Stan Math Library  2.11.0
reverse mode automatic differentiation
owens_t.hpp
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1 #ifndef STAN_MATH_REV_SCAL_FUN_OWENS_T_HPP
2 #define STAN_MATH_REV_SCAL_FUN_OWENS_T_HPP
3 
4 #include <math.h>
5 #include <stan/math/rev/core.hpp>
8 #include <boost/math/special_functions/owens_t.hpp>
9 #include <cmath>
10 
11 #ifdef _MSC_VER
12 #include <boost/math/special_functions/erf.hpp>
13 using boost::math::erf;
14 #endif
15 
16 namespace stan {
17  namespace math {
18 
19  namespace {
20  class owens_t_vv_vari : public op_vv_vari {
21  public:
22  owens_t_vv_vari(vari* avi, vari* bvi) :
23  op_vv_vari(boost::math::owens_t(avi->val_, bvi->val_), avi, bvi) {
24  }
25  void chain() {
26  const double neg_avi_sq_div_2 = -square(avi_->val_) * 0.5;
27  const double one_p_bvi_sq = 1.0 + square(bvi_->val_);
28 
29  avi_->adj_ += adj_ * ::erf(bvi_->val_ * avi_->val_ * INV_SQRT_2)
30  * std::exp(neg_avi_sq_div_2) * INV_SQRT_TWO_PI * -0.5;
31  bvi_->adj_ += adj_ * std::exp(neg_avi_sq_div_2 * one_p_bvi_sq)
32  / (one_p_bvi_sq * 2.0 * pi());
33  }
34  };
35 
36  class owens_t_vd_vari : public op_vd_vari {
37  public:
38  owens_t_vd_vari(vari* avi, double b) :
39  op_vd_vari(boost::math::owens_t(avi->val_, b), avi, b) {
40  }
41  void chain() {
42  avi_->adj_ += adj_ * ::erf(bd_ * avi_->val_ * INV_SQRT_2)
43  * std::exp(-square(avi_->val_) * 0.5)
44  * INV_SQRT_TWO_PI * -0.5;
45  }
46  };
47 
48  class owens_t_dv_vari : public op_dv_vari {
49  public:
50  owens_t_dv_vari(double a, vari* bvi) :
51  op_dv_vari(boost::math::owens_t(a, bvi->val_), a, bvi) {
52  }
53  void chain() {
54  const double one_p_bvi_sq = 1.0 + square(bvi_->val_);
55  bvi_->adj_ += adj_ * std::exp(-0.5 * square(ad_) * one_p_bvi_sq)
56  / (one_p_bvi_sq * 2.0 * pi());
57  }
58  };
59  }
60 
71  inline var owens_t(const var& h, const var& a) {
72  return var(new owens_t_vv_vari(h.vi_, a.vi_));
73  }
74 
85  inline var owens_t(const var& h, double a) {
86  return var(new owens_t_vd_vari(h.vi_, a));
87  }
88 
99  inline var owens_t(double h, const var& a) {
100  return var(new owens_t_dv_vari(h, a.vi_));
101  }
102 
103  }
104 }
105 #endif
const double INV_SQRT_TWO_PI
Definition: constants.hpp:166
Reimplementing boost functionality.
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:31
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Definition: owens_t.hpp:14
const double INV_SQRT_2
The value of 1 over the square root of 2, .
Definition: constants.hpp:27
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
vari * vi_
Pointer to the implementation of this variable.
Definition: var.hpp:43
double pi()
Return the value of pi.
Definition: constants.hpp:86

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