// Ceres Solver - A fast non-linear least squares minimizer

// Copyright 2015 Google Inc. All rights reserved.

// http://ceres-solver.org/

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

#ifndef CERES_INTERNAL_DOGLEG_STRATEGY_H_

#define CERES_INTERNAL_DOGLEG_STRATEGY_H_

#include "ceres/linear_solver.h"

#include "ceres/trust_region_strategy.h"

namespace ceres {

namespace internal {

// Dogleg step computation and trust region sizing strategy based on

// on "Methods for Nonlinear Least Squares" by K. Madsen, H.B. Nielsen

// and O. Tingleff. Available to download from

//

// http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf

//

// One minor modification is that instead of computing the pure

// Gauss-Newton step, we compute a regularized version of it. This is

// because the Jacobian is often rank-deficient and in such cases

// using a direct solver leads to numerical failure.

//

// If SUBSPACE is passed as the type argument to the constructor, the

// DoglegStrategy follows the approach by Shultz, Schnabel, Byrd.

// This finds the exact optimum over the two-dimensional subspace

// spanned by the two Dogleg vectors.

class DoglegStrategy : public TrustRegionStrategy {

 public:

  explicit DoglegStrategy(const TrustRegionStrategy::Options& options);

  virtual ~DoglegStrategy() {}

  // TrustRegionStrategy interface

  virtual Summary ComputeStep(const PerSolveOptions& per_solve_options,

                              SparseMatrix* jacobian,

                              const double* residuals,

                              double* step);

  virtual void StepAccepted(double step_quality);

  virtual void StepRejected(double step_quality);

  virtual void StepIsInvalid();

  virtual double Radius() const;

  // These functions are predominantly for testing.

  Vector gradient() const { return gradient_; }

  Vector gauss_newton_step() const { return gauss_newton_step_; }

  Matrix subspace_basis() const { return subspace_basis_; }

  Vector subspace_g() const { return subspace_g_; }

  Matrix subspace_B() const { return subspace_B_; }

 private:

  typedef Eigen::Matrix<double, 2, 1, Eigen::DontAlign> Vector2d;

  typedef Eigen::Matrix<double, 2, 2, Eigen::DontAlign> Matrix2d;

  LinearSolver::Summary ComputeGaussNewtonStep(

      const PerSolveOptions& per_solve_options,

      SparseMatrix* jacobian,

      const double* residuals);

  void ComputeCauchyPoint(SparseMatrix* jacobian);

  void ComputeGradient(SparseMatrix* jacobian, const double* residuals);

  void ComputeTraditionalDoglegStep(double* step);

  bool ComputeSubspaceModel(SparseMatrix* jacobian);

  void ComputeSubspaceDoglegStep(double* step);

  bool FindMinimumOnTrustRegionBoundary(Vector2d* minimum) const;

  Vector MakePolynomialForBoundaryConstrainedProblem() const;

  Vector2d ComputeSubspaceStepFromRoot(double lambda) const;

  double EvaluateSubspaceModel(const Vector2d& x) const;

  LinearSolver* linear_solver_;

  double radius_;

  const double max_radius_;

  const double min_diagonal_;

  const double max_diagonal_;

  // mu is used to scale the diagonal matrix used to make the

  // Gauss-Newton solve full rank. In each solve, the strategy starts

  // out with mu = min_mu, and tries values upto max_mu. If the user

  // reports an invalid step, the value of mu_ is increased so that

  // the next solve starts with a stronger regularization.

  //

  // If a successful step is reported, then the value of mu_ is

  // decreased with a lower bound of min_mu_.

  double mu_;

  const double min_mu_;

  const double max_mu_;

  const double mu_increase_factor_;

  const double increase_threshold_;

  const double decrease_threshold_;

  Vector diagonal_;  // sqrt(diag(J^T J))

  Vector lm_diagonal_;

  Vector gradient_;

  Vector gauss_newton_step_;

  // cauchy_step = alpha * gradient

  double alpha_;

  double dogleg_step_norm_;

  // When, ComputeStep is called, reuse_ indicates whether the

  // Gauss-Newton and Cauchy steps from the last call to ComputeStep

  // can be reused or not.

  //

  // If the user called StepAccepted, then it is expected that the

  // user has recomputed the Jacobian matrix and new Gauss-Newton

  // solve is needed and reuse is set to false.

  //

  // If the user called StepRejected, then it is expected that the

  // user wants to solve the trust region problem with the same matrix

  // but a different trust region radius and the Gauss-Newton and

  // Cauchy steps can be reused to compute the Dogleg, thus reuse is

  // set to true.

  //

  // If the user called StepIsInvalid, then there was a numerical

  // problem with the step computed in the last call to ComputeStep,

  // and the regularization used to do the Gauss-Newton solve is

  // increased and a new solve should be done when ComputeStep is

  // called again, thus reuse is set to false.

  bool reuse_;

  // The dogleg type determines how the minimum of the local

  // quadratic model is found.

  DoglegType dogleg_type_;

  // If the type is SUBSPACE_DOGLEG, the two-dimensional

  // model 1/2 x^T B x + g^T x has to be computed and stored.

  bool subspace_is_one_dimensional_;

  Matrix subspace_basis_;

  Vector2d subspace_g_;

  Matrix2d subspace_B_;

};

}  // namespace internal

}  // namespace ceres

#endif  // CERES_INTERNAL_DOGLEG_STRATEGY_H_