grad_inc_beta.hpp

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#ifndef STAN_MATH_PRIM_FUN_GRAD_INC_BETA_HPP
#define STAN_MATH_PRIM_FUN_GRAD_INC_BETA_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/fun/beta.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/fma.hpp>
#include <stan/math/prim/fun/grad_2F1.hpp>
#include <stan/math/prim/fun/inv.hpp>
#include <stan/math/prim/fun/inc_beta.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/log1m.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
// Gradient of the incomplete beta function beta(a, b, z)
// with respect to the first two arguments, using the
// equivalence to a hypergeometric function.
// See http://dlmf.nist.gov/8.17#ii
inline void grad_inc_beta(double& g1, double& g2, double a, double b,
                          double z) {
  using std::exp;
  using std::log;
 
  double c1 = log(z);
  double c2 = log1m(z);
  double c3 = beta(a, b) * inc_beta(a, b, z);
  double C = exp(a * c1 + b * c2) / a;
  double dF1 = 0;
  double dF2 = 0;
  double dF3 = 0;
  double dFz = 0;
  if (C) {
    std::forward_as_tuple(dF1, dF2, dF3, dFz)
        = grad_2F1<true>(a + b, 1.0, a + 1, z);
  }
  g1 = fma((c1 - inv(a)), c3, C * (dF1 + dF3));
  g2 = fma(c2, c3, C * dF1);
}
 
}  // namespace math
}  // namespace stan
#endif