Stan Math Library  2.20.0
reverse mode automatic differentiation
beta.hpp
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1 #ifndef STAN_MATH_REV_SCAL_FUN_BETA_HPP
2 #define STAN_MATH_REV_SCAL_FUN_BETA_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 beta_vv_vari : public op_vv_vari {
14  public:
15  beta_vv_vari(vari* avi, vari* bvi)
16  : op_vv_vari(beta(avi->val_, bvi->val_), avi, bvi) {}
17  void chain() {
18  const double adj_val = this->adj_ * this->val_;
19  const double digamma_ab = digamma(avi_->val_ + bvi_->val_);
20  avi_->adj_ += adj_val * (digamma(avi_->val_) - digamma_ab);
21 
22  bvi_->adj_ += adj_val * (digamma(bvi_->val_) - digamma_ab);
23  }
24 };
25 
26 class beta_vd_vari : public op_vd_vari {
27  public:
28  beta_vd_vari(vari* avi, double b) : op_vd_vari(beta(avi->val_, b), avi, b) {}
29  void chain() {
30  avi_->adj_ += adj_ * (digamma(avi_->val_) - digamma(avi_->val_ + bd_))
31  * this->val_;
32  }
33 };
34 
35 class beta_dv_vari : public op_dv_vari {
36  public:
37  beta_dv_vari(double a, vari* bvi) : op_dv_vari(beta(a, bvi->val_), a, bvi) {}
38  void chain() {
39  bvi_->adj_ += adj_ * (digamma(bvi_->val_) - digamma(ad_ + bvi_->val_))
40  * this->val_;
41  }
42 };
43 } // namespace internal
44 /*
45  * Returns the beta function and gradients for two var inputs.
46  *
47  \f[
48  \mathrm{beta}(a,b) = \left(B\left(a,b\right)\right)
49  \f]
50 
51  \f[
52  \frac{\partial }{\partial a} = \left(\psi^{\left(0\right)}\left(a\right)
53  - \psi^{\left(0\right)}
54  \left(a + b\right)\right)
55  * \mathrm{beta}(a,b)
56  \f]
57 
58  \f[
59  \frac{\partial }{\partial b} = \left(\psi^{\left(0\right)}\left(b\right)
60  - \psi^{\left(0\right)}
61  \left(a + b\right)\right)
62  * \mathrm{beta}(a,b)
63  \f]
64  *
65  * @param a var Argument
66  * @param b var Argument
67  * @return Result of beta function
68  */
69 inline var beta(const var& a, const var& b) {
70  return var(new internal::beta_vv_vari(a.vi_, b.vi_));
71 }
72 
73 /*
74  * Returns the beta function and gradient for first var input.
75  *
76  \f[
77  \mathrm{beta}(a,b) = \left(B\left(a,b\right)\right)
78  \f]
79 
80  \f[
81  \frac{\partial }{\partial a} = \left(\psi^{\left(0\right)}\left(a\right)
82  - \psi^{\left(0\right)}
83  \left(a + b\right)\right)
84  * \mathrm{beta}(a,b)
85  \f]
86  *
87  * @param a var Argument
88  * @param b double Argument
89  * @return Result of beta function
90  */
91 inline var beta(const var& a, double b) {
92  return var(new internal::beta_vd_vari(a.vi_, b));
93 }
94 
95 /*
96  * Returns the beta function and gradient for second var input.
97  *
98  \f[
99  \mathrm{beta}(a,b) = \left(B\left(a,b\right)\right)
100  \f]
101 
102  \f[
103  \frac{\partial }{\partial b} = \left(\psi^{\left(0\right)}\left(b\right)
104  - \psi^{\left(0\right)}
105  \left(a + b\right)\right)
106  * \mathrm{beta}(a,b)
107  \f]
108  *
109  * @param a double Argument
110  * @param b var Argument
111  * @return Result of beta function
112  */
113 inline var beta(double a, const var& b) {
114  return var(new internal::beta_dv_vari(a, b.vi_));
115 }
116 
117 } // namespace math
118 } // namespace stan
119 #endif
The variable implementation base class.
Definition: vari.hpp:30
beta_vd_vari(vari *avi, double b)
Definition: beta.hpp:28
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
beta_dv_vari(double a, vari *bvi)
Definition: beta.hpp:37
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
vari * vi_
Pointer to the implementation of this variable.
Definition: var.hpp:45
void chain()
Apply the chain rule to this variable based on the variables on which it depends. ...
Definition: beta.hpp:29
void chain()
Apply the chain rule to this variable based on the variables on which it depends. ...
Definition: beta.hpp:17
void chain()
Apply the chain rule to this variable based on the variables on which it depends. ...
Definition: beta.hpp:38
double adj_
The adjoint of this variable, which is the partial derivative of this variable with respect to the ro...
Definition: vari.hpp:44
beta_vv_vari(vari *avi, vari *bvi)
Definition: beta.hpp:15
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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