normal.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__NORMAL_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__NORMAL_HPP__
 
#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.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_loc, typename T_scale,
              class Policy>
    typename return_type<T_y,T_loc,T_scale>::type
    normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
               const Policy& /*policy*/) {
      static const char* function = "stan::prob::normal_log(%1%)";
 
      using std::log;
      using stan::is_constant_struct;
      using stan::math::check_positive;
      using stan::math::check_finite;
      using stan::math::check_not_nan;
      using stan::math::check_consistent_sizes;
      using stan::math::value_of;
      using stan::prob::include_summand;
 
      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(mu) 
            && stan::length(sigma)))
        return 0.0;
 
      // set up return value accumulator
      double logp(0.0);
 
      // validate args (here done over var, which should be OK)
      if (!check_not_nan(function, y, "Random variable", &logp, Policy()))
        return logp;
      if (!check_finite(function, mu, "Location parameter", 
                        &logp, Policy()))
        return logp;
      if (!check_positive(function, sigma, "Scale parameter", 
                          &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   y,mu,sigma,
                                   "Random variable","Location parameter","Scale parameter",
                                   &logp, Policy())))
        return logp;
 
      // check if no variables are involved and prop-to
      if (!include_summand<propto,T_y,T_loc,T_scale>::value)
        return 0.0;
      
      // set up template expressions wrapping scalars into vector views
      agrad::OperandsAndPartials<T_y, T_loc, T_scale> operands_and_partials(y, mu, sigma);
 
      VectorView<const T_y> y_vec(y);
      VectorView<const T_loc> mu_vec(mu);
      VectorView<const T_scale> sigma_vec(sigma);
      size_t N = max_size(y, mu, sigma);
 
      DoubleVectorView<true,T_scale> inv_sigma(length(sigma));
      DoubleVectorView<include_summand<propto,T_scale>::value,T_scale> log_sigma(length(sigma));
      for (size_t i = 0; i < length(sigma); i++) {
        inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
        if (include_summand<propto,T_scale>::value)
          log_sigma[i] = log(value_of(sigma_vec[i]));
      }
 
      for (size_t n = 0; n < N; n++) {
        // pull out values of arguments
        const double y_dbl = value_of(y_vec[n]);
        const double mu_dbl = value_of(mu_vec[n]);
      
        // reusable subexpression values
        const double y_minus_mu_over_sigma 
          = (y_dbl - mu_dbl) * inv_sigma[n];
        const double y_minus_mu_over_sigma_squared 
          = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
 
        static double NEGATIVE_HALF = - 0.5;
 
        // log probability
        if (include_summand<propto>::value)
          logp += NEG_LOG_SQRT_TWO_PI;
        if (include_summand<propto,T_scale>::value)
          logp -= log_sigma[n];
        if (include_summand<propto,T_y,T_loc,T_scale>::value)
          logp += NEGATIVE_HALF * y_minus_mu_over_sigma_squared;
 
        // gradients
        double scaled_diff = inv_sigma[n] * y_minus_mu_over_sigma;
        if (!is_constant_struct<T_y>::value)
          operands_and_partials.d_x1[n] -= scaled_diff;
        if (!is_constant_struct<T_loc>::value)
          operands_and_partials.d_x2[n] += scaled_diff;
        if (!is_constant_struct<T_scale>::value)
          operands_and_partials.d_x3[n] 
            += -inv_sigma[n] + inv_sigma[n] * y_minus_mu_over_sigma_squared;
      }
      return operands_and_partials.to_var(logp);
    }
 
 
    template <bool propto,
              typename T_y, typename T_loc, typename T_scale>
    inline
    typename return_type<T_y,T_loc,T_scale>::type
    normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
      return normal_log<propto>(y,mu,sigma,stan::math::default_policy());
    }
 
    template <typename T_y, typename T_loc, typename T_scale, 
              class Policy>
    inline
    typename return_type<T_y,T_loc,T_scale>::type
    normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma, 
               const Policy&) {
      return normal_log<false>(y,mu,sigma,Policy());
    }
 
    template <typename T_y, typename T_loc, typename T_scale>
    inline
    typename return_type<T_y,T_loc,T_scale>::type
    normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
      return normal_log<false>(y,mu,sigma,stan::math::default_policy());
    }
 
 
    template <typename T_y, typename T_loc, typename T_scale,
              class Policy>
    typename return_type<T_y,T_loc,T_scale>::type
    normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma, 
             const Policy&) {
      static const char* function = "stan::prob::normal_cdf(%1%)";
 
      using stan::math::check_positive;
      using stan::math::check_finite;
      using stan::math::check_not_nan;
      using stan::math::check_consistent_sizes;
 
      typename return_type<T_y, T_loc, T_scale>::type cdf(1);
      if (!check_not_nan(function, y, "Random variable", &cdf, Policy()))
        return cdf;
      if (!check_finite(function, mu, "Location parameter", &cdf, Policy()))
        return cdf;
      if (!check_not_nan(function, sigma, "Scale parameter", 
                         &cdf, Policy()))
        return cdf;
      if (!check_positive(function, sigma, "Scale parameter", 
                          &cdf, Policy()))
        return cdf;
      if (!(check_consistent_sizes(function,
                                   y,mu,sigma,
                                   "Random variable","Location parameter","Scale parameter",
                                   &cdf, Policy())))
        return cdf;
 
      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(mu) 
            && stan::length(sigma)))
        return 0.0;
 
      VectorView<const T_y> y_vec(y);
      VectorView<const T_loc> mu_vec(mu);
      VectorView<const T_scale> sigma_vec(sigma);
      size_t N = max_size(y, mu, sigma);
      
      for (size_t n = 0; n < N; n++) {
        cdf *= 0.5 + 0.5 * erf((y_vec[n] - mu_vec[n]) / (sigma_vec[n] * SQRT_2));
      }
      return cdf;
    }
 
    template <typename T_y, typename T_loc, typename T_scale>
    inline
    typename return_type<T_y, T_loc, T_scale>::type
    normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
      return normal_cdf(y,mu,sigma,stan::math::default_policy());
    }
 
 
    template <typename T_loc, typename T_scale, class RNG>
    inline double
    normal_random(const T_loc& mu, const T_scale& sigma, RNG& rng) {
      using boost::variate_generator;
      using boost::normal_distribution;
      using stan::math::value_of;
      variate_generator<RNG&, normal_distribution<> >
        rng_unit_norm(rng, normal_distribution<>());
      return value_of(mu)  + value_of(sigma) * rng_unit_norm();
    }
  }
}
#endif