Stan Math Library  2.15.0
reverse mode automatic differentiation
grad_inc_beta.hpp
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1 #ifndef STAN_MATH_REV_SCAL_FUN_GRAD_INC_BETA_HPP
2 #define STAN_MATH_REV_SCAL_FUN_GRAD_INC_BETA_HPP
3 
4 #include <stan/math/rev/core.hpp>
18 #include <cmath>
19 
20 namespace stan {
21  namespace math {
22 
36  inline void grad_inc_beta(var& g1, var& g2,
37  const var& a, const var& b, const var& z) {
38  var c1 = log(z);
39  var c2 = log1m(z);
40  var c3 = exp(lbeta(a, b)) * inc_beta(a, b, z);
41  var C = exp(a * c1 + b * c2) / a;
42  var dF1 = 0;
43  var dF2 = 0;
44  if (value_of(value_of(C)))
45  grad_2F1(dF1, dF2, a + b, var(1.0), a + 1, z);
46  g1 = (c1 - 1.0 / a) * c3 + C * (dF1 + dF2);
47  g2 = c2 * c3 + C * dF1;
48  }
49 
50  }
51 }
52 #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_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
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...
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:30
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:13

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