Stan Math Library  2.20.0
reverse mode automatic differentiation
lbeta.hpp
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1 #ifndef STAN_MATH_REV_SCAL_FUN_LBETA_HPP
2 #define STAN_MATH_REV_SCAL_FUN_LBETA_HPP
3 
4 #include <stan/math/rev/meta.hpp>
5 #include <stan/math/rev/core.hpp>
8 
9 namespace stan {
10 namespace math {
11 
12 namespace internal {
13 class lbeta_vv_vari : public op_vv_vari {
14  public:
15  lbeta_vv_vari(vari* avi, vari* bvi)
16  : op_vv_vari(lbeta(avi->val_, bvi->val_), avi, bvi) {}
17  void chain() {
18  const double digamma_ab = digamma(avi_->val_ + bvi_->val_);
19  avi_->adj_ += adj_ * (digamma(avi_->val_) - digamma_ab);
20 
21  bvi_->adj_ += adj_ * (digamma(bvi_->val_) - digamma_ab);
22  }
23 };
24 
25 class lbeta_vd_vari : public op_vd_vari {
26  public:
27  lbeta_vd_vari(vari* avi, double b)
28  : op_vd_vari(lbeta(avi->val_, b), avi, b) {}
29  void chain() {
30  avi_->adj_ += adj_ * (digamma(avi_->val_) - digamma(avi_->val_ + bd_));
31  }
32 };
33 
34 class lbeta_dv_vari : public op_dv_vari {
35  public:
36  lbeta_dv_vari(double a, vari* bvi)
37  : op_dv_vari(lbeta(a, bvi->val_), a, bvi) {}
38  void chain() {
39  bvi_->adj_ += adj_ * (digamma(bvi_->val_) - digamma(ad_ + bvi_->val_));
40  }
41 };
42 } // namespace internal
43 
44 /*
45  * Returns the natural logarithm of the beta function and its gradients.
46  *
47  \f[
48  \mathrm{lbeta}(a,b) = \ln\left(B\left(a,b\right)\right)
49  \f]
50 
51  \f[
52  \frac{\partial }{\partial a} = \psi^{\left(0\right)}\left(a\right)
53  - \psi^{\left(0\right)}\left(a + b\right)
54  \f]
55 
56  \f[
57  \frac{\partial }{\partial b} = \psi^{\left(0\right)}\left(b\right)
58  - \psi^{\left(0\right)}\left(a + b\right)
59  \f]
60  * @param a var Argument
61  * @param b var Argument
62  * @return Result of log beta function
63  */
64 inline var lbeta(const var& a, const var& b) {
65  return var(new internal::lbeta_vv_vari(a.vi_, b.vi_));
66 }
67 
68 /*
69  * Returns the natural logarithm of the beta function and its gradients.
70  *
71  \f[
72  \mathrm{lbeta}(a,b) = \ln\left(B\left(a,b\right)\right)
73  \f]
74 
75  \f[
76  \frac{\partial }{\partial a} = \psi^{\left(0\right)}\left(a\right)
77  - \psi^{\left(0\right)}\left(a + b\right)
78  \f]
79  * @param a var Argument
80  * @param b double Argument
81  * @return Result of log beta function
82  */
83 inline var lbeta(const var& a, double b) {
84  return var(new internal::lbeta_vd_vari(a.vi_, b));
85 }
86 
87 /*
88  * Returns the natural logarithm of the beta function and its gradients.
89  *
90  \f[
91  \mathrm{lbeta}(a,b) = \ln\left(B\left(a,b\right)\right)
92  \f]
93 
94  \f[
95  \frac{\partial }{\partial b} = \psi^{\left(0\right)}\left(b\right)
96  - \psi^{\left(0\right)}\left(a + b\right)
97  \f]
98  * @param a double Argument
99  * @param b var Argument
100  * @return Result of log beta function
101  */
102 inline var lbeta(double a, const var& b) {
103  return var(new internal::lbeta_dv_vari(a, b.vi_));
104 }
105 
106 } // namespace math
107 } // namespace stan
108 #endif
void chain()
Apply the chain rule to this variable based on the variables on which it depends. ...
Definition: lbeta.hpp:17
void chain()
Apply the chain rule to this variable based on the variables on which it depends. ...
Definition: lbeta.hpp:38
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:14
lbeta_dv_vari(double a, vari *bvi)
Definition: lbeta.hpp:36
The variable implementation base class.
Definition: vari.hpp:30
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:33
friend class var
Definition: vari.hpp:32
const double val_
The value of this variable.
Definition: vari.hpp:38
void chain()
Apply the chain rule to this variable based on the variables on which it depends. ...
Definition: lbeta.hpp:29
lbeta_vv_vari(vari *avi, vari *bvi)
Definition: lbeta.hpp:15
vari * vi_
Pointer to the implementation of this variable.
Definition: var.hpp:45
double adj_
The adjoint of this variable, which is the partial derivative of this variable with respect to the ro...
Definition: vari.hpp:44
lbeta_vd_vari(vari *avi, double b)
Definition: lbeta.hpp:27
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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