stan::length(y) && stan::length(nu) ) ) return 1.0;
          
      // Error checks
      static const char* function = "stan::prob::inv_chi_square_cdf(%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::check_nonnegative;
          
      using boost::math::tools::promote_args;
      using stan::math::value_of;
          
      double P(1.0);
          
      if (!check_finite(function, nu, "Degrees of freedom parameter", &P, Policy()))
        return P;
          
      if (!check_positive(function, nu, "Degrees of freedom parameter", &P, Policy()))
        return P;
          
      if (!check_not_nan(function, y, "Random variable", &P, Policy()))
        return P;
          
      if (!check_nonnegative(function, y, "Random variable", &P, Policy()))
        return P;
          
      if (!(check_consistent_sizes(function, y, nu,
                                   "Random variable", "Degrees of freedom parameter",
                                   &P, Policy())))
        return P;
          
      // Wrap arguments in vectors
      VectorView<const T_y> y_vec(y);
      VectorView<const T_dof> nu_vec(nu);
      size_t N = max_size(y, nu);
          
      agrad::OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
          
      std::fill(operands_and_partials.all_partials,
                operands_and_partials.all_partials + operands_and_partials.nvaris, 0.0);
        
      // 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 operands_and_partials.to_var(0.0);
        
      // Compute CDF and its gradients
      using boost::math::gamma_p_derivative;
      using boost::math::gamma_q;
      using boost::math::tgamma;
      using boost::math::digamma;
          
      // Cache a few expensive function calls if nu is a parameter
      DoubleVectorView<!is_constant_struct<T_dof>::value,
                       is_vector<T_dof>::value> gamma_vec(stan::length(nu));
      DoubleVectorView<!is_constant_struct<T_dof>::value, 
                       is_vector<T_dof>::value> digamma_vec(stan::length(nu));
          
      if (!is_constant_struct<T_dof>::value)  {
              
        for (size_t i = 0; i < stan::length(nu); i++) {
          const double nu_dbl = value_of(nu_vec[i]);
          gamma_vec[i] = tgamma(0.5 * nu_dbl);
          digamma_vec[i] = digamma(0.5 * nu_dbl);
        }
              
      }
          
      // Compute vectorized CDF and gradient
      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;
        }

        // Pull out values
        const double y_dbl = value_of(y_vec[n]);
        const double y_inv_dbl = 1.0 / y_dbl;
        const double nu_dbl = value_of(nu_vec[n]);
                  
        // Compute
        const double Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
                  
        P *= Pn;
                  
        if (!is_constant_struct<T_y>::value)
          operands_and_partials.d_x1[n] 
            += 0.5 * y_inv_dbl * y_inv_dbl
            * gamma_p_derivative(0.5 * nu_dbl, 0.5 * y_inv_dbl) / Pn;
                  
        if (!is_constant_struct<T_dof>::value)
          operands_and_partials.d_x2[n] 
            += 0.5 * stan::math::gradRegIncGamma(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) 
          operands_and_partials.d_x1[n] *= P;
                  
      if (!is_constant_struct<T_dof>::value)
        for (size_t n = 0; n < stan::length(nu); ++n) 
          operands_and_partials.d_x2[n] *= P;
          
      return operands_and_partials.to_var(P);
    }
      
    template <typename T_y, typename T_dof>
    inline typename return_type<T_y,T_dof>::type
    inv_chi_square_cdf(const T_y& y, const T_dof& nu) {
      return inv_chi_square_cdf(y, nu, stan::math::default_policy());
    }

    template <class RNG>
    inline double
    inv_chi_square_rng(const double nu,
                       RNG& rng) {
      using boost::variate_generator;
      using boost::random::chi_squared_distribution;
      variate_generator<RNG&, chi_squared_distribution<> >
        chi_square_rng(rng, chi_squared_distribution<>(nu));
      return 1 / chi_square_rng();
    }
    
  }
}

#endif