barzilai_borwein_step_size.hpp

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#ifndef STAN_MATH_MIX_FUNCTOR_BARZILAI_BORWEIN_STEP_SIZE_HPP
#define STAN_MATH_MIX_FUNCTOR_BARZILAI_BORWEIN_STEP_SIZE_HPP
#include <stan/math/prim/fun/Eigen.hpp>
#include <algorithm>
#include <numeric>
#include <cmath>
 
namespace stan::math::internal {
inline double barzilai_borwein_step_size(const Eigen::VectorXd& s,
                                         const Eigen::VectorXd& g_curr,
                                         const Eigen::VectorXd& g_prev,
                                         double prev_step, int last_backtracks,
                                         double min_alpha, double max_alpha) {
  // Fallbacks
  auto safe_fallback = [&]() -> double {
    double a = std::clamp(
        prev_step > 0.0 && std::isfinite(prev_step) ? prev_step : 1.0,
        min_alpha, max_alpha);
    return a;
  };
 
  const Eigen::VectorXd y = g_curr - g_prev;
  const double sty = s.dot(y);
  const double sts = s.squaredNorm();
  const double yty = y.squaredNorm();
 
  // Basic validity checks
  constexpr double eps = 1e-16;
  if (!(std::isfinite(sty) && std::isfinite(sts) && std::isfinite(yty))
      || sts <= eps || yty <= eps || sty <= eps || last_backtracks == -1) {
    return safe_fallback();
  }
 
  // BB candidates
  double alpha_bb1 = std::clamp(std::abs(sts / sty), min_alpha, max_alpha);
  double alpha_bb2 = std::clamp(std::abs(sty / yty), min_alpha, max_alpha);
 
  // Safeguard candidates
  if (!std::isfinite(alpha_bb1) || !std::isfinite(alpha_bb2) || alpha_bb1 <= 0.0
      || alpha_bb2 <= 0.0) {
    return safe_fallback();
  }
 
  // Spectral cosine r = cos^2(angle(s, y)) in [0,1]
  const double r = (sty * sty) / (sts * yty);
 
  // Heuristic thresholds (robust defaults)
  constexpr double kLoose = 0.9;  // "nice" curvature
  constexpr double kTight = 0.1;  // "dodgy" curvature
 
  double alpha0 = alpha_bb2;  // default to short BB for robustness
  if (r > kLoose && last_backtracks <= 1) {
    // Spectrum looks friendly and line search was not harsh -> try long BB
    alpha0 = alpha_bb1;
  } else if (r >= kTight && r <= kLoose) {
    // Neither clearly friendly nor clearly dodgy -> neutral middle
    alpha0 = std::sqrt(alpha_bb1 * alpha_bb2);
  }  // else keep alpha_bb2
 
  // Clip to user bounds
  alpha0 = std::clamp(alpha0, min_alpha, max_alpha);
 
  if (!std::isfinite(alpha0) || alpha0 <= 0.0) {
    return safe_fallback();
  }
  return alpha0;
}
 
}  // namespace stan::math::internal
#endif