pow.hpp

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#ifndef STAN__AGRAD__FWD__FUNCTIONS__POW_HPP
#define STAN__AGRAD__FWD__FUNCTIONS__POW_HPP

#include <stan/agrad/fwd/fvar.hpp>
#include <stan/meta/traits.hpp>
#include <stan/agrad/fwd/functions/inv.hpp>
#include <stan/agrad/fwd/functions/inv_sqrt.hpp>
#include <stan/agrad/fwd/functions/inv_square.hpp>

namespace stan {

  namespace agrad {

    template <typename T>
    inline
    fvar<T>
    pow(const fvar<T>& x1, const fvar<T>& x2) {
      using std::pow;
      using std::log;
      T pow_x1_x2(pow(x1.val_,x2.val_));
      return fvar<T>(pow_x1_x2,
                     (x2.d_ * log(x1.val_) 
                      + x2.val_ * x1.d_ / x1.val_) * pow_x1_x2);
    }

    template <typename T>
    inline
    fvar<T>
    pow(const double x1, const fvar<T>& x2) {
      using std::pow;
      using std::log;
      T u = pow(x1,x2.val_);
      return fvar<T>(u, x2.d_ * log(x1) * u);
    }

    template <typename T>
    inline
    fvar<T>
    pow(const fvar<T>& x1, const double x2) {
      using std::pow;
      using stan::agrad::inv;
      using stan::agrad::inv_sqrt;
      using stan::agrad::inv_square;
      using std::sqrt;
      using stan::math::square;

      if (x2 == -2)
        return inv_square(x1);
      if (x2 == -1)
        return inv(x1);
      if (x2 == -0.5)
        return inv_sqrt(x1);
      if (x2 == 0.5)
        return sqrt(x1);
      if (x2 == 1.0)
        return x1;
      if (x2 == 2.0)
        return square(x1);

      return fvar<T>(pow(x1.val_, x2),
                     x1.d_ * x2 * pow(x1.val_, x2 - 1));
    }
  }
}
#endif