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reverse mode automatic differentiation
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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 
4 #include <cmath>
5 
6 namespace stan {
7 
8  namespace math {
9 
10  // Gradient of the hypergeometric function 2F1(a, b | c | z)
11  // with respect to a and c
12  template<typename T>
13  void grad_2F1(T& gradA, T& gradC, T a, T b, T c, T z, T precision = 1e-6) {
14  using std::fabs;
15 
16  gradA = 0;
17  gradC = 0;
18 
19  T gradAold = 0;
20  T gradCold = 0;
21 
22  int k = 0;
23  T tDak = 1.0 / (a - 1);
24 
25  while (fabs(tDak * (a + (k - 1)) ) > precision || k == 0) {
26  const T r = ( (a + k) / (c + k) ) * ( (b + k) / (T)(k + 1) ) * z;
27  tDak = r * tDak * (a + (k - 1)) / (a + k);
28 
29  if (r == 0) break;
30 
31  gradAold = r * gradAold + tDak;
32  gradCold = r * gradCold - tDak * ((a + k) / (c + k));
33 
34  gradA += gradAold;
35  gradC += gradCold;
36 
37  ++k;
38 
39  if (k > 200) break;
40  }
41  }
42 
43 
44  }
45 
46 }
47 
48 #endif
fvar< T > fabs(const fvar< T > &x)
Definition: fabs.hpp:14
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:95
void grad_2F1(T &gradA, T &gradC, T a, T b, T c, T z, T precision=1e-6)
Definition: grad_2F1.hpp:13

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