Stan Math Library  2.15.0
reverse mode automatic differentiation
grad_F32.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_FUN_GRAD_F32_HPP
2 #define STAN_MATH_PRIM_SCAL_FUN_GRAD_F32_HPP
3 
7 #include <cmath>
8 #include <limits>
9 
10 namespace stan {
11  namespace math {
12 
35  template<typename T>
36  void grad_F32(T* g, const T& a1, const T& a2, const T& a3, const T& b1,
37  const T& b2, const T& z, const T& precision = 1e-6,
38  int max_steps = 1e5) {
39  check_3F2_converges("grad_F32", a1, a2, a3, b1, b2, z);
40 
41  using std::log;
42  using std::fabs;
43  using std::exp;
44 
45  for (int i = 0; i < 6; ++i)
46  g[i] = 0.0;
47 
48  T log_g_old[6];
49  for (int i = 0; i < 6; ++i)
50  log_g_old[i] = -std::numeric_limits<double>::infinity();
51 
52  T log_t_old = 0.0;
53  T log_t_new = 0.0;
54 
55  T log_z = log(z);
56 
57  double log_t_new_sign = 1.0;
58  double log_t_old_sign = 1.0;
59  double log_g_old_sign[6];
60  for (int i = 0; i < 6; ++i)
61  log_g_old_sign[i] = 1.0;
62 
63  for (int k = 0; k <= max_steps; ++k) {
64  T p = (a1 + k) * (a2 + k) * (a3 + k) / ((b1 + k) * (b2 + k) * (1 + k));
65  if (p == 0)
66  return;
67 
68  log_t_new += log(fabs(p)) + log_z;
69  log_t_new_sign = p >= 0.0 ? log_t_new_sign : -log_t_new_sign;
70 
71 // g_old[0] = t_new * (g_old[0] / t_old + 1.0 / (a1 + k));
72  T term = log_g_old_sign[0] * log_t_old_sign *
73  exp(log_g_old[0] - log_t_old) + inv(a1 + k);
74  log_g_old[0] = log_t_new + log(fabs(term));
75  log_g_old_sign[0] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
76 
77 // g_old[1] = t_new * (g_old[1] / t_old + 1.0 / (a2 + k));
78  term = log_g_old_sign[1] * log_t_old_sign *
79  exp(log_g_old[1] - log_t_old) + inv(a2 + k);
80  log_g_old[1] = log_t_new + log(fabs(term));
81  log_g_old_sign[1] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
82 
83 // g_old[2] = t_new * (g_old[2] / t_old + 1.0 / (a3 + k));
84  term = log_g_old_sign[2] * log_t_old_sign *
85  exp(log_g_old[2] - log_t_old) + inv(a3 + k);
86  log_g_old[2] = log_t_new + log(fabs(term));
87  log_g_old_sign[2] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
88 
89 // g_old[3] = t_new * (g_old[3] / t_old - 1.0 / (b1 + k));
90  term = log_g_old_sign[3] * log_t_old_sign *
91  exp(log_g_old[3] - log_t_old) - inv(b1 + k);
92  log_g_old[3] = log_t_new + log(fabs(term));
93  log_g_old_sign[3] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
94 
95 // g_old[4] = t_new * (g_old[4] / t_old - 1.0 / (b2 + k));
96  term = log_g_old_sign[4] * log_t_old_sign *
97  exp(log_g_old[4] - log_t_old) - inv(b2 + k);
98  log_g_old[4] = log_t_new + log(fabs(term));
99  log_g_old_sign[4] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
100 
101 // g_old[5] = t_new * (g_old[5] / t_old + 1.0 / z);
102  term = log_g_old_sign[5] * log_t_old_sign *
103  exp(log_g_old[5] - log_t_old) + inv(z);
104  log_g_old[5] = log_t_new + log(fabs(term));
105  log_g_old_sign[5] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
106 
107  for (int i = 0; i < 6; ++i) {
108  g[i] += log_g_old_sign[i] * exp(log_g_old[i]);
109  }
110 
111  if (log_t_new <= log(precision))
112  return; // implicit abs
113 
114  log_t_old = log_t_new;
115  log_t_old_sign = log_t_new_sign;
116  }
117  domain_error("grad_F32", "k (internal counter)", max_steps,
118  "exceeded ", " iterations, hypergeometric function gradient "
119  "did not converge.");
120  return;
121  }
122 
123  }
124 }
125 #endif
fvar< T > fabs(const fvar< T > &x)
Definition: fabs.hpp:15
void check_3F2_converges(const char *function, const T_a1 &a1, const T_a2 &a2, const T_a3 &a3, const T_b1 &b1, const T_b2 &b2, const T_z &z)
Check if the hypergeometric function (3F2) called with supplied arguments will converge, assuming arguments are finite values.
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void domain_error(const char *function, const char *name, const T &y, const char *msg1, const char *msg2)
Throw a domain error with a consistently formatted message.
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:94
void grad_F32(T *g, const T &a1, const T &a2, const T &a3, const T &b1, const T &b2, const T &z, const T &precision=1e-6, int max_steps=1e5)
Gradients of the hypergeometric function, 3F2.
Definition: grad_F32.hpp:36
fvar< T > inv(const fvar< T > &x)
Definition: inv.hpp:14

     [ Stan Home Page ] © 2011–2016, Stan Development Team.