Stan Math Library  2.20.0
reverse mode automatic differentiation
beta.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_BETA_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_BETA_HPP
3 
4 #include <stan/math/fwd/meta.hpp>
5 #include <stan/math/fwd/core.hpp>
8 
9 namespace stan {
10 namespace math {
11 
50 template <typename T>
51 inline fvar<T> beta(const fvar<T>& x1, const fvar<T>& x2) {
52  const T beta_ab = beta(x1.val_, x2.val_);
53  return fvar<T>(beta_ab,
54  beta_ab
55  * (x1.d_ * digamma(x1.val_) + x2.d_ * digamma(x2.val_)
56  - (x1.d_ + x2.d_) * digamma(x1.val_ + x2.val_)));
57 }
58 
59 template <typename T>
60 inline fvar<T> beta(double x1, const fvar<T>& x2) {
61  const T beta_ab = beta(x1, x2.val_);
62  return fvar<T>(beta_ab,
63  x2.d_ * (digamma(x2.val_) - digamma(x1 + x2.val_)) * beta_ab);
64 }
65 
66 template <typename T>
67 inline fvar<T> beta(const fvar<T>& x1, double x2) {
68  const T beta_ab = beta(x1.val_, x2);
69  return fvar<T>(beta_ab,
70  x1.d_ * (digamma(x1.val_) - digamma(x1.val_ + x2)) * beta_ab);
71 }
72 } // namespace math
73 } // namespace stan
74 #endif
T d_
The tangent (derivative) of this variable.
Definition: fvar.hpp:50
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
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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