gamma_p.hpp

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#ifndef STAN__AGRAD__REV__FUNCTIONS__GAMMA_P_HPP
#define STAN__AGRAD__REV__FUNCTIONS__GAMMA_P_HPP

#include <valarray>
#include <stan/agrad/rev/var.hpp>
#include <stan/agrad/rev/internal/vv_vari.hpp>
#include <stan/agrad/rev/internal/dv_vari.hpp>
#include <stan/agrad/rev/internal/vd_vari.hpp>
#include <stan/math/functions/gamma_p.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/math/special_functions/digamma.hpp>

namespace stan {
  namespace agrad {

    namespace {
      class gamma_p_vv_vari : public op_vv_vari {
      public:
        gamma_p_vv_vari(vari* avi, vari* bvi) :
          op_vv_vari(stan::math::gamma_p(avi->val_,bvi->val_),
                     avi,bvi) {
        }
        void chain() {

          double u = stan::math::gamma_p(avi_->val_, bvi_->val_);
      
          double S = 0.0;
          double s = 1.0;
          double l = std::log(bvi_->val_);
          double g = boost::math::tgamma(avi_->val_);
          double dig = boost::math::digamma(avi_->val_);
      
          int k = 0;
          double delta = s / (avi_->val_ * avi_->val_);
      
          while (std::fabs(delta) > 1e-6) {
            S += delta;
            ++k;
            s *= -bvi_->val_ / k;
            delta = s / ((k + avi_->val_) * (k + avi_->val_));
          }
          

          avi_->adj_ -= adj_ * ((u) * ( dig - l ) + std::exp( avi_->val_ * l ) * S / g);
          bvi_->adj_ += adj_ * (std::exp(-bvi_->val_) * std::pow(bvi_->val_, avi_->val_ - 1.0) / g);
        }
      };

      class gamma_p_vd_vari : public op_vd_vari {
      public:
        gamma_p_vd_vari(vari* avi, double b) :
          op_vd_vari(stan::math::gamma_p(avi->val_,b),
                     avi,b) {
        }
        void chain() {

          double u = stan::math::gamma_p(avi_->val_, bd_);
      
          double S = 0.0;
          double s = 1.0;
          double l = std::log(bd_);
          double g = boost::math::tgamma(avi_->val_);
          double dig = boost::math::digamma(avi_->val_);
      
          int k = 0;
          double delta = s / (avi_->val_ * avi_->val_);
      
          while (std::fabs(delta) > 1e-6) {
            S += delta;
            ++k;
            s *= -bd_ / k;
            delta = s / ((k + avi_->val_) * (k + avi_->val_));
          }

          avi_->adj_ -= adj_ * ((u) * ( dig - l ) + std::exp( avi_->val_ * l ) * S / g);
        }
      };

      class gamma_p_dv_vari : public op_dv_vari {
      public:
        gamma_p_dv_vari(double a, vari* bvi) :
          op_dv_vari(stan::math::gamma_p(a,bvi->val_),
                     a,bvi) {
        }
        void chain() {
          bvi_->adj_ += adj_ * (std::exp(-bvi_->val_) * std::pow(bvi_->val_, ad_ - 1.0) / boost::math::tgamma(ad_));     
        }
      };
    }

    inline var gamma_p(const stan::agrad::var& a,
                       const stan::agrad::var& b) {
      return var(new gamma_p_vv_vari(a.vi_,b.vi_));
    }

    inline var gamma_p(const stan::agrad::var& a,
                       const double& b) {
      return var(new gamma_p_vd_vari(a.vi_,b));
    }

    inline var gamma_p(const double& a,
                       const stan::agrad::var& b) {
      return var(new gamma_p_dv_vari(a,b.vi_));
    }

  }
}
#endif