binomial.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__BINOMIAL_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__BINOMIAL_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/traits.hpp>
#include <stan/prob/constants.hpp>

namespace stan {

  namespace prob {

    // Binomial(n|N,theta)  [N >= 0;  0 <= n <= N;  0 <= theta <= 1]
    template <bool propto,
              typename T_n,
              typename T_N,
              typename T_prob, 
              class Policy>
    typename return_type<T_prob>::type
    binomial_log(const T_n& n, 
                 const T_N& N, 
                 const T_prob& theta, 
                 const Policy&) {

      static const char* function = "stan::prob::binomial_log(%1%)";
      
      using stan::math::check_finite;
      using stan::math::check_bounded;
      using stan::math::check_nonnegative;
      using stan::math::value_of;
      using stan::math::check_consistent_sizes;
      using stan::prob::include_summand;
      
      // check if any vectors are zero length
      if (!(stan::length(n)
            && stan::length(N)
            && stan::length(theta)))
        return 0.0;

      typename return_type<T_prob>::type logp(0.0);
      if (!check_bounded(function, n, 0, N,
                         "Successes variable",
                         &logp, Policy()))
        return logp;
      if (!check_nonnegative(function, N,
                             "Population size parameter",
                             &logp, Policy()))
        return logp;
      if (!check_finite(function, theta,
                        "Probability parameter",
                        &logp, Policy()))
        return logp;
      if (!check_bounded(function, theta, 0.0, 1.0,
                         "Probability parameter",
                         &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   n,N,theta,
                                   "Successes variable","Population size parameter","Probability parameter",
                                   &logp, Policy())))
        return logp;


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

      // set up template expressions wrapping scalars into vector views
      VectorView<const T_n> n_vec(n);
      VectorView<const T_N> N_vec(N);
      VectorView<const T_prob> theta_vec(theta);
      size_t size = max_size(n, N, theta);
      //agrad::OperandsAndPartials<T_prob> operands_and_partials(theta);
      
      using stan::math::multiply_log;
      using stan::math::binomial_coefficient_log;
      using stan::math::log1m;
        
      for (size_t i = 0; i < size; i++) {
        if (include_summand<propto>::value)
          logp += binomial_coefficient_log(N_vec[i],n_vec[i]);
        if (include_summand<propto,T_prob>::value) 
          logp += multiply_log(n_vec[i],theta_vec[i])
            + (N_vec[i] - n_vec[i]) * log1m(theta_vec[i]);
      }
      return logp;
    }

    template <bool propto,
              typename T_n,
              typename T_N,
              typename T_prob>
    inline
    typename return_type<T_prob>::type
    binomial_log(const T_n& n, 
                 const T_N& N, 
                 const T_prob& theta) {
      return binomial_log<propto>(n,N,theta,stan::math::default_policy());
    }


    template <typename T_n,
              typename T_N,
              typename T_prob, 
              class Policy>
    inline
    typename return_type<T_prob>::type
    binomial_log(const T_n& n, 
                 const T_N& N, 
                 const T_prob& theta, 
                 const Policy&) {
      return binomial_log<false>(n,N,theta,Policy());
    }


    template <typename T_n, 
              typename T_N,
              typename T_prob>
    inline
    typename return_type<T_prob>::type
    binomial_log(const T_n& n, 
                 const T_N& N, 
                 const T_prob& theta) {
      return binomial_log<false>(n,N,theta,stan::math::default_policy());
    }


    
  }
}
#endif