Stan Math Library  2.10.0
reverse mode automatic differentiation
falling_factorial.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
3 
4 #include <stan/math/fwd/core.hpp>
5 
7 #include <boost/math/special_functions/digamma.hpp>
8 
9 namespace stan {
10 
11  namespace math {
12 
13  template<typename T>
14  inline fvar<T>
15  falling_factorial(const fvar<T>& x, const fvar<T>& n) {
18 
19  T falling_fact(falling_factorial(x.val_, n.val_));
20  return fvar<T>(falling_fact,
21  falling_fact
22  * (digamma(x.val_ + 1) - digamma(x.val_ - n.val_ + 1))
23  * x.d_
24  + falling_fact
25  * digamma(x.val_ - n.val_ + 1) * n.d_);
26  }
27 
28  template<typename T>
29  inline fvar<T>
30  falling_factorial(const fvar<T>& x, const double n) {
33 
34  T falling_fact(falling_factorial(x.val_, n));
35  return fvar<T>(falling_fact,
36  falling_fact
37  * (digamma(x.val_ + 1) - digamma(x.val_ - n + 1))
38  * x.d_);
39  }
40 
41  template<typename T>
42  inline fvar<T>
43  falling_factorial(const double x, const fvar<T>& n) {
46 
47  T falling_fact(falling_factorial(x, n.val_));
48  return fvar<T>(falling_fact,
49  falling_fact
50  * digamma(x - n.val_ + 1) * n.d_);
51  }
52  }
53 }
54 #endif
fvar< T > falling_factorial(const fvar< T > &x, const fvar< T > &n)
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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