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reverse mode automatic differentiation
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rising_factorial.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_RISING_FACTORIAL_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_RISING_FACTORIAL_HPP
3 
4 #include <stan/math/fwd/core.hpp>
7 #include <iostream>
8 
9 namespace stan {
10 
11  namespace math {
12 
13  template<typename T>
14  inline
15  fvar<T>
16  rising_factorial(const fvar<T>& x, const fvar<T>& n) {
18 
19  T rising_fact(rising_factorial(x.val_, n.val_));
20  return fvar<T>(rising_fact,
21  rising_fact * (digamma(x.val_ + n.val_)
22  * (x.d_ + n.d_) - digamma(x.val_) * x.d_));
23  }
24 
25  template<typename T>
26  inline
27  fvar<T>
28  rising_factorial(const fvar<T>& x, const double n) {
31 
32  T rising_fact(rising_factorial(x.val_, n));
33  return fvar<T>(rising_fact,
34  rising_fact * x.d_
35  * (digamma(x.val_ + n) - digamma(x.val_)));
36  }
37 
38  template<typename T>
39  inline
40  fvar<T>
41  rising_factorial(const double x, const fvar<T>& n) {
44 
45  T rising_fact(rising_factorial(x, n.val_));
46  return fvar<T>(rising_fact,
47  rising_fact * (digamma(x + n.val_) * n.d_));
48  }
49  }
50 }
51 #endif
fvar< T > rising_factorial(const fvar< T > &x, const fvar< T > &n)
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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