1 #ifndef STAN_MATH_FWD_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
3
4 #include <stan/math/fwd/core.hpp>
5
6 #include <boost/math/special_functions/digamma.hpp>
7 #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
8
9 namespace stan {
10 namespace math {
11
12 template <typename T>
binomial_coefficient_log(const fvar<T> & x1,const fvar<T> & x2)13 inline fvar<T> binomial_coefficient_log(const fvar<T>& x1, const fvar<T>& x2) {
14 using boost::math::digamma;
15 using std::log;
16 const double cutoff = 1000;
17 if ((x1.val_ < cutoff) || (x1.val_ - x2.val_ < cutoff)) {
18 return fvar<T>(binomial_coefficient_log(x1.val_, x2.val_),
19 x1.d_ * digamma(x1.val_ + 1) - x2.d_ * digamma(x2.val_ + 1)
20 - (x1.d_ - x2.d_) * digamma(x1.val_ - x2.val_ + 1));
21 } else {
22 return fvar<T>(
23 binomial_coefficient_log(x1.val_, x2.val_),
24 x2.d_ * log(x1.val_ - x2.val_)
25 + x2.val_ * (x1.d_ - x2.d_) / (x1.val_ - x2.val_)
26 + x1.d_ * log(x1.val_ / (x1.val_ - x2.val_))
27 + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2.val_))
28 * (x1.d_ * (x1.val_ - x2.val_) - (x1.d_ - x2.d_) * x1.val_)
29 / ((x1.val_ - x2.val_) * (x1.val_ - x2.val_))
30 - x1.d_ / (12.0 * x1.val_ * x1.val_) - x2.d_
31 + (x1.d_ - x2.d_)
32 / (12.0 * (x1.val_ - x2.val_) * (x1.val_ - x2.val_))
33 - digamma(x2.val_ + 1) * x2.d_);
34 }
35 }
36
37 template <typename T>
binomial_coefficient_log(const fvar<T> & x1,double x2)38 inline fvar<T> binomial_coefficient_log(const fvar<T>& x1, double x2) {
39 using boost::math::digamma;
40 using std::log;
41 const double cutoff = 1000;
42 if ((x1.val_ < cutoff) || (x1.val_ - x2 < cutoff)) {
43 return fvar<T>(
44 binomial_coefficient_log(x1.val_, x2),
45 x1.d_ * digamma(x1.val_ + 1) - x1.d_ * digamma(x1.val_ - x2 + 1));
46 } else {
47 return fvar<T>(binomial_coefficient_log(x1.val_, x2),
48 x2 * x1.d_ / (x1.val_ - x2)
49 + x1.d_ * log(x1.val_ / (x1.val_ - x2))
50 + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2))
51 * (x1.d_ * (x1.val_ - x2) - x1.d_ * x1.val_)
52 / ((x1.val_ - x2) * (x1.val_ - x2))
53 - x1.d_ / (12.0 * x1.val_ * x1.val_)
54 + x1.d_ / (12.0 * (x1.val_ - x2) * (x1.val_ - x2)));
55 }
56 }
57
58 template <typename T>
binomial_coefficient_log(double x1,const fvar<T> & x2)59 inline fvar<T> binomial_coefficient_log(double x1, const fvar<T>& x2) {
60 using boost::math::digamma;
61 using std::log;
62 const double cutoff = 1000;
63 if ((x1 < cutoff) || (x1 - x2.val_ < cutoff)) {
64 return fvar<T>(
65 binomial_coefficient_log(x1, x2.val_),
66 -x2.d_ * digamma(x2.val_ + 1) - x2.d_ * digamma(x1 - x2.val_ + 1));
67 } else {
68 return fvar<T>(binomial_coefficient_log(x1, x2.val_),
69 x2.d_ * log(x1 - x2.val_) + x2.val_ * -x2.d_ / (x1 - x2.val_)
70 - x2.d_
71 - x2.d_ / (12.0 * (x1 - x2.val_) * (x1 - x2.val_))
72 + x2.d_ * (x1 + 0.5) / (x1 - x2.val_)
73 - digamma(x2.val_ + 1) * x2.d_);
74 }
75 }
76 } // namespace math
77 } // namespace stan
78 #endif
79