Stan Math Library  2.10.0
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 
5 #include <stan/math/rev/core.hpp>
15 #include <cmath>
16 
17 namespace stan {
18  namespace math {
19 
20  // Gradient of the incomplete beta function beta(a, b, z)
21  // with respect to the first two arguments, using the
22  // equivalence to a hypergeometric function.
23  // See http://dlmf.nist.gov/8.17#ii
24  void grad_inc_beta(var& g1, var& g2,
25  const var& a, const var& b, const var& z) {
26  var c1 = log(z);
27  var c2 = log1m(z);
28  var c3 = exp(lbeta(a, b)) * inc_beta(a, b, z);
29  var C = exp(a * c1 + b * c2) / a;
30  var dF1 = 0;
31  var dF2 = 0;
32  if (value_of(value_of(C)))
33  grad_2F1(dF1, dF2, a + b, var(1.0), a + 1, z);
34  g1 = (c1 - 1.0 / a) * c3 + C * (dF1 + dF2);
35  g2 = c2 * c3 + C * dF1;
36  }
37 
38  }
39 }
40 #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:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:31
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
void grad_inc_beta(stan::math::fvar< T > &g1, stan::math::fvar< T > &g2, stan::math::fvar< T > a, stan::math::fvar< T > b, stan::math::fvar< T > z)
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16
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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