gamma_p.hpp

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#ifndef STAN_MATH_FWD_FUN_GAMMA_P_HPP
#define STAN_MATH_FWD_FUN_GAMMA_P_HPP
 
#include <stan/math/fwd/meta.hpp>
#include <stan/math/fwd/core.hpp>
#include <stan/math/fwd/fun/exp.hpp>
#include <stan/math/fwd/fun/lgamma.hpp>
#include <stan/math/fwd/fun/log.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/grad_reg_lower_inc_gamma.hpp>
#include <stan/math/prim/fun/gamma_p.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename T>
inline fvar<T> gamma_p(const fvar<T> &x1, const fvar<T> &x2) {
  T u = gamma_p(x1.val_, x2.val_);
  if (is_inf(x1.val_)) {
    return fvar<T>(u, NOT_A_NUMBER);
  }
  if (is_inf(x2.val_)) {
    return fvar<T>(u, NOT_A_NUMBER);
  }
 
  T der1 = grad_reg_lower_inc_gamma(x1.val_, x2.val_, 1.0e-10);
  T der2 = exp(-x2.val_ + (x1.val_ - 1.0) * log(x2.val_) - lgamma(x1.val_));
 
  return fvar<T>(u, x1.d_ * der1 + x2.d_ * der2);
}
 
template <typename T>
inline fvar<T> gamma_p(const fvar<T> &x1, double x2) {
  T u = gamma_p(x1.val_, x2);
  if (is_inf(x1.val_)) {
    return fvar<T>(u, NOT_A_NUMBER);
  }
  if (is_inf(x2)) {
    return fvar<T>(u, NOT_A_NUMBER);
  }
 
  T der1 = grad_reg_lower_inc_gamma(x1.val_, x2, 1.0e-10);
 
  return fvar<T>(u, x1.d_ * der1);
}
 
template <typename T>
inline fvar<T> gamma_p(double x1, const fvar<T> &x2) {
  T u = gamma_p(x1, x2.val_);
  if (is_inf(x1)) {
    return fvar<T>(u, NOT_A_NUMBER);
  }
 
  T der2 = exp(-x2.val_ + (x1 - 1.0) * log(x2.val_) - lgamma(x1));
 
  return fvar<T>(u, x2.d_ * der2);
}
 
}  // namespace math
}  // namespace stan
#endif