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 (at) 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 42 namespace ceres { 43 namespace 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): 773782. 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): 62 class 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
