Phi_approx.hpp

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#ifndef STAN_MATH_REV_FUN_PHI_APPROX_HPP
#define STAN_MATH_REV_FUN_PHI_APPROX_HPP
 
#include <stan/math/rev/meta.hpp>
#include <stan/math/rev/core.hpp>
#include <stan/math/prim/fun/inv_logit.hpp>
 
namespace stan {
namespace math {
 
inline var Phi_approx(const var& a) {
  double av_squared = a.val() * a.val();
  double f = inv_logit(0.07056 * a.val() * av_squared + 1.5976 * a.val());
  double da = f * (1 - f) * (3.0 * 0.07056 * av_squared + 1.5976);
  return make_callback_var(
      f, [a, da](auto& vi) mutable { a.adj() += vi.adj() * da; });
}
 
template <typename T, require_var_matrix_t<T>* = nullptr>
inline auto Phi_approx(const T& a) {
  arena_t<value_type_t<T>> f(a.rows(), a.cols());
  arena_t<value_type_t<T>> da(a.rows(), a.cols());
  for (Eigen::Index j = 0; j < a.cols(); ++j) {
    for (Eigen::Index i = 0; i < a.rows(); ++i) {
      const auto a_val = a.val().coeff(i, j);
      const auto av_squared = a_val * a_val;
      f.coeffRef(i, j) = inv_logit(0.07056 * a_val * av_squared
                                   + 1.5976 * a.val().coeff(i, j));
      da.coeffRef(i, j) = f.coeff(i, j) * (1 - f.coeff(i, j))
                          * (3.0 * 0.07056 * av_squared + 1.5976);
    }
  }
  return make_callback_var(f, [a, da](auto& vi) mutable {
    a.adj().array() += vi.adj().array() * da.array();
  });
}
 
}  // namespace math
}  // namespace stan
#endif