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#include "ceres/levenberg_marquardt_strategy.h" 32 33#include <cmath> 34#include "Eigen/Core" 35#include "ceres/array_utils.h" 36#include "ceres/internal/eigen.h" 37#include "ceres/linear_least_squares_problems.h" 38#include "ceres/linear_solver.h" 39#include "ceres/sparse_matrix.h" 40#include "ceres/trust_region_strategy.h" 41#include "ceres/types.h" 42#include "glog/logging.h" 43 44namespace ceres { 45namespace internal { 46 47LevenbergMarquardtStrategy::LevenbergMarquardtStrategy( 48 const TrustRegionStrategy::Options& options) 49 : linear_solver_(options.linear_solver), 50 radius_(options.initial_radius), 51 max_radius_(options.max_radius), 52 min_diagonal_(options.min_lm_diagonal), 53 max_diagonal_(options.max_lm_diagonal), 54 decrease_factor_(2.0), 55 reuse_diagonal_(false) { 56 CHECK_NOTNULL(linear_solver_); 57 CHECK_GT(min_diagonal_, 0.0); 58 CHECK_LE(min_diagonal_, max_diagonal_); 59 CHECK_GT(max_radius_, 0.0); 60} 61 62LevenbergMarquardtStrategy::~LevenbergMarquardtStrategy() { 63} 64 65TrustRegionStrategy::Summary LevenbergMarquardtStrategy::ComputeStep( 66 const TrustRegionStrategy::PerSolveOptions& per_solve_options, 67 SparseMatrix* jacobian, 68 const double* residuals, 69 double* step) { 70 CHECK_NOTNULL(jacobian); 71 CHECK_NOTNULL(residuals); 72 CHECK_NOTNULL(step); 73 74 const int num_parameters = jacobian->num_cols(); 75 if (!reuse_diagonal_) { 76 if (diagonal_.rows() != num_parameters) { 77 diagonal_.resize(num_parameters, 1); 78 } 79 80 jacobian->SquaredColumnNorm(diagonal_.data()); 81 for (int i = 0; i < num_parameters; ++i) { 82 diagonal_[i] = min(max(diagonal_[i], min_diagonal_), max_diagonal_); 83 } 84 } 85 86 lm_diagonal_ = (diagonal_ / radius_).array().sqrt(); 87 88 LinearSolver::PerSolveOptions solve_options; 89 solve_options.D = lm_diagonal_.data(); 90 solve_options.q_tolerance = per_solve_options.eta; 91 // Disable r_tolerance checking. Since we only care about 92 // termination via the q_tolerance. As Nash and Sofer show, 93 // r_tolerance based termination is essentially useless in 94 // Truncated Newton methods. 95 solve_options.r_tolerance = -1.0; 96 97 // Invalidate the output array lm_step, so that we can detect if 98 // the linear solver generated numerical garbage. This is known 99 // to happen for the DENSE_QR and then DENSE_SCHUR solver when 100 // the Jacobin is severly rank deficient and mu is too small. 101 InvalidateArray(num_parameters, step); 102 103 // Instead of solving Jx = -r, solve Jy = r. 104 // Then x can be found as x = -y, but the inputs jacobian and residuals 105 // do not need to be modified. 106 LinearSolver::Summary linear_solver_summary = 107 linear_solver_->Solve(jacobian, residuals, solve_options, step); 108 if (linear_solver_summary.termination_type == FAILURE || 109 !IsArrayValid(num_parameters, step)) { 110 LOG(WARNING) << "Linear solver failure. Failed to compute a finite step."; 111 linear_solver_summary.termination_type = FAILURE; 112 } else { 113 VectorRef(step, num_parameters) *= -1.0; 114 } 115 reuse_diagonal_ = true; 116 117 if (per_solve_options.dump_format_type == CONSOLE || 118 (per_solve_options.dump_format_type != CONSOLE && 119 !per_solve_options.dump_filename_base.empty())) { 120 if (!DumpLinearLeastSquaresProblem(per_solve_options.dump_filename_base, 121 per_solve_options.dump_format_type, 122 jacobian, 123 solve_options.D, 124 residuals, 125 step, 126 0)) { 127 LOG(ERROR) << "Unable to dump trust region problem." 128 << " Filename base: " << per_solve_options.dump_filename_base; 129 } 130 } 131 132 133 TrustRegionStrategy::Summary summary; 134 summary.residual_norm = linear_solver_summary.residual_norm; 135 summary.num_iterations = linear_solver_summary.num_iterations; 136 summary.termination_type = linear_solver_summary.termination_type; 137 return summary; 138} 139 140void LevenbergMarquardtStrategy::StepAccepted(double step_quality) { 141 CHECK_GT(step_quality, 0.0); 142 radius_ = radius_ / std::max(1.0 / 3.0, 143 1.0 - pow(2.0 * step_quality - 1.0, 3)); 144 radius_ = std::min(max_radius_, radius_); 145 decrease_factor_ = 2.0; 146 reuse_diagonal_ = false; 147} 148 149void LevenbergMarquardtStrategy::StepRejected(double step_quality) { 150 radius_ = radius_ / decrease_factor_; 151 decrease_factor_ *= 2.0; 152 reuse_diagonal_ = true; 153} 154 155double LevenbergMarquardtStrategy::Radius() const { 156 return radius_; 157} 158 159} // namespace internal 160} // namespace ceres 161