Stan Math Library  2.20.0
reverse mode automatic differentiation
falling_factorial.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_FALLING_FACTORIAL_HPP
3 
4 #include <stan/math/fwd/meta.hpp>
5 #include <stan/math/fwd/core.hpp>
6 
9 
10 namespace stan {
11 namespace math {
12 
26 template <typename T>
27 inline fvar<T> falling_factorial(const fvar<T>& x, int n) {
28  T falling_fact(falling_factorial(x.val_, n));
29  return fvar<T>(
30  falling_fact,
31  falling_fact * (digamma(x.val_ + 1) - digamma(x.val_ - n + 1)) * x.d_);
32 }
33 } // namespace math
34 } // namespace stan
35 #endif
T d_
The tangent (derivative) of this variable.
Definition: fvar.hpp:50
fvar< T > falling_factorial(const fvar< T > &x, int n)
Return autodiff variable with the gradient and result of the falling factorial function applied to th...
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

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