Stan Math Library  2.11.0
reverse mode automatic differentiation
binomial_coefficient_log.hpp
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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>
8 
9 namespace stan {
10 
11  namespace math {
12 
13  template <typename T>
14  inline
15  fvar<T>
16  binomial_coefficient_log(const fvar<T>& x1, const fvar<T>& x2) {
18  using std::log;
20  const double cutoff = 1000;
21  if ((x1.val_ < cutoff) || (x1.val_ - x2.val_ < cutoff)) {
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 {
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_)
33  - (x1.d_ - x2.d_) * x1.val_)
34  / ((x1.val_ - x2.val_) * (x1.val_ - x2.val_))
35  - x1.d_ / (12.0 * x1.val_ * x1.val_)
36  - x2.d_
37  + (x1.d_ - x2.d_) / (12.0 * (x1.val_ - x2.val_)
38  * (x1.val_ - x2.val_))
39  - digamma(x2.val_ + 1) * x2.d_);
40  }
41  }
42 
43  template <typename T>
44  inline
45  fvar<T>
46  binomial_coefficient_log(const fvar<T>& x1, const double x2) {
48  using std::log;
50  const double cutoff = 1000;
51  if ((x1.val_ < cutoff) || (x1.val_ - x2 < cutoff)) {
52  return fvar<T>(binomial_coefficient_log(x1.val_, x2),
53  x1.d_ * digamma(x1.val_ + 1)
54  - x1.d_ * digamma(x1.val_ - x2 + 1));
55  } else {
56  return fvar<T>(binomial_coefficient_log(x1.val_, x2),
57  x2 * x1.d_ / (x1.val_ - x2)
58  + x1.d_ * log(x1.val_ / (x1.val_ - x2))
59  + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2))
60  * (x1.d_ * (x1.val_ - x2) - x1.d_ * x1.val_)
61  / ((x1.val_ - x2) * (x1.val_ - x2))
62  - x1.d_ / (12.0 * x1.val_ * x1.val_)
63  + x1.d_ / (12.0 * (x1.val_ - x2) * (x1.val_ - x2)));
64  }
65  }
66 
67  template <typename T>
68  inline
69  fvar<T>
70  binomial_coefficient_log(const double x1, const fvar<T>& x2) {
72  using std::log;
74  const double cutoff = 1000;
75  if ((x1 < cutoff) || (x1 - x2.val_ < cutoff)) {
76  return fvar<T>(binomial_coefficient_log(x1, x2.val_),
77  -x2.d_ * digamma(x2.val_ + 1)
78  - x2.d_ * digamma(x1 - x2.val_ + 1));
79  } else {
80  return fvar<T>(binomial_coefficient_log(x1, x2.val_),
81  x2.d_ * log(x1 - x2.val_)
82  + x2.val_ * -x2.d_ / (x1 - x2.val_)
83  - x2.d_
84  - x2.d_ / (12.0 * (x1 - x2.val_) * (x1 - x2.val_))
85  + x2.d_ * (x1 + 0.5) / (x1 - x2.val_)
86  - digamma(x2.val_ + 1) * x2.d_);
87  }
88  }
89  }
90 }
91 #endif
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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