Stan Math Library  2.12.0
reverse mode automatic differentiation
gamma_p.hpp
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1 #ifndef STAN_MATH_REV_SCAL_FUN_GAMMA_P_HPP
2 #define STAN_MATH_REV_SCAL_FUN_GAMMA_P_HPP
3 
4 #include <stan/math/rev/core.hpp>
6 #include <boost/math/special_functions/gamma.hpp>
7 #include <boost/math/special_functions/digamma.hpp>
8 #include <valarray>
9 
10 namespace stan {
11  namespace math {
12 
13  namespace {
14  class gamma_p_vv_vari : public op_vv_vari {
15  public:
16  gamma_p_vv_vari(vari* avi, vari* bvi) :
17  op_vv_vari(gamma_p(avi->val_, bvi->val_),
18  avi, bvi) {
19  }
20  void chain() {
21  // return zero derivative as gamma_p is flat
22  // to machine precision for b / a > 10
23  if (std::fabs(bvi_->val_ / avi_->val_) > 10 ) return;
24 
25  double u = gamma_p(avi_->val_, bvi_->val_);
26 
27  double S = 0.0;
28  double s = 1.0;
29  double l = std::log(bvi_->val_);
30  double g = boost::math::tgamma(avi_->val_);
31  double dig = boost::math::digamma(avi_->val_);
32 
33  int k = 0;
34  double delta = s / (avi_->val_ * avi_->val_);
35 
36  while (std::fabs(delta) > 1e-6) {
37  S += delta;
38  ++k;
39  s *= -bvi_->val_ / k;
40  delta = s / ((k + avi_->val_) * (k + avi_->val_));
41  }
42 
43  avi_->adj_ -= adj_ * ((u) * (dig - l)
44  + std::exp(avi_->val_ * l) * S / g);
45  bvi_->adj_ += adj_ * (std::exp(-bvi_->val_)
46  * std::pow(bvi_->val_, avi_->val_ - 1.0) / g);
47  }
48  };
49 
50  class gamma_p_vd_vari : public op_vd_vari {
51  public:
52  gamma_p_vd_vari(vari* avi, double b) :
53  op_vd_vari(gamma_p(avi->val_, b),
54  avi, b) {
55  }
56  void chain() {
57  // return zero derivative as gamma_p is flat
58  // to machine precision for b / a > 10
59  if (std::fabs(bd_ / avi_->val_) > 10)
60  return;
61 
62  double u = gamma_p(avi_->val_, bd_);
63 
64  double S = 0.0;
65  double s = 1.0;
66  double l = std::log(bd_);
67  double g = boost::math::tgamma(avi_->val_);
68  double dig = boost::math::digamma(avi_->val_);
69 
70  int k = 0;
71  double delta = s / (avi_->val_ * avi_->val_);
72 
73  while (std::fabs(delta) > 1e-6) {
74  S += delta;
75  ++k;
76  s *= -bd_ / k;
77  delta = s / ((k + avi_->val_) * (k + avi_->val_));
78  }
79 
80  avi_->adj_ -= adj_ * ((u) * (dig - l)
81  + std::exp(avi_->val_ * l) * S / g);
82  }
83  };
84 
85  class gamma_p_dv_vari : public op_dv_vari {
86  public:
87  gamma_p_dv_vari(double a, vari* bvi) :
88  op_dv_vari(gamma_p(a, bvi->val_),
89  a, bvi) {
90  }
91  void chain() {
92  // return zero derivative as gamma_p is flat to
93  // machine precision for b / a > 10
94  if (std::fabs(bvi_->val_ / ad_) > 10 )
95  return;
96  bvi_->adj_ += adj_
97  * (std::exp(-bvi_->val_) * std::pow(bvi_->val_, ad_ - 1.0)
98  / boost::math::tgamma(ad_));
99  }
100  };
101  }
102 
103  inline var gamma_p(const var& a,
104  const var& b) {
105  return var(new gamma_p_vv_vari(a.vi_, b.vi_));
106  }
107 
108  inline var gamma_p(const var& a,
109  double b) {
110  return var(new gamma_p_vd_vari(a.vi_, b));
111  }
112 
113  inline var gamma_p(double a,
114  const var& b) {
115  return var(new gamma_p_dv_vari(a, b.vi_));
116  }
117 
118  }
119 }
120 #endif
fvar< T > fabs(const fvar< T > &x)
Definition: fabs.hpp:15
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:30
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
vari * vi_
Pointer to the implementation of this variable.
Definition: var.hpp:42
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:14
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:94
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:14
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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