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reverse mode automatic differentiation
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inc_beta.hpp
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1 #ifndef STAN_MATH_FWD_SCAL_FUN_INC_BETA_HPP
2 #define STAN_MATH_FWD_SCAL_FUN_INC_BETA_HPP
3 
4 #include <boost/math/special_functions/beta.hpp>
11 #include <stan/math/fwd/core.hpp>
14 
15 namespace stan {
16 
17  namespace math {
18 
19  template<typename T>
20  inline fvar<T> inc_beta(const fvar<T>& a,
21  const fvar<T>& b,
22  const fvar<T>& x) {
23  using stan::math::digamma;
26  using stan::math::lbeta;
27  using stan::math::digamma;
28  using stan::math::lbeta;
29  using stan::math::pow;
30  using std::exp;
31  using std::pow;
32 
33  T d_a; T d_b; T d_x;
34 
35  grad_reg_inc_beta(d_a, d_b, a.val_, b.val_, x.val_,
36  digamma(a.val_), digamma(b.val_),
37  digamma(a.val_+b.val_),
38  exp(lbeta(a.val_, b.val_)));
39  d_x = pow((1-x.val_), b.val_-1)*pow(x.val_, a.val_-1)
40  / exp(lbeta(a.val_, b.val_));
41  return fvar<T>(inc_beta(a.val_, b.val_, x.val_),
42  a.d_ * d_a + b.d_ * d_b + x.d_ * d_x);
43  }
44  }
45 }
46 
47 #endif
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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