Stan Math Library  2.12.0
reverse mode automatic differentiation
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  namespace math {
11 
12  template<typename T>
13  inline
14  fvar<T>
15  rising_factorial(const fvar<T>& x, const fvar<T>& n) {
16  T rising_fact(rising_factorial(x.val_, n.val_));
17  return fvar<T>(rising_fact,
18  rising_fact * (digamma(x.val_ + n.val_)
19  * (x.d_ + n.d_) - digamma(x.val_) * x.d_));
20  }
21 
22  template<typename T>
23  inline
24  fvar<T>
25  rising_factorial(const fvar<T>& x, const double n) {
27 
28  T rising_fact(rising_factorial(x.val_, n));
29  return fvar<T>(rising_fact,
30  rising_fact * x.d_
31  * (digamma(x.val_ + n) - digamma(x.val_)));
32  }
33 
34  template<typename T>
35  inline
36  fvar<T>
37  rising_factorial(const double x, const fvar<T>& n) {
39 
40  T rising_fact(rising_factorial(x, n.val_));
41  return fvar<T>(rising_fact,
42  rising_fact * (digamma(x + n.val_) * n.d_));
43  }
44  }
45 }
46 #endif
fvar< T > rising_factorial(const fvar< T > &x, const fvar< T > &n)
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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