Stan Math Library  2.11.0
reverse mode automatic differentiation
log_falling_factorial.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_LOG_FALLING_FACTORIAL_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_LOG_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  log_falling_factorial(const fvar<T>& x, const fvar<T>& n) {
18 
20  (digamma(x.val_ + 1)
21  - digamma(x.val_ - n.val_ + 1)) * x.d_
22  + digamma(x.val_ - n.val_ + 1) * n.d_);
23  }
24 
25  template<typename T>
26  inline fvar<T>
27  log_falling_factorial(const double x, const fvar<T>& n) {
30 
31  return fvar<T>(log_falling_factorial(x, n.val_),
32  digamma(x - n.val_ + 1) * n.d_);
33  }
34 
35  template<typename T>
36  inline fvar<T>
37  log_falling_factorial(const fvar<T>& x, const double n) {
40 
41  return fvar<T>(log_falling_factorial(x.val_, n),
42  (digamma(x.val_ + 1)
43  - digamma(x.val_ - n + 1)) * x.d_);
44  }
45  }
46 }
47 #endif
fvar< T > log_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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