#ifndef FESA_ANALYSIS_HHT_TIME_INTEGRATION_H_
#define FESA_ANALYSIS_HHT_TIME_INTEGRATION_H_

#include "fesa/core/status.h"
#include "fesa/math/vector.h"

namespace fesa {

/// @brief Stores the coupled original negative-alpha HHT coefficients.
struct HhtParameters {
  double alpha;
  double beta;
  double gamma;
};

/// @brief Stores the displacement and velocity Newmark predictors.
struct HhtPredictor {
  Vector coordinates;
  Vector velocity;
};

/// @brief Separates physical chart rates from the auxiliary acceleration.
struct HhtRates {
  Vector velocity;
  Vector acceleration;
  Vector algorithmic_acceleration;
};

/// @brief Builds coupled coefficients for alpha in [-1/3, 0].
/// @note The public INP subset uses only alpha=-0.05.
Result<HhtParameters> MakeHhtParameters(double alpha);

/// @brief Predicts q and v using the old auxiliary acceleration.
/// @param time_increment Finite positive duration in input time units.
Result<HhtPredictor> PredictHht(const Vector& coordinates,
                              const Vector& velocity,
                              const Vector& algorithmic_acceleration,
                              double time_increment,
                              const HhtParameters& parameters);

/// @brief Recovers physical and auxiliary rates from one trial coordinate.
/// @param old_acceleration Physical endpoint acceleration at the old time.
Result<HhtRates> EvaluateHhtRates(const Vector& coordinates,
                                const HhtPredictor& predictor,
                                const Vector& old_acceleration,
                                double time_increment,
                                const HhtParameters& parameters);

}  // namespace fesa
#endif  // FESA_ANALYSIS_HHT_TIME_INTEGRATION_H_