beta.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__BETA_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__BETA_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_scale_succ, typename T_scale_fail,
              class Policy>
    typename return_type<T_y,T_scale_succ,T_scale_fail>::type
    beta_log(const T_y& y, const T_scale_succ& alpha, const T_scale_fail& beta, 
             const Policy&) {
      static const char* function = "stan::prob::beta_log(%1%)";

      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::multiply_log;
      using stan::math::log1m;
      using stan::math::value_of;
      using stan::prob::include_summand;
      using boost::math::digamma;

      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(alpha) 
            && stan::length(beta)))
        return 0.0;

      // set up return value accumulator
      double logp(0.0);
      
      // validate args (here done over var, which should be OK)
      if (!check_finite(function, alpha,
                        "First shape parameter",
                        &logp, Policy()))
        return logp;
      if (!check_positive(function, alpha, 
                          "First shape parameter",
                          &logp, Policy()))
        return logp;
      if (!check_finite(function, beta, 
                          "Second shape parameter",
                          &logp, Policy()))
        return logp;
      if (!check_positive(function, beta, 
                          "Second shape parameter",
                          &logp, Policy()))
        return logp;
      if (!check_not_nan(function, y, "Random variable", &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   y,alpha,beta,
                                   "Random variable","First shape parameter","Second shape parameter",
                                   &logp, Policy())))
        return logp;

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

      VectorView<const T_y> y_vec(y);
      VectorView<const T_scale_succ> alpha_vec(alpha);
      VectorView<const T_scale_fail> beta_vec(beta);
      size_t N = max_size(y, alpha, beta);

      for (size_t n = 0; n < N; n++) {
        const double y_dbl = value_of(y_vec[n]);
        if (y_dbl < 0 || y_dbl > 1)
          return LOG_ZERO;
      }

      // set up template expressions wrapping scalars into vector views
      agrad::OperandsAndPartials<T_y, T_scale_succ, T_scale_fail> operands_and_partials(y, alpha, beta);


      DoubleVectorView<include_summand<propto,T_y,T_scale_succ>::value,T_y> log_y(length(y));
      DoubleVectorView<include_summand<propto,T_y,T_scale_fail>::value,T_y> log1m_y(length(y));
      
      for (size_t n = 0; n < length(y); n++) {
        if (include_summand<propto,T_y,T_scale_succ>::value)
          log_y[n] = log(value_of(y_vec[n]));
        if (include_summand<propto,T_y,T_scale_fail>::value)
          log1m_y[n] = log1m(value_of(y_vec[n]));
      }

    DoubleVectorView<include_summand<propto,T_scale_succ>::value,T_scale_succ> lgamma_alpha(length(alpha));
      DoubleVectorView<!is_constant_struct<T_scale_succ>::value,T_scale_succ> digamma_alpha(length(alpha));
      for (size_t n = 0; n < length(alpha); n++) {
        if (include_summand<propto,T_scale_succ>::value) 
          lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
        if (!is_constant_struct<T_scale_succ>::value)
          digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
      }


      DoubleVectorView<include_summand<propto,T_scale_fail>::value,T_scale_fail> lgamma_beta(length(beta));
      DoubleVectorView<!is_constant_struct<T_scale_fail>::value,T_scale_fail> digamma_beta(length(beta));
      for (size_t n = 0; n < length(beta); n++) {
        if (include_summand<propto,T_scale_fail>::value) 
          lgamma_beta[n] = lgamma(value_of(beta_vec[n]));
        if (!is_constant_struct<T_scale_fail>::value)
          digamma_beta[n] = digamma(value_of(beta_vec[n]));
      }

      DoubleVectorView<include_summand<propto,T_scale_succ,T_scale_fail>::value,
        double,
        is_vector<T_scale_succ>::value||is_vector<T_scale_fail>::value>
        lgamma_alpha_beta(max_size(alpha,beta));
      DoubleVectorView<!is_constant_struct<T_scale_succ>::value||!is_constant_struct<T_scale_fail>::value,
        double,
        is_vector<T_scale_succ>::value||is_vector<T_scale_fail>::value>
        digamma_alpha_beta(max_size(alpha,beta));
      for (size_t n = 0; n < max_size(alpha,beta); n++) {
        const double alpha_beta = value_of(alpha_vec[n]) + value_of(beta_vec[n]);
        if (include_summand<propto,T_scale_succ,T_scale_fail>::value)
          lgamma_alpha_beta[n] = lgamma(alpha_beta);
        if (!is_constant_struct<T_scale_succ>::value||!is_constant_struct<T_scale_fail>::value)
          digamma_alpha_beta[n] = digamma(alpha_beta);
      }

      for (size_t n = 0; n < N; n++) {
        // pull out values of arguments
        const double y_dbl = value_of(y_vec[n]);
        const double alpha_dbl = value_of(alpha_vec[n]);
        const double beta_dbl = value_of(beta_vec[n]);

        // log probability
        if (include_summand<propto,T_scale_succ,T_scale_fail>::value)
          logp += lgamma_alpha_beta[n];
        if (include_summand<propto,T_scale_succ>::value)
          logp -= lgamma_alpha[n];
        if (include_summand<propto,T_scale_fail>::value)
          logp -= lgamma_beta[n];
        if (include_summand<propto,T_y,T_scale_succ>::value)
          logp += (alpha_dbl-1.0) * log_y[n];
        if (include_summand<propto,T_y,T_scale_fail>::value)
          logp += (beta_dbl-1.0) * log1m_y[n];

        // gradients
        if (!is_constant_struct<T_y>::value)
          operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl + (beta_dbl-1)/(y_dbl-1);
        if (!is_constant_struct<T_scale_succ>::value)
          operands_and_partials.d_x2[n] += log_y[n] + digamma_alpha_beta[n] - digamma_alpha[n];
        if (!is_constant_struct<T_scale_fail>::value)
          operands_and_partials.d_x3[n] += log1m_y[n] + digamma_alpha_beta[n] - digamma_beta[n];
      }
      return operands_and_partials.to_var(logp);
    }

    template <bool propto,
              typename T_y, typename T_scale_succ, typename T_scale_fail>
    inline 
    typename return_type<T_y,T_scale_succ,T_scale_fail>::type
    beta_log(const T_y& y, const T_scale_succ& alpha, const T_scale_fail& beta) {
      return beta_log<propto>(y,alpha,beta,stan::math::default_policy());
    }

    template <typename T_y, typename T_scale_succ, typename T_scale_fail,
              class Policy>
    typename return_type<T_y,T_scale_succ,T_scale_fail>::type
    beta_log(const T_y& y, const T_scale_succ& alpha, const T_scale_fail& beta, 
             const Policy&) {
      return beta_log<false>(y,alpha,beta,Policy());
    }

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

    
    template <typename T_y, typename T_scale_succ, typename T_scale_fail,
              class Policy>
    typename return_type<T_y,T_scale_succ,T_scale_fail>::type
    beta_cdf(const T_y& y, const T_scale_succ& alpha, const T_scale_fail& beta, 
             const Policy&) {
      static const char* function = "stan::prob::beta_cdf(%1%)";

      using stan::math::check_positive;
      using stan::math::check_finite;
      using stan::math::check_not_nan;
      using boost::math::tools::promote_args;
      
      typename promote_args<T_y,T_scale_succ,T_scale_fail>::type lp;
      if (!check_finite(function, alpha,
                        "First shape parameter",
                        &lp, Policy()))
        return lp;
      if (!check_positive(function, alpha, 
                          "First shape parameter",
                          &lp, Policy()))
        return lp;
      if (!check_finite(function, beta, 
                          "Second shape parameter",
                          &lp, Policy()))
        return lp;
      if (!check_positive(function, beta, 
                          "Second shape parameter",
                          &lp, Policy()))
        return lp;
      if (!check_not_nan(function, y, "Random variable", &lp, Policy()))
        return lp;
      
      if (y < 0.0)
        return 0;
      if (y > 1.0)
        return 1.0;
      
      return stan::math::ibeta(alpha, beta, y);
    }

    template <typename T_y, typename T_scale_succ, typename T_scale_fail>
    typename return_type<T_y,T_scale_succ,T_scale_fail>::type
    beta_cdf(const T_y& y, const T_scale_succ& alpha, const T_scale_fail& beta) {
      return beta_cdf(y,alpha,beta,stan::math::default_policy());
    }
  }
}
#endif