1// Ceres Solver - A fast non-linear least squares minimizer
2// Copyright 2012 Google Inc. All rights reserved.
3// http://code.google.com/p/ceres-solver/
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28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30//
31// Limited memory positive definite approximation to the inverse
32// Hessian, using the LBFGS algorithm
33
34#ifndef CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_
35#define CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_
36
37#include <list>
38
39#include "ceres/internal/eigen.h"
40#include "ceres/linear_operator.h"
41
42namespace ceres {
43namespace internal {
44
45// LowRankInverseHessian is a positive definite approximation to the
46// Hessian using the limited memory variant of the
47// Broyden-Fletcher-Goldfarb-Shanno (BFGS)secant formula for
48// approximating the Hessian.
49//
50// Other update rules like the Davidon-Fletcher-Powell (DFP) are
51// possible, but the BFGS rule is considered the best performing one.
52//
53// The limited memory variant was developed by Nocedal and further
54// enhanced with scaling rule by Byrd, Nocedal and Schanbel.
55//
56// Nocedal, J. (1980). "Updating Quasi-Newton Matrices with Limited
57// Storage". Mathematics of Computation 35 (151): 773–782.
58//
59// Byrd, R. H.; Nocedal, J.; Schnabel, R. B. (1994).
60// "Representations of Quasi-Newton Matrices and their use in
61// Limited Memory Methods". Mathematical Programming 63 (4):
62class LowRankInverseHessian : public LinearOperator {
63 public:
64  // num_parameters is the row/column size of the Hessian.
65  // max_num_corrections is the rank of the Hessian approximation.
66  // use_approximate_eigenvalue_scaling controls whether the initial
67  // inverse Hessian used during Right/LeftMultiply() is scaled by
68  // the approximate eigenvalue of the true inverse Hessian at the
69  // current operating point.
70  // The approximation uses:
71  // 2 * max_num_corrections * num_parameters + max_num_corrections
72  // doubles.
73  LowRankInverseHessian(int num_parameters,
74                        int max_num_corrections,
75                        bool use_approximate_eigenvalue_scaling);
76  virtual ~LowRankInverseHessian() {}
77
78  // Update the low rank approximation. delta_x is the change in the
79  // domain of Hessian, and delta_gradient is the change in the
80  // gradient.  The update copies the delta_x and delta_gradient
81  // vectors, and gets rid of the oldest delta_x and delta_gradient
82  // vectors if the number of corrections is already equal to
83  // max_num_corrections.
84  bool Update(const Vector& delta_x, const Vector& delta_gradient);
85
86  // LinearOperator interface
87  virtual void RightMultiply(const double* x, double* y) const;
88  virtual void LeftMultiply(const double* x, double* y) const {
89    RightMultiply(x, y);
90  }
91  virtual int num_rows() const { return num_parameters_; }
92  virtual int num_cols() const { return num_parameters_; }
93
94 private:
95  const int num_parameters_;
96  const int max_num_corrections_;
97  const bool use_approximate_eigenvalue_scaling_;
98  double approximate_eigenvalue_scale_;
99  ColMajorMatrix delta_x_history_;
100  ColMajorMatrix delta_gradient_history_;
101  Vector delta_x_dot_delta_gradient_;
102  std::list<int> indices_;
103};
104
105}  // namespace internal
106}  // namespace ceres
107
108#endif  // CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_
109