pareto.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__PARETO_HPP__
#define __STAN__PROB__DISTRIBUTIONS__PARETO_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 {

    // Pareto(y|y_m,alpha)  [y > y_m;  y_m > 0;  alpha > 0]
    template <bool propto,
              typename T_y, typename T_scale, typename T_shape, 
              class Policy>
    typename return_type<T_y,T_scale,T_shape>::type
    pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha, 
               const Policy&) {
      static const char* function = "stan::prob::pareto_log(%1%)";
      
      using stan::math::value_of;
      using stan::math::check_finite;
      using stan::math::check_positive;
      using stan::math::check_not_nan;
      using stan::math::check_consistent_sizes;

      
      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(y_min) 
            && stan::length(alpha)))
        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, y_min, "Scale parameter",
                        &logp, Policy()))
        return logp;
      if (!check_positive(function, y_min, "Scale parameter", 
                          &logp, Policy()))
        return logp;
      if (!check_finite(function, alpha, "Shape parameter", 
                        &logp, Policy()))
        return logp;
      if (!check_positive(function, alpha, "Shape parameter", 
                          &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   y,y_min,alpha,
                                   "Random variable","Scale parameter","Shape parameter",
                                   &logp, Policy())))
        return logp;

      // check if no variables are involved and prop-to
      if (!include_summand<propto,T_y,T_scale,T_shape>::value)
        return 0.0;
      
      VectorView<const T_y> y_vec(y);
      VectorView<const T_scale> y_min_vec(y_min);
      VectorView<const T_shape> alpha_vec(alpha);
      size_t N = max_size(y, y_min, alpha);

      for (size_t n = 0; n < N; n++) {
        if (y_vec[n] < y_min_vec[n])
          return LOG_ZERO;
      }

      // set up template expressions wrapping scalars into vector views
      agrad::OperandsAndPartials<T_y,T_scale,T_shape> operands_and_partials(y, y_min, alpha);
      
      DoubleVectorView<include_summand<propto,T_y,T_shape>::value,T_y> log_y(length(y));
      if (include_summand<propto,T_y,T_shape>::value)
        for (size_t n = 0; n < length(y); n++)
          log_y[n] = log(value_of(y_vec[n]));
      DoubleVectorView<!is_constant_struct<T_y>::value||!is_constant_struct<T_shape>::value,T_y> inv_y(length(y));
      if (!is_constant_struct<T_y>::value||!is_constant_struct<T_shape>::value)
        for (size_t n = 0; n < length(y); n++)
          inv_y[n] = 1 / value_of(y_vec[n]);
      DoubleVectorView<include_summand<propto,T_scale,T_shape>::value,T_scale> 
        log_y_min(length(y_min));
      if (include_summand<propto,T_scale,T_shape>::value)
        for (size_t n = 0; n < length(y_min); n++)
          log_y_min[n] = log(value_of(y_min_vec[n]));
      DoubleVectorView<include_summand<propto,T_shape>::value,T_shape> log_alpha(length(alpha));
      if (include_summand<propto,T_shape>::value)
        for (size_t n = 0; n < length(alpha); n++)
          log_alpha[n] = log(value_of(alpha_vec[n]));
      
      DoubleVectorView<!is_constant_struct<T_shape>::value,T_shape> inv_alpha(length(alpha));
      if (!is_constant_struct<T_shape>::value)
        for (size_t n = 0; n < length(alpha); n++)
          inv_alpha[n] = 1 / value_of(alpha_vec[n]);
      
      using stan::math::multiply_log;

      for (size_t n = 0; n < N; n++) {
        const double alpha_dbl = value_of(alpha_vec[n]);
        // log probability
        if (include_summand<propto,T_shape>::value)
          logp += log_alpha[n];
        if (include_summand<propto,T_scale,T_shape>::value)
          logp += alpha_dbl * log_y_min[n];
        if (include_summand<propto,T_y,T_shape>::value)
          logp -= alpha_dbl * log_y[n] + log_y[n];
        
        // gradients
        if (!is_constant_struct<T_y>::value)
          operands_and_partials.d_x1[n] -= alpha_dbl * inv_y[n] + inv_y[n];
        if (!is_constant_struct<T_scale>::value)
          operands_and_partials.d_x2[n] += alpha_dbl / value_of(y_min_vec[n]);
        if (!is_constant_struct<T_shape>::value)
          operands_and_partials.d_x3[n] += 1 / alpha_dbl + log_y_min[n] - log_y[n];
      }
      return operands_and_partials.to_var(logp);
    }


    template <bool propto,
              typename T_y, typename T_scale, typename T_shape>
    inline
    typename return_type<T_y,T_scale,T_shape>::type
    pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
      return pareto_log<propto>(y,y_min,alpha,stan::math::default_policy());
    }

    template <typename T_y, typename T_scale, typename T_shape, 
              class Policy>
    inline
    typename return_type<T_y,T_scale,T_shape>::type
    pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha, 
               const Policy&) {
      return pareto_log<false>(y,y_min,alpha,Policy());
    }

    template <typename T_y, typename T_scale, typename T_shape>
    inline
    typename return_type<T_y,T_scale,T_shape>::type
    pareto_log(const T_y& y, const T_scale& y_min, const T_shape& alpha) {
      return pareto_log<false>(y,y_min,alpha,stan::math::default_policy());
    }


  }
}
#endif