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// Author: sameeragarwal@google.com (Sameer Agarwal)

//

// Limited memory positive definite approximation to the inverse

// Hessian, using the LBFGS algorithm

#ifndef CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_

#define CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_

#include <list>

#include "ceres/internal/eigen.h"

#include "ceres/linear_operator.h"

namespace ceres {

namespace internal {

// LowRankInverseHessian is a positive definite approximation to the

// Hessian using the limited memory variant of the

// Broyden-Fletcher-Goldfarb-Shanno (BFGS)secant formula for

// approximating the Hessian.

//

// Other update rules like the Davidon-Fletcher-Powell (DFP) are

// possible, but the BFGS rule is considered the best performing one.

//

// The limited memory variant was developed by Nocedal and further

// enhanced with scaling rule by Byrd, Nocedal and Schanbel.

//

// Nocedal, J. (1980). "Updating Quasi-Newton Matrices with Limited

// Storage". Mathematics of Computation 35 (151): 773–782.

//

// Byrd, R. H.; Nocedal, J.; Schnabel, R. B. (1994).

// "Representations of Quasi-Newton Matrices and their use in

// Limited Memory Methods". Mathematical Programming 63 (4):

class LowRankInverseHessian : public LinearOperator {

 public:

  // num_parameters is the row/column size of the Hessian.

  // max_num_corrections is the rank of the Hessian approximation.

  // use_approximate_eigenvalue_scaling controls whether the initial

  // inverse Hessian used during Right/LeftMultiply() is scaled by

  // the approximate eigenvalue of the true inverse Hessian at the

  // current operating point.

  // The approximation uses:

  // 2 * max_num_corrections * num_parameters + max_num_corrections

  // doubles.

  LowRankInverseHessian(int num_parameters,

                        int max_num_corrections,

                        bool use_approximate_eigenvalue_scaling);

  virtual ~LowRankInverseHessian() {}

  // Update the low rank approximation. delta_x is the change in the

  // domain of Hessian, and delta_gradient is the change in the

  // gradient.  The update copies the delta_x and delta_gradient

  // vectors, and gets rid of the oldest delta_x and delta_gradient

  // vectors if the number of corrections is already equal to

  // max_num_corrections.

  bool Update(const Vector& delta_x, const Vector& delta_gradient);

  // LinearOperator interface

  virtual void RightMultiply(const double* x, double* y) const;

  virtual void LeftMultiply(const double* x, double* y) const {

    RightMultiply(x, y);

  }

  virtual int num_rows() const { return num_parameters_; }

  virtual int num_cols() const { return num_parameters_; }

 private:

  const int num_parameters_;

  const int max_num_corrections_;

  const bool use_approximate_eigenvalue_scaling_;

  double approximate_eigenvalue_scale_;

  ColMajorMatrix delta_x_history_;

  ColMajorMatrix delta_gradient_history_;

  Vector delta_x_dot_delta_gradient_;

  std::list<int> indices_;

};

}  // namespace internal

}  // namespace ceres

#endif  // CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_