Stan Math Library  2.15.0
reverse mode automatic differentiation
grad_2F1.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_FUN_GRAD_2F1_HPP
2 #define STAN_MATH_PRIM_SCAL_FUN_GRAD_2F1_HPP
3 
7 #include <cmath>
8 #include <limits>
9 
10 namespace stan {
11  namespace math {
12 
34  template<typename T>
35  void grad_2F1(T& g_a1, T& g_b1, const T& a1, const T& a2, const T& b1,
36  const T& z, const T& precision = 1e-10, int max_steps = 1e5) {
37  check_2F1_converges("grad_2F1", a1, a2, b1, z);
38 
39  using std::log;
40  using std::fabs;
41  using std::exp;
42 
43  g_a1 = 0.0;
44  g_b1 = 0.0;
45 
46  T log_g_old[2];
47  for (int i = 0; i < 2; ++i)
48  log_g_old[i] = -std::numeric_limits<T>::infinity();
49 
50  T log_t_old = 0.0;
51  T log_t_new = 0.0;
52 
53  T log_z = log(z);
54 
55  double log_t_new_sign = 1.0;
56  double log_t_old_sign = 1.0;
57  double log_g_old_sign[2];
58  for (int i = 0; i < 2; ++i)
59  log_g_old_sign[i] = 1.0;
60 
61  for (int k = 0; k <= max_steps; ++k) {
62  T p = (a1 + k) * (a2 + k) / ((b1 + k) * (1 + k));
63  if (p == 0)
64  return;
65 
66  log_t_new += log(fabs(p)) + log_z;
67  log_t_new_sign = p >= 0.0 ? log_t_new_sign : -log_t_new_sign;
68 
69  T term = log_g_old_sign[0] * log_t_old_sign *
70  exp(log_g_old[0] - log_t_old) + 1 / (a1 + k);
71  log_g_old[0] = log_t_new + log(fabs(term));
72  log_g_old_sign[0] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
73 
74  term = log_g_old_sign[1] * log_t_old_sign *
75  exp(log_g_old[1] - log_t_old) - 1 / (b1 + k);
76  log_g_old[1] = log_t_new + log(fabs(term));
77  log_g_old_sign[1] = term >= 0.0 ? log_t_new_sign : -log_t_new_sign;
78 
79  g_a1 += log_g_old_sign[0] > 0 ? exp(log_g_old[0]) : -exp(log_g_old[0]);
80  g_b1 += log_g_old_sign[1] > 0 ? exp(log_g_old[1]) : -exp(log_g_old[1]);
81 
82  if (log_t_new <= log(precision))
83  return; // implicit abs
84 
85  log_t_old = log_t_new;
86  log_t_old_sign = log_t_new_sign;
87  }
88  domain_error("grad_2F1", "k (internal counter)", max_steps,
89  "exceeded ", " iterations, hypergeometric function gradient "
90  "did not converge.");
91  return;
92  }
93 
94  }
95 }
96 #endif
fvar< T > fabs(const fvar< T > &x)
Definition: fabs.hpp:15
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
void grad_2F1(T &g_a1, T &g_b1, const T &a1, const T &a2, const T &b1, const T &z, const T &precision=1e-10, int max_steps=1e5)
Gradients of the hypergeometric function, 2F1.
Definition: grad_2F1.hpp:35
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 check_2F1_converges(const char *function, const T_a1 &a1, const T_a2 &a2, const T_b1 &b1, const T_z &z)
Check if the hypergeometric function (2F1) called with supplied arguments will converge, assuming arguments are finite values.

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