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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/core.hpp>
5
6 #include <stan/math/prim/scal/fun/falling_factorial.hpp>
7 #include <boost/math/special_functions/digamma.hpp>
8
9 namespace stan {
10 namespace math {
11
12 template<typename T>
13 inline fvar<T>
14 falling_factorial(const fvar<T>& x, const fvar<T>& n) {
15 using boost::math::digamma;
16
17 T falling_fact(falling_factorial(x.val_, n.val_));
18 return fvar<T>(falling_fact,
19 falling_fact
20 * (digamma(x.val_ + 1) - digamma(x.val_ - n.val_ + 1))
21 * x.d_
22 + falling_fact
23 * digamma(x.val_ - n.val_ + 1) * n.d_);
24 }
25
26 template<typename T>
27 inline fvar<T>
28 falling_factorial(const fvar<T>& x, const double n) {
29 using boost::math::digamma;
30
31 T falling_fact(falling_factorial(x.val_, n));
32 return fvar<T>(falling_fact,
33 falling_fact
34 * (digamma(x.val_ + 1) - digamma(x.val_ - n + 1))
35 * x.d_);
36 }
37
38 template<typename T>
39 inline fvar<T>
40 falling_factorial(const double x, const fvar<T>& n) {
41 using boost::math::digamma;
42
43 T falling_fact(falling_factorial(x, n.val_));
44 return fvar<T>(falling_fact,
45 falling_fact
46 * digamma(x - n.val_ + 1) * n.d_);
47 }
48 }
49 }
50 #endif
falling_factorial.hpp
core.hpp
stan::math::fvar::d_
T d_
Definition: fvar.hpp:14
stan
Definition: log_sum_exp.hpp:8
stan::math::fvar::val_
T val_
Definition: fvar.hpp:13
stan::math::falling_factorial
fvar< T > falling_factorial(const fvar< T > &x, const fvar< T > &n)
Definition: falling_factorial.hpp:14
stan::math::fvar
Definition: fvar.hpp:12
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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