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binomial_coefficient_log.hpp
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1 #ifndef STAN__AGRAD__FWD__FUNCTIONS__BINOMIAL_COEFFICIENT_LOG_HPP
2 #define STAN__AGRAD__FWD__FUNCTIONS__BINOMIAL_COEFFICIENT_LOG_HPP
3 
4 #include <stan/agrad/fwd/fvar.hpp>
5 #include <stan/meta/traits.hpp>
6 #include <boost/math/special_functions/digamma.hpp>
7 #include <stan/math/functions/binomial_coefficient_log.hpp>
8 
9 namespace stan {
10 
11  namespace agrad {
12 
13  template <typename T>
14  inline
15  fvar<T>
16  binomial_coefficient_log(const fvar<T>& x1, const fvar<T>& x2) {
17  using boost::math::digamma;
18  using std::log;
19  using stan::math::binomial_coefficient_log;
20  const double cutoff = 1000;
21  if ((x1.val_ < cutoff) || (x1.val_ - x2.val_ < cutoff)) {
22  return fvar<T>(binomial_coefficient_log(x1.val_, x2.val_),
23  x1.d_ * digamma(x1.val_ + 1)
24  - x2.d_ * digamma(x2.val_ + 1)
25  - (x1.d_ - x2.d_) * digamma(x1.val_ - x2.val_ + 1));
26  } else {
27  return fvar<T>(binomial_coefficient_log(x1.val_, x2.val_),
28  x2.d_ * log(x1.val_ - x2.val_)
29  + x2.val_ * (x1.d_ - x2.d_) / (x1.val_ - x2.val_)
30  + x1.d_ * log(x1.val_ / (x1.val_ - x2.val_))
31  + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2.val_))
32  * (x1.d_ * (x1.val_ - x2.val_) - (x1.d_ - x2.d_) * x1.val_)
33  / ((x1.val_ - x2.val_) * (x1.val_ - x2.val_))
34  - x1.d_ / (12.0 * x1.val_ * x1.val_)
35  - x2.d_
36  + (x1.d_ - x2.d_) / (12.0 * (x1.val_ - x2.val_)
37  * (x1.val_ - x2.val_))
38  - digamma(x2.val_ + 1) * x2.d_);
39  }
40  }
41 
42  template <typename T>
43  inline
44  fvar<T>
45  binomial_coefficient_log(const fvar<T>& x1, const double x2) {
46  using boost::math::digamma;
47  using std::log;
48  using stan::math::binomial_coefficient_log;
49  const double cutoff = 1000;
50  if ((x1.val_ < cutoff) || (x1.val_ - x2 < cutoff)) {
51  return fvar<T>(binomial_coefficient_log(x1.val_, x2),
52  x1.d_ * digamma(x1.val_ + 1)
53  - x1.d_ * digamma(x1.val_ - x2 + 1));
54  } else {
55  return fvar<T>(binomial_coefficient_log(x1.val_, x2),
56  x2 * x1.d_ / (x1.val_ - x2)
57  + x1.d_ * log(x1.val_ / (x1.val_ - x2))
58  + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2))
59  * (x1.d_ * (x1.val_ - x2) - x1.d_ * x1.val_)
60  / ((x1.val_ - x2) * (x1.val_ - x2))
61  - x1.d_ / (12.0 * x1.val_ * x1.val_)
62  + x1.d_ / (12.0 * (x1.val_ - x2) * (x1.val_ - x2)));
63  }
64  }
65 
66  template <typename T>
67  inline
68  fvar<T>
69  binomial_coefficient_log(const double x1, const fvar<T>& x2) {
70  using boost::math::digamma;
71  using std::log;
72  using stan::math::binomial_coefficient_log;
73  const double cutoff = 1000;
74  if ((x1 < cutoff) || (x1 - x2.val_ < cutoff)) {
75  return fvar<T>(binomial_coefficient_log(x1, x2.val_),
76  -x2.d_ * digamma(x2.val_ + 1)
77  - x2.d_ * digamma(x1 - x2.val_ + 1));
78  } else {
79  return fvar<T>(binomial_coefficient_log(x1, x2.val_),
80  x2.d_ * log(x1 - x2.val_)
81  + x2.val_ * -x2.d_ / (x1 - x2.val_)
82  - x2.d_
83  - x2.d_ / (12.0 * (x1 - x2.val_) * (x1 - x2.val_))
84  + x2.d_ * (x1 + 0.5) / (x1 - x2.val_)
85  - digamma(x2.val_ + 1) * x2.d_);
86  }
87  }
88  }
89 }
90 #endif
stan::math::binomial_coefficient_log
boost::math::tools::promote_args< T_N, T_n >::type binomial_coefficient_log(const T_N N, const T_n n)
Return the log of the binomial coefficient for the specified arguments.
Definition: binomial_coefficient_log.hpp:63
stan::agrad::binomial_coefficient_log
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: binomial_coefficient_log.hpp:16
stan::agrad::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16
binomial_coefficient_log.hpp
stan::agrad::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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