Stan Math Library  2.14.0
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  namespace math {
11 
12  template<typename T>
13  inline fvar<T>
14  falling_factorial(const fvar<T>& x, const fvar<T>& n) {
16 
17  T falling_fact(falling_factorial(x.val_, n.val_));
18  return fvar<T>(falling_fact,
19  falling_fact
20  * (digamma(x.val_ + 1) - digamma(x.val_ - n.val_ + 1))
21  * x.d_
22  + falling_fact
23  * digamma(x.val_ - n.val_ + 1) * n.d_);
24  }
25 
26  template<typename T>
27  inline fvar<T>
28  falling_factorial(const fvar<T>& x, double n) {
30 
31  T falling_fact(falling_factorial(x.val_, n));
32  return fvar<T>(falling_fact,
33  falling_fact
34  * (digamma(x.val_ + 1) - digamma(x.val_ - n + 1))
35  * x.d_);
36  }
37 
38  template<typename T>
39  inline fvar<T>
40  falling_factorial(double x, const fvar<T>& n) {
42 
43  T falling_fact(falling_factorial(x, n.val_));
44  return fvar<T>(falling_fact,
45  falling_fact
46  * digamma(x - n.val_ + 1) * n.d_);
47  }
48  }
49 }
50 #endif
fvar< T > falling_factorial(const fvar< T > &x, const fvar< T > &n)
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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