Stan Math Library  2.20.0
reverse mode automatic differentiation
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/meta.hpp>
5 #include <stan/math/fwd/core.hpp>
8 
9 namespace stan {
10 namespace math {
11 
12 template <typename T>
13 inline fvar<T> log_rising_factorial(const fvar<T>& x, const fvar<T>& n) {
14  return fvar<T>(
16  digamma(x.val_ + n.val_) * (x.d_ + n.d_) - digamma(x.val_) * x.d_);
17 }
18 
19 template <typename T>
20 inline fvar<T> log_rising_factorial(const fvar<T>& x, double n) {
21  return fvar<T>(log_rising_factorial(x.val_, n),
22  (digamma(x.val_ + n) - digamma(x.val_)) * x.d_);
23 }
24 
25 template <typename T>
26 inline fvar<T> log_rising_factorial(double x, const fvar<T>& n) {
27  return fvar<T>(log_rising_factorial(x, n.val_), digamma(x + n.val_) * n.d_);
28 }
29 
30 } // namespace math
31 } // namespace stan
32 #endif
T d_
The tangent (derivative) of this variable.
Definition: fvar.hpp:50
T val_
The value of this variable.
Definition: fvar.hpp:45
fvar< T > log_rising_factorial(const fvar< T > &x, const fvar< T > &n)
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

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