poisson.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__POISSON_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__POISSON_HPP__
 
#include <limits>
 
#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 {
 
    // Poisson(n|lambda)  [lambda > 0;  n >= 0]
    template <bool propto,
              typename T_n, typename T_rate, 
              class Policy>
    typename return_type<T_rate>::type
    poisson_log(const T_n& n, const T_rate& lambda, 
                const Policy&) {
 
      static const char* function = "stan::prob::poisson_log(%1%)";
      
      using stan::math::check_not_nan;
      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(lambda)))
        return 0.0;
 
      // set up return value accumulator
      double logp(0.0);
 
      // validate args
      if (!check_nonnegative(function, n, "Random variable", &logp, Policy()))
        return logp;
      if (!check_not_nan(function, lambda,
                         "Rate parameter", &logp, Policy()))
        return logp;
      if (!check_nonnegative(function, lambda,
                             "Rate parameter", &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   n,lambda,
                                   "Random variable","Rate parameter",
                                   &logp, Policy())))
        return logp;
      
      // check if no variables are involved and prop-to
      if (!include_summand<propto,T_rate>::value)
        return 0.0;
 
      // set up expression templates wrapping scalars/vecs into vector views
      VectorView<const T_n> n_vec(n);
      VectorView<const T_rate> lambda_vec(lambda);
      size_t size = max_size(n, lambda);
 
      for (size_t i = 0; i < size; i++)
        if (std::isinf(lambda_vec[i]))
          return LOG_ZERO;
      for (size_t i = 0; i < size; i++)
        if (lambda_vec[i] == 0 && n_vec[i] != 0)
          return LOG_ZERO;
      
      // return accumulator with gradients
      agrad::OperandsAndPartials<T_rate> operands_and_partials(lambda);
 
      using stan::math::multiply_log;
      for (size_t i = 0; i < size; i++) {
        if (!(lambda_vec[i] == 0 && n_vec[i] == 0)) {
          if (include_summand<propto>::value)
            logp -= lgamma(n_vec[i] + 1.0);
          if (include_summand<propto,T_rate>::value)
            logp += multiply_log(n_vec[i], value_of(lambda_vec[i])) 
              - value_of(lambda_vec[i]);
        }
 
        // gradients
        if (!is_constant_struct<T_rate>::value)
          operands_and_partials.d_x1[i] += n_vec[i] / value_of(lambda_vec[i]) - 1.0;
        
      }
 
 
      return operands_and_partials.to_var(logp);
    }
    
    template <bool propto,
              typename T_n,
              typename T_rate>
    inline
    typename return_type<T_rate>::type
    poisson_log(const T_n& n, const T_rate& lambda) {
      return poisson_log<propto>(n,lambda,stan::math::default_policy());
    }
 
 
    template <typename T_n,
              typename T_rate, 
              class Policy>
    inline
    typename return_type<T_rate>::type
    poisson_log(const T_n& n, const T_rate& lambda, 
                const Policy&) {
      return poisson_log<false>(n,lambda,Policy());
    }
 
 
    template <typename T_n,
              typename T_rate>
    inline
    typename return_type<T_rate>::type
    poisson_log(const T_n& n, const T_rate& lambda) {
      return poisson_log<false>(n,lambda,stan::math::default_policy());
    }
 
 
 
 
 
    // PoissonLog(n|alpha)  [n >= 0]   = Poisson(n|exp(alpha))
    template <bool propto,
              typename T_n, typename T_log_rate, 
              class Policy>
    typename return_type<T_log_rate>::type
    poisson_log_log(const T_n& n, const T_log_rate& alpha, 
                const Policy&) {
 
      static const char* function = "stan::prob::poisson_log_log(%1%)";
      
      using std::exp;
      using stan::math::check_not_nan;
      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(alpha)))
        return 0.0;
 
      // set up return value accumulator
      double logp(0.0);
 
      // validate args
      if (!check_nonnegative(function, n, "Random variable", &logp, Policy()))
        return logp;
      if (!check_not_nan(function, alpha,
                         "Log rate parameter", &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   n,alpha,
                                   "Random variable","Log rate parameter",
                                   &logp, Policy())))
        return logp;
      
      // check if no variables are involved and prop-to
      if (!include_summand<propto,T_log_rate>::value)
        return 0.0;
 
      // set up expression templates wrapping scalars/vecs into vector views
      VectorView<const T_n> n_vec(n);
      VectorView<const T_log_rate> alpha_vec(alpha);
      size_t size = max_size(n, alpha);
 
      // FIXME: first loop size of alpha_vec, second loop if-ed for size==1
      for (size_t i = 0; i < size; i++)
        if (std::numeric_limits<double>::infinity() == alpha_vec[i])
          return LOG_ZERO;
      for (size_t i = 0; i < size; i++)
        if (-std::numeric_limits<double>::infinity() == alpha_vec[i] 
            && n_vec[i] != 0)
          return LOG_ZERO;
      
      // return accumulator with gradients
      agrad::OperandsAndPartials<T_log_rate> operands_and_partials(alpha);
 
      // FIXME: cache value_of for alpha_vec?  faster if only one?
      
      using stan::math::multiply_log;
      for (size_t i = 0; i < size; i++) {
        if (!(alpha_vec[i] == -std::numeric_limits<double>::infinity() 
              && n_vec[i] == 0)) {
          if (include_summand<propto>::value)
            logp -= lgamma(n_vec[i] + 1.0);
          if (include_summand<propto,T_log_rate>::value)
            logp += n_vec[i] * value_of(alpha_vec[i]) - exp(value_of(alpha_vec[i]));
        }
 
        // gradients
        if (!is_constant_struct<T_log_rate>::value)
          operands_and_partials.d_x1[i] += n_vec[i] - exp(value_of(alpha_vec[i]));
      }
      return operands_and_partials.to_var(logp);
    }
    
    template <bool propto,
              typename T_n,
              typename T_log_rate>
    inline
    typename return_type<T_log_rate>::type
    poisson_log_log(const T_n& n, const T_log_rate& alpha) {
      return poisson_log_log<propto>(n,alpha,stan::math::default_policy());
    }
 
 
    template <typename T_n,
              typename T_log_rate, 
              class Policy>
    inline
    typename return_type<T_log_rate>::type
    poisson_log_log(const T_n& n, const T_log_rate& alpha, 
                const Policy&) {
      return poisson_log_log<false>(n,alpha,Policy());
    }
 
 
    template <typename T_n,
              typename T_log_rate>
    inline
    typename return_type<T_log_rate>::type
    poisson_log_log(const T_n& n, const T_log_rate& alpha) {
      return poisson_log_log<false>(n,alpha,stan::math::default_policy());
    }
 
 
  }
}
#endif