Stan Math Library  2.14.0
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 <stan/math/rev/core.hpp>
9 #include <cmath>
10 
11 namespace stan {
12  namespace math {
13 
14  namespace {
15  class owens_t_vv_vari : public op_vv_vari {
16  public:
17  owens_t_vv_vari(vari* avi, vari* bvi) :
18  op_vv_vari(owens_t(avi->val_, bvi->val_), avi, bvi) {
19  }
20  void chain() {
21  const double neg_avi_sq_div_2 = -square(avi_->val_) * 0.5;
22  const double one_p_bvi_sq = 1.0 + square(bvi_->val_);
23 
24  avi_->adj_ += adj_ * erf(bvi_->val_ * avi_->val_ * INV_SQRT_2)
25  * std::exp(neg_avi_sq_div_2) * INV_SQRT_TWO_PI * -0.5;
26  bvi_->adj_ += adj_ * std::exp(neg_avi_sq_div_2 * one_p_bvi_sq)
27  / (one_p_bvi_sq * 2.0 * pi());
28  }
29  };
30 
31  class owens_t_vd_vari : public op_vd_vari {
32  public:
33  owens_t_vd_vari(vari* avi, double b) :
34  op_vd_vari(owens_t(avi->val_, b), avi, b) {
35  }
36  void chain() {
37  avi_->adj_ += adj_ * erf(bd_ * avi_->val_ * INV_SQRT_2)
38  * std::exp(-square(avi_->val_) * 0.5)
39  * INV_SQRT_TWO_PI * -0.5;
40  }
41  };
42 
43  class owens_t_dv_vari : public op_dv_vari {
44  public:
45  owens_t_dv_vari(double a, vari* bvi) :
46  op_dv_vari(owens_t(a, bvi->val_), a, bvi) {
47  }
48  void chain() {
49  const double one_p_bvi_sq = 1.0 + square(bvi_->val_);
50  bvi_->adj_ += adj_ * std::exp(-0.5 * square(ad_) * one_p_bvi_sq)
51  / (one_p_bvi_sq * 2.0 * pi());
52  }
53  };
54  }
55 
66  inline var owens_t(const var& h, const var& a) {
67  return var(new owens_t_vv_vari(h.vi_, a.vi_));
68  }
69 
80  inline var owens_t(const var& h, double a) {
81  return var(new owens_t_vd_vari(h.vi_, a));
82  }
83 
94  inline var owens_t(double h, const var& a) {
95  return var(new owens_t_dv_vari(h, a.vi_));
96  }
97 
98  }
99 }
100 #endif
const double INV_SQRT_TWO_PI
Definition: constants.hpp:164
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:30
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:14
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Return Owen&#39;s T function applied to the specified arguments.
Definition: owens_t.hpp:23
const double INV_SQRT_2
The value of 1 over the square root of 2, .
Definition: constants.hpp:26
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
vari * vi_
Pointer to the implementation of this variable.
Definition: var.hpp:42
double pi()
Return the value of pi.
Definition: constants.hpp:85

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