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/ 4// 5// Redistribution and use in source and binary forms, with or without 6// modification, are permitted provided that the following conditions are met: 7// 8// * Redistributions of source code must retain the above copyright notice, 9// this list of conditions and the following disclaimer. 10// * Redistributions in binary form must reproduce the above copyright notice, 11// this list of conditions and the following disclaimer in the documentation 12// and/or other materials provided with the distribution. 13// * Neither the name of Google Inc. nor the names of its contributors may be 14// used to endorse or promote products derived from this software without 15// specific prior written permission. 16// 17// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27// POSSIBILITY OF SUCH DAMAGE. 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