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reverse mode automatic differentiation
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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) * x.d_ - digamma(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) {
28 
29  return fvar<T>(log_falling_factorial(x, n.val_),
30  -digamma(n.val_ + 1) * n.d_);
31  }
32 
33  template<typename T>
34  inline fvar<T>
35  log_falling_factorial(const fvar<T>& x, const double n) {
38 
39  return fvar<T>(log_falling_factorial(x.val_, n),
40  digamma(x.val_ + 1) * x.d_);
41  }
42  }
43 }
44 #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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