Stan Math Library  2.20.0
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/meta.hpp>
5 #include <stan/math/fwd/core.hpp>
6 
7 #include <boost/math/special_functions/digamma.hpp>
9 
10 namespace stan {
11 namespace math {
12 
13 template <typename T>
14 inline fvar<T> binomial_coefficient_log(const fvar<T>& x1, const fvar<T>& x2) {
16  using std::log;
17  const double cutoff = 1000;
18  if ((x1.val_ < cutoff) || (x1.val_ - x2.val_ < cutoff)) {
20  x1.d_ * digamma(x1.val_ + 1) - x2.d_ * digamma(x2.val_ + 1)
21  - (x1.d_ - x2.d_) * digamma(x1.val_ - x2.val_ + 1));
22  } else {
23  return fvar<T>(
25  x2.d_ * log(x1.val_ - x2.val_)
26  + x2.val_ * (x1.d_ - x2.d_) / (x1.val_ - x2.val_)
27  + x1.d_ * log(x1.val_ / (x1.val_ - x2.val_))
28  + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2.val_))
29  * (x1.d_ * (x1.val_ - x2.val_) - (x1.d_ - x2.d_) * x1.val_)
30  / ((x1.val_ - x2.val_) * (x1.val_ - x2.val_))
31  - x1.d_ / (12.0 * x1.val_ * x1.val_) - x2.d_
32  + (x1.d_ - x2.d_)
33  / (12.0 * (x1.val_ - x2.val_) * (x1.val_ - x2.val_))
34  - digamma(x2.val_ + 1) * x2.d_);
35  }
36 }
37 
38 template <typename T>
39 inline fvar<T> binomial_coefficient_log(const fvar<T>& x1, double x2) {
41  using std::log;
42  const double cutoff = 1000;
43  if ((x1.val_ < cutoff) || (x1.val_ - x2 < cutoff)) {
44  return fvar<T>(
46  x1.d_ * digamma(x1.val_ + 1) - x1.d_ * digamma(x1.val_ - x2 + 1));
47  } else {
48  return fvar<T>(binomial_coefficient_log(x1.val_, x2),
49  x2 * x1.d_ / (x1.val_ - x2)
50  + x1.d_ * log(x1.val_ / (x1.val_ - x2))
51  + (x1.val_ + 0.5) / (x1.val_ / (x1.val_ - x2))
52  * (x1.d_ * (x1.val_ - x2) - x1.d_ * x1.val_)
53  / ((x1.val_ - x2) * (x1.val_ - x2))
54  - x1.d_ / (12.0 * x1.val_ * x1.val_)
55  + x1.d_ / (12.0 * (x1.val_ - x2) * (x1.val_ - x2)));
56  }
57 }
58 
59 template <typename T>
60 inline fvar<T> binomial_coefficient_log(double x1, const fvar<T>& x2) {
62  using std::log;
63  const double cutoff = 1000;
64  if ((x1 < cutoff) || (x1 - x2.val_ < cutoff)) {
65  return fvar<T>(
67  -x2.d_ * digamma(x2.val_ + 1) - x2.d_ * digamma(x1 - x2.val_ + 1));
68  } else {
69  return fvar<T>(binomial_coefficient_log(x1, x2.val_),
70  x2.d_ * log(x1 - x2.val_) + x2.val_ * -x2.d_ / (x1 - x2.val_)
71  - x2.d_
72  - x2.d_ / (12.0 * (x1 - x2.val_) * (x1 - x2.val_))
73  + x2.d_ * (x1 + 0.5) / (x1 - x2.val_)
74  - digamma(x2.val_ + 1) * x2.d_);
75  }
76 }
77 } // namespace math
78 } // namespace stan
79 #endif
T d_
The tangent (derivative) of this variable.
Definition: fvar.hpp:50
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
T val_
The value of this variable.
Definition: fvar.hpp:45
This template class represents scalars used in forward-mode automatic differentiation, which consist of values and directional derivatives of the specified template type.
Definition: fvar.hpp:41
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

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