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reverse mode automatic differentiation
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log_rising_factorial.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_LOG_RISING_FACTORIAL_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_LOG_RISING_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
15  fvar<T>
16  log_rising_factorial(const fvar<T>& x, const fvar<T>& n) {
19 
21  (digamma(x.val_ + n.val_) * (x.d_ + n.d_)
22  - digamma(x.val_) * x.d_));
23  }
24 
25  template<typename T>
26  inline
27  fvar<T>
28  log_rising_factorial(const fvar<T>& x, const double n) {
31 
32  return fvar<T>(log_rising_factorial(x.val_, n),
33  (digamma(x.val_ + n) - digamma(x.val_)) * x.d_);
34  }
35 
36  template<typename T>
37  inline
38  fvar<T>
39  log_rising_factorial(const double x, const fvar<T>& n) {
42 
43  return fvar<T>(log_rising_factorial(x, n.val_),
44  (digamma(x + n.val_) * n.d_));
45  }
46  }
47 }
48 #endif
fvar< T > log_rising_factorial(const fvar< T > &x, const fvar< T > &n)
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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