Stan Math Library  2.20.0
reverse mode automatic differentiation
log_falling_factorial.hpp
Go to the documentation of this file.
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/meta.hpp>
5 #include <stan/math/fwd/core.hpp>
6 
8 #include <boost/math/special_functions/digamma.hpp>
9 
10 namespace stan {
11 namespace math {
12 
13 template <typename T>
14 inline fvar<T> log_falling_factorial(const fvar<T>& x, const fvar<T>& n) {
16 
18  (digamma(x.val_ + 1) - digamma(x.val_ - n.val_ + 1)) * x.d_
19  + digamma(x.val_ - n.val_ + 1) * n.d_);
20 }
21 
22 template <typename T>
23 inline fvar<T> log_falling_factorial(double x, const fvar<T>& n) {
25 
26  return fvar<T>(log_falling_factorial(x, n.val_),
27  digamma(x - n.val_ + 1) * n.d_);
28 }
29 
30 template <typename T>
31 inline fvar<T> log_falling_factorial(const fvar<T>& x, double n) {
33 
34  return fvar<T>(log_falling_factorial(x.val_, n),
35  (digamma(x.val_ + 1) - digamma(x.val_ - n + 1)) * x.d_);
36 }
37 } // namespace math
38 } // namespace stan
39 #endif
fvar< T > log_falling_factorial(const fvar< T > &x, const fvar< T > &n)
T d_
The tangent (derivative) of this variable.
Definition: fvar.hpp:50
T val_
The value of this variable.
Definition: fvar.hpp:45
This template class represents scalars used in forward-mode automatic differentiation, which consist of values and directional derivatives of the specified template type.
Definition: fvar.hpp:41
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

     [ Stan Home Page ] © 2011–2018, Stan Development Team.