Stan Math Library  2.12.0
reverse mode automatic differentiation
grad_inc_beta.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_GRAD_INC_BETA_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_GRAD_INC_BETA_HPP
3 
11 #include <stan/math/fwd/core.hpp>
14 #include <cmath>
15 
16 namespace stan {
17  namespace math {
18 
33  template<typename T>
35  fvar<T>& g2,
36  fvar<T> a,
37  fvar<T> b,
38  fvar<T> z) {
39  fvar<T> c1 = log(z);
40  fvar<T> c2 = log1m(z);
41  fvar<T> c3 = exp(lbeta(a, b)) * inc_beta(a, b, z);
42 
43  fvar<T> C = exp(a * c1 + b * c2) / a;
44 
45  fvar<T> dF1 = 0;
46  fvar<T> dF2 = 0;
47 
48  if (value_of(value_of(C)))
49  grad_2F1(dF1, dF2, a + b,
50  fvar<T>(1.0),
51  a + 1, z);
52 
53  g1 = (c1 - 1.0 / a) * c3 + C * (dF1 + dF2);
54  g2 = c2 * c3 + C * dF1;
55  }
56 
57  }
58 }
59 #endif
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
void grad_inc_beta(fvar< T > &g1, fvar< T > &g2, fvar< T > a, fvar< T > b, fvar< T > z)
Gradient of the incomplete beta function beta(a, b, z) with respect to the first two arguments...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:15
void grad_2F1(T &gradA, T &gradC, T a, T b, T c, T z, T precision=1e-6)
Definition: grad_2F1.hpp:12

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