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 "ceres/internal/eigen.h" 38 #include "ceres/linear_operator.h" 39 40 namespace ceres { 41 namespace internal { 42 43 // LowRankInverseHessian is a positive definite approximation to the 44 // Hessian using the limited memory variant of the 45 // Broyden-Fletcher-Goldfarb-Shanno (BFGS)secant formula for 46 // approximating the Hessian. 47 // 48 // Other update rules like the Davidon-Fletcher-Powell (DFP) are 49 // possible, but the BFGS rule is considered the best performing one. 50 // 51 // The limited memory variant was developed by Nocedal and further 52 // enhanced with scaling rule by Byrd, Nocedal and Schanbel. 53 // 54 // Nocedal, J. (1980). "Updating Quasi-Newton Matrices with Limited 55 // Storage". Mathematics of Computation 35 (151): 773782. 56 // 57 // Byrd, R. H.; Nocedal, J.; Schnabel, R. B. (1994). 58 // "Representations of Quasi-Newton Matrices and their use in 59 // Limited Memory Methods". Mathematical Programming 63 (4): 60 class LowRankInverseHessian : public LinearOperator { 61 public: 62 // num_parameters is the row/column size of the Hessian. 63 // max_num_corrections is the rank of the Hessian approximation. 64 // use_approximate_eigenvalue_scaling controls whether the initial 65 // inverse Hessian used during Right/LeftMultiply() is scaled by 66 // the approximate eigenvalue of the true inverse Hessian at the 67 // current operating point. 68 // The approximation uses: 69 // 2 * max_num_corrections * num_parameters + max_num_corrections 70 // doubles. 71 LowRankInverseHessian(int num_parameters, 72 int max_num_corrections, 73 bool use_approximate_eigenvalue_scaling); 74 virtual ~LowRankInverseHessian() {} 75 76 // Update the low rank approximation. delta_x is the change in the 77 // domain of Hessian, and delta_gradient is the change in the 78 // gradient. The update copies the delta_x and delta_gradient 79 // vectors, and gets rid of the oldest delta_x and delta_gradient 80 // vectors if the number of corrections is already equal to 81 // max_num_corrections. 82 bool Update(const Vector& delta_x, const Vector& delta_gradient); 83 84 // LinearOperator interface 85 virtual void RightMultiply(const double* x, double* y) const; 86 virtual void LeftMultiply(const double* x, double* y) const { 87 RightMultiply(x, y); 88 } 89 virtual int num_rows() const { return num_parameters_; } 90 virtual int num_cols() const { return num_parameters_; } 91 92 private: 93 const int num_parameters_; 94 const int max_num_corrections_; 95 const bool use_approximate_eigenvalue_scaling_; 96 int num_corrections_; 97 double approximate_eigenvalue_scale_; 98 Matrix delta_x_history_; 99 Matrix delta_gradient_history_; 100 Vector delta_x_dot_delta_gradient_; 101 }; 102 103 } // namespace internal 104 } // namespace ceres 105 106 #endif // CERES_INTERNAL_LOW_RANK_INVERSE_HESSIAN_H_ 107
