grad_F32.hpp

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#ifndef STAN_MATH_PRIM_FUN_GRAD_F32_HPP
#define STAN_MATH_PRIM_FUN_GRAD_F32_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/fabs.hpp>
#include <stan/math/prim/fun/inv.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <bool grad_a1 = true, bool grad_a2 = true, bool grad_a3 = true,
          bool grad_b1 = true, bool grad_b2 = true, bool grad_z = true,
          typename T1, typename T2, typename T3, typename T4, typename T5,
          typename T6, typename T7, typename T8 = double>
void grad_F32(T1* g, const T2& a1, const T3& a2, const T4& a3, const T5& b1,
              const T6& b2, const T7& z, const T8& precision = 1e-6,
              int max_steps = 1e5) {
  check_3F2_converges("grad_F32", a1, a2, a3, b1, b2, z);
 
  for (int i = 0; i < 6; ++i) {
    g[i] = 0.0;
  }
 
  T1 log_g_old[6];
  for (auto& x : log_g_old) {
    x = NEGATIVE_INFTY;
  }
 
  T1 log_t_old = 0.0;
  T1 log_t_new = 0.0;
 
  T7 log_z = log(z);
 
  T1 log_t_new_sign = 1.0;
  T1 log_t_old_sign = 1.0;
  T1 log_g_old_sign[6];
  for (int i = 0; i < 6; ++i) {
    log_g_old_sign[i] = 1.0;
  }
  std::array<T1, 6> term{0};
  for (int k = 0; k <= max_steps; ++k) {
    T1 p = (a1 + k) * (a2 + k) * (a3 + k) / ((b1 + k) * (b2 + k) * (1 + k));
    if (p == 0) {
      return;
    }
 
    log_t_new += log(fabs(p)) + log_z;
    log_t_new_sign = p >= 0.0 ? log_t_new_sign : -log_t_new_sign;
    if constexpr (grad_a1) {
      term[0]
          = log_g_old_sign[0] * log_t_old_sign * exp(log_g_old[0] - log_t_old)
            + inv(a1 + k);
      log_g_old[0] = log_t_new + log(fabs(term[0]));
      log_g_old_sign[0] = term[0] >= 0.0 ? log_t_new_sign : -log_t_new_sign;
      g[0] += log_g_old_sign[0] * exp(log_g_old[0]);
    }
 
    if constexpr (grad_a2) {
      term[1]
          = log_g_old_sign[1] * log_t_old_sign * exp(log_g_old[1] - log_t_old)
            + inv(a2 + k);
      log_g_old[1] = log_t_new + log(fabs(term[1]));
      log_g_old_sign[1] = term[1] >= 0.0 ? log_t_new_sign : -log_t_new_sign;
      g[1] += log_g_old_sign[1] * exp(log_g_old[1]);
    }
 
    if constexpr (grad_a3) {
      term[2]
          = log_g_old_sign[2] * log_t_old_sign * exp(log_g_old[2] - log_t_old)
            + inv(a3 + k);
      log_g_old[2] = log_t_new + log(fabs(term[2]));
      log_g_old_sign[2] = term[2] >= 0.0 ? log_t_new_sign : -log_t_new_sign;
      g[2] += log_g_old_sign[2] * exp(log_g_old[2]);
    }
 
    if constexpr (grad_b1) {
      term[3]
          = log_g_old_sign[3] * log_t_old_sign * exp(log_g_old[3] - log_t_old)
            - inv(b1 + k);
      log_g_old[3] = log_t_new + log(fabs(term[3]));
      log_g_old_sign[3] = term[3] >= 0.0 ? log_t_new_sign : -log_t_new_sign;
      g[3] += log_g_old_sign[3] * exp(log_g_old[3]);
    }
 
    if constexpr (grad_b2) {
      term[4]
          = log_g_old_sign[4] * log_t_old_sign * exp(log_g_old[4] - log_t_old)
            - inv(b2 + k);
      log_g_old[4] = log_t_new + log(fabs(term[4]));
      log_g_old_sign[4] = term[4] >= 0.0 ? log_t_new_sign : -log_t_new_sign;
      g[4] += log_g_old_sign[4] * exp(log_g_old[4]);
    }
 
    if constexpr (grad_z) {
      term[5]
          = log_g_old_sign[5] * log_t_old_sign * exp(log_g_old[5] - log_t_old)
            + inv(z);
      log_g_old[5] = log_t_new + log(fabs(term[5]));
      log_g_old_sign[5] = term[5] >= 0.0 ? log_t_new_sign : -log_t_new_sign;
      g[5] += log_g_old_sign[5] * exp(log_g_old[5]);
    }
 
    if (log_t_new <= log(precision)) {
      return;  // implicit abs
    }
 
    log_t_old = log_t_new;
    log_t_old_sign = log_t_new_sign;
  }
  throw_domain_error("grad_F32", "k (internal counter)", max_steps, "exceeded ",
                     " iterations, hypergeometric function gradient "
                     "did not converge.");
  return;
}
 
}  // namespace math
}  // namespace stan
#endif