Stan Math Library  2.12.0
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  namespace math {
11 
12  template <typename T>
13  inline
14  fvar<T>
15  binomial_coefficient_log(const fvar<T>& x1, const fvar<T>& x2) {
17  using std::log;
18  const double cutoff = 1000;
19  if ((x1.val_ < cutoff) || (x1.val_ - x2.val_ < cutoff)) {
21  x1.d_ * digamma(x1.val_ + 1)
22  - x2.d_ * digamma(x2.val_ + 1)
23  - (x1.d_ - x2.d_) * digamma(x1.val_ - x2.val_ + 1));
24  } else {
26  x2.d_ * log(x1.val_ - x2.val_)
27  + x2.val_ * (x1.d_ - x2.d_) / (x1.val_ - x2.val_)
28  + x1.d_ * log(x1.val_ / (x1.val_ - x2.val_))
29  + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2.val_))
30  * (x1.d_ * (x1.val_ - x2.val_)
31  - (x1.d_ - x2.d_) * x1.val_)
32  / ((x1.val_ - x2.val_) * (x1.val_ - x2.val_))
33  - x1.d_ / (12.0 * x1.val_ * x1.val_)
34  - x2.d_
35  + (x1.d_ - x2.d_) / (12.0 * (x1.val_ - x2.val_)
36  * (x1.val_ - x2.val_))
37  - digamma(x2.val_ + 1) * x2.d_);
38  }
39  }
40 
41  template <typename T>
42  inline
43  fvar<T>
44  binomial_coefficient_log(const fvar<T>& x1, const double x2) {
46  using std::log;
47  const double cutoff = 1000;
48  if ((x1.val_ < cutoff) || (x1.val_ - x2 < cutoff)) {
49  return fvar<T>(binomial_coefficient_log(x1.val_, x2),
50  x1.d_ * digamma(x1.val_ + 1)
51  - x1.d_ * digamma(x1.val_ - x2 + 1));
52  } else {
53  return fvar<T>(binomial_coefficient_log(x1.val_, x2),
54  x2 * x1.d_ / (x1.val_ - x2)
55  + x1.d_ * log(x1.val_ / (x1.val_ - x2))
56  + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2))
57  * (x1.d_ * (x1.val_ - x2) - x1.d_ * x1.val_)
58  / ((x1.val_ - x2) * (x1.val_ - x2))
59  - x1.d_ / (12.0 * x1.val_ * x1.val_)
60  + x1.d_ / (12.0 * (x1.val_ - x2) * (x1.val_ - x2)));
61  }
62  }
63 
64  template <typename T>
65  inline
66  fvar<T>
67  binomial_coefficient_log(const double x1, const fvar<T>& x2) {
69  using std::log;
70  const double cutoff = 1000;
71  if ((x1 < cutoff) || (x1 - x2.val_ < cutoff)) {
72  return fvar<T>(binomial_coefficient_log(x1, x2.val_),
73  -x2.d_ * digamma(x2.val_ + 1)
74  - x2.d_ * digamma(x1 - x2.val_ + 1));
75  } else {
76  return fvar<T>(binomial_coefficient_log(x1, x2.val_),
77  x2.d_ * log(x1 - x2.val_)
78  + x2.val_ * -x2.d_ / (x1 - x2.val_)
79  - x2.d_
80  - x2.d_ / (12.0 * (x1 - x2.val_) * (x1 - x2.val_))
81  + x2.d_ * (x1 + 0.5) / (x1 - x2.val_)
82  - digamma(x2.val_ + 1) * x2.d_);
83  }
84  }
85  }
86 }
87 #endif
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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