exponential.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__EXPONENTIAL_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__EXPONENTIAL_HPP__

#include <boost/random/exponential_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>

namespace stan {
  
  namespace prob {

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

      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(beta)))
  return 0.0;
      
      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;
      
      double logp(0.0);
      if(!check_not_nan(function, y, "Random variable", &logp, Policy()))
        return logp;
      if(!check_finite(function, beta, "Inverse scale parameter", &logp, Policy()))
        return logp;
      if(!check_positive(function, beta, "Inverse scale parameter", &logp, Policy()))
        return logp;

      if (!(check_consistent_sizes(function,
                                   y,beta,
           "Random variable","Inverse scale parameter",
                                   &logp, Policy())))
        return logp;
      
      
      // set up template expressions wrapping scalars into vector views
      VectorView<const T_y> y_vec(y);
      VectorView<const T_inv_scale> beta_vec(beta);
      size_t N = max_size(y, beta);
      
      DoubleVectorView<
  include_summand<propto,T_inv_scale>::value,
  is_vector<T_inv_scale>::value> log_beta(length(beta));
      for (size_t i = 0; i < length(beta); i++)
  if (include_summand<propto,T_inv_scale>::value)
    log_beta[i] = log(value_of(beta_vec[i]));

      agrad::OperandsAndPartials<T_y,T_inv_scale> operands_and_partials(y, beta);

      for (size_t n = 0; n < N; n++) {
  const double beta_dbl = value_of(beta_vec[n]);
  const double y_dbl = value_of(y_vec[n]);
  if (include_summand<propto,T_inv_scale>::value)
    logp += log_beta[n];
  if (include_summand<propto,T_y,T_inv_scale>::value)
    logp -= beta_dbl * y_dbl;
  
  if (!is_constant_struct<T_y>::value) 
    operands_and_partials.d_x1[n] -= beta_dbl;
  if (!is_constant_struct<T_inv_scale>::value) 
    operands_and_partials.d_x2[n] += 1 / beta_dbl - y_dbl;
      }
      return operands_and_partials.to_var(logp);
    }
    
    template <bool propto,
              typename T_y, typename T_inv_scale>
    inline
    typename return_type<T_y,T_inv_scale>::type
    exponential_log(const T_y& y, const T_inv_scale& beta) {
      return exponential_log<propto>(y,beta,stan::math::default_policy());
    }

    template <typename T_y, typename T_inv_scale,
              class Policy>
    inline
    typename return_type<T_y,T_inv_scale>::type
    exponential_log(const T_y& y, const T_inv_scale& beta, const Policy&) {
      return exponential_log<false>(y,beta,Policy());
    }

    template <typename T_y, typename T_inv_scale>
    inline
    typename return_type<T_y,T_inv_scale>::type
    exponential_log(const T_y& y, const T_inv_scale& beta) {
      return exponential_log<false>(y,beta,stan::math::default_policy());
    }



    template <typename T_y, 
              typename T_inv_scale, 
              class Policy>
    typename boost::math::tools::promote_args<T_y,T_inv_scale>::type
    exponential_cdf(const T_y& y, 
                  const T_inv_scale& beta, 
                  const Policy&) {

      static const char* function = "stan::prob::exponential_cdf(%1%)";

      using stan::math::check_finite;
      using stan::math::check_positive;
      using stan::math::check_not_nan;
      using boost::math::tools::promote_args;

      typename promote_args<T_y,T_inv_scale>::type lp;
      if(!check_not_nan(function, y, "Random variable", &lp, Policy()))
        return lp;
      if(!check_finite(function, beta, "Inverse scale parameter", &lp, Policy()))
        return lp;
      if(!check_positive(function, beta, "Inverse scale parameter", &lp, Policy()))
        return lp;
      
      if (y < 0)
        return 1.0;

      return 1.0 - exp(-beta * y);
    }

    template <typename T_y, 
              typename T_inv_scale>
    inline
    typename boost::math::tools::promote_args<T_y,T_inv_scale>::type
    exponential_cdf(const T_y& y, 
                  const T_inv_scale& beta) {
      return exponential_cdf(y,beta,stan::math::default_policy());
    }
    
    template <class RNG>
    inline double
    exponential_rng(const double beta,
                    RNG& rng) {
      using boost::variate_generator;
      using boost::exponential_distribution;
      variate_generator<RNG&, exponential_distribution<> >
       exp_rng(rng, exponential_distribution<>(beta));
      return exp_rng();
    }
  }
}

#endif