10ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Ceres Solver - A fast non-linear least squares minimizer 20ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Copyright 2012 Google Inc. All rights reserved. 30ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// http://code.google.com/p/ceres-solver/ 40ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 50ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Redistribution and use in source and binary forms, with or without 60ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// modification, are permitted provided that the following conditions are met: 70ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 80ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Redistributions of source code must retain the above copyright notice, 90ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// this list of conditions and the following disclaimer. 100ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Redistributions in binary form must reproduce the above copyright notice, 110ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// this list of conditions and the following disclaimer in the documentation 120ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// and/or other materials provided with the distribution. 130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Neither the name of Google Inc. nor the names of its contributors may be 140ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// used to endorse or promote products derived from this software without 150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// specific prior written permission. 160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 190ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 200ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 210ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 220ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 230ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 240ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 250ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 260ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 270ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// POSSIBILITY OF SUCH DAMAGE. 280ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 290ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Author: sameeragarwal@google.com (Sameer Agarwal) 300ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 310ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/levenberg_marquardt_strategy.h" 320ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 330ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include <cmath> 340ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "Eigen/Core" 350ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/array_utils.h" 360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/internal/eigen.h" 371d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling#include "ceres/linear_least_squares_problems.h" 380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/linear_solver.h" 390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/sparse_matrix.h" 400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/trust_region_strategy.h" 410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/types.h" 420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "glog/logging.h" 430ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 440ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongnamespace ceres { 450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongnamespace internal { 460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 470ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus KongLevenbergMarquardtStrategy::LevenbergMarquardtStrategy( 480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const TrustRegionStrategy::Options& options) 490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong : linear_solver_(options.linear_solver), 500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong radius_(options.initial_radius), 510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong max_radius_(options.max_radius), 521d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling min_diagonal_(options.min_lm_diagonal), 531d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling max_diagonal_(options.max_lm_diagonal), 540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong decrease_factor_(2.0), 550ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong reuse_diagonal_(false) { 560ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_NOTNULL(linear_solver_); 570ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_GT(min_diagonal_, 0.0); 580ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_LE(min_diagonal_, max_diagonal_); 590ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_GT(max_radius_, 0.0); 600ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 610ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 620ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus KongLevenbergMarquardtStrategy::~LevenbergMarquardtStrategy() { 630ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 640ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 650ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus KongTrustRegionStrategy::Summary LevenbergMarquardtStrategy::ComputeStep( 660ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const TrustRegionStrategy::PerSolveOptions& per_solve_options, 670ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong SparseMatrix* jacobian, 680ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const double* residuals, 690ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong double* step) { 700ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_NOTNULL(jacobian); 710ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_NOTNULL(residuals); 720ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_NOTNULL(step); 730ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 740ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const int num_parameters = jacobian->num_cols(); 750ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong if (!reuse_diagonal_) { 760ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong if (diagonal_.rows() != num_parameters) { 770ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong diagonal_.resize(num_parameters, 1); 780ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 790ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 800ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong jacobian->SquaredColumnNorm(diagonal_.data()); 810ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong for (int i = 0; i < num_parameters; ++i) { 820ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong diagonal_[i] = min(max(diagonal_[i], min_diagonal_), max_diagonal_); 830ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 840ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 850ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 860ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong lm_diagonal_ = (diagonal_ / radius_).array().sqrt(); 870ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 880ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong LinearSolver::PerSolveOptions solve_options; 890ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong solve_options.D = lm_diagonal_.data(); 900ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong solve_options.q_tolerance = per_solve_options.eta; 910ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // Disable r_tolerance checking. Since we only care about 920ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // termination via the q_tolerance. As Nash and Sofer show, 930ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // r_tolerance based termination is essentially useless in 940ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // Truncated Newton methods. 950ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong solve_options.r_tolerance = -1.0; 960ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 970ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // Invalidate the output array lm_step, so that we can detect if 980ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // the linear solver generated numerical garbage. This is known 990ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // to happen for the DENSE_QR and then DENSE_SCHUR solver when 1000ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // the Jacobin is severly rank deficient and mu is too small. 1010ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong InvalidateArray(num_parameters, step); 1020ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1030ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // Instead of solving Jx = -r, solve Jy = r. 1040ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // Then x can be found as x = -y, but the inputs jacobian and residuals 1050ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // do not need to be modified. 1060ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong LinearSolver::Summary linear_solver_summary = 1070ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong linear_solver_->Solve(jacobian, residuals, solve_options, step); 10879397c21138f54fcff6ec067b44b847f1f7e0e98Carlos Hernandez 10979397c21138f54fcff6ec067b44b847f1f7e0e98Carlos Hernandez if (linear_solver_summary.termination_type == LINEAR_SOLVER_FATAL_ERROR) { 11079397c21138f54fcff6ec067b44b847f1f7e0e98Carlos Hernandez LOG(WARNING) << "Linear solver fatal error."; 11179397c21138f54fcff6ec067b44b847f1f7e0e98Carlos Hernandez } else if (linear_solver_summary.termination_type == LINEAR_SOLVER_FAILURE || 11279397c21138f54fcff6ec067b44b847f1f7e0e98Carlos Hernandez !IsArrayValid(num_parameters, step)) { 1130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong LOG(WARNING) << "Linear solver failure. Failed to compute a finite step."; 11479397c21138f54fcff6ec067b44b847f1f7e0e98Carlos Hernandez linear_solver_summary.termination_type = LINEAR_SOLVER_FAILURE; 1150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } else { 1160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong VectorRef(step, num_parameters) *= -1.0; 1170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 1180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong reuse_diagonal_ = true; 1190ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1201d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling if (per_solve_options.dump_format_type == CONSOLE || 1211d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling (per_solve_options.dump_format_type != CONSOLE && 1221d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling !per_solve_options.dump_filename_base.empty())) { 1231d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling if (!DumpLinearLeastSquaresProblem(per_solve_options.dump_filename_base, 1241d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling per_solve_options.dump_format_type, 1251d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling jacobian, 1261d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling solve_options.D, 1271d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling residuals, 1281d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling step, 1291d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling 0)) { 1301d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling LOG(ERROR) << "Unable to dump trust region problem." 1311d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling << " Filename base: " << per_solve_options.dump_filename_base; 1321d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling } 1331d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling } 1341d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling 1351d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling 1360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong TrustRegionStrategy::Summary summary; 1370ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong summary.residual_norm = linear_solver_summary.residual_norm; 1380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong summary.num_iterations = linear_solver_summary.num_iterations; 1390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong summary.termination_type = linear_solver_summary.termination_type; 1400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return summary; 1410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 1420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1430ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongvoid LevenbergMarquardtStrategy::StepAccepted(double step_quality) { 1440ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong CHECK_GT(step_quality, 0.0); 1450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong radius_ = radius_ / std::max(1.0 / 3.0, 1460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1.0 - pow(2.0 * step_quality - 1.0, 3)); 1470ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong radius_ = std::min(max_radius_, radius_); 1480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong decrease_factor_ = 2.0; 1490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong reuse_diagonal_ = false; 1500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 1510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1520ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongvoid LevenbergMarquardtStrategy::StepRejected(double step_quality) { 1530ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong radius_ = radius_ / decrease_factor_; 1540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong decrease_factor_ *= 2.0; 1550ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong reuse_diagonal_ = true; 1560ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 1570ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1580ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongdouble LevenbergMarquardtStrategy::Radius() const { 1590ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return radius_; 1600ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 1610ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1620ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} // namespace internal 1630ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} // namespace ceres 164