Stan Math Library  2.12.0
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  namespace math {
11 
12  template<typename T>
13  inline fvar<T>
14  log_falling_factorial(const fvar<T>& x, const fvar<T>& n) {
16 
18  (digamma(x.val_ + 1)
19  - digamma(x.val_ - n.val_ + 1)) * x.d_
20  + digamma(x.val_ - n.val_ + 1) * n.d_);
21  }
22 
23  template<typename T>
24  inline fvar<T>
25  log_falling_factorial(const double x, const fvar<T>& n) {
27 
28  return fvar<T>(log_falling_factorial(x, n.val_),
29  digamma(x - n.val_ + 1) * n.d_);
30  }
31 
32  template<typename T>
33  inline fvar<T>
34  log_falling_factorial(const fvar<T>& x, const double n) {
36 
37  return fvar<T>(log_falling_factorial(x.val_, n),
38  (digamma(x.val_ + 1)
39  - digamma(x.val_ - n + 1)) * x.d_);
40  }
41  }
42 }
43 #endif
fvar< T > log_falling_factorial(const fvar< T > &x, const fvar< T > &n)
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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