10ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Ceres Solver - A fast non-linear least squares minimizer 20ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Copyright 2010, 2011, 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// An example program that minimizes Powell's singular function. 320ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 330ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2) 340ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 350ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// f1 = x1 + 10*x2; 360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// f2 = sqrt(5) * (x3 - x4) 370ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// f3 = (x2 - 2*x3)^2 380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// f4 = sqrt(10) * (x1 - x4)^2 390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1. 410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// The minimum is 0 at (x1, x2, x3, x4) = 0. 420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// 430ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S. 440ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software, 450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Vol 7(1), March 1981. 460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 470ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include <vector> 480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/ceres.h" 490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "gflags/gflags.h" 500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "glog/logging.h" 510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 520ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::AutoDiffCostFunction; 530ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::CostFunction; 540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::Problem; 550ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::Solver; 560ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongusing ceres::Solve; 570ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 581d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberlingstruct F1 { 590ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong template <typename T> bool operator()(const T* const x1, 600ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const T* const x2, 610ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong T* residual) const { 620ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // f1 = x1 + 10 * x2; 630ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong residual[0] = x1[0] + T(10.0) * x2[0]; 640ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return true; 650ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 660ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong}; 670ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 681d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberlingstruct F2 { 690ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong template <typename T> bool operator()(const T* const x3, 700ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const T* const x4, 710ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong T* residual) const { 720ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // f2 = sqrt(5) (x3 - x4) 730ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong residual[0] = T(sqrt(5.0)) * (x3[0] - x4[0]); 740ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return true; 750ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 760ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong}; 770ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 781d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberlingstruct F3 { 790ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong template <typename T> bool operator()(const T* const x2, 800ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const T* const x4, 810ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong T* residual) const { 820ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // f3 = (x2 - 2 x3)^2 830ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong residual[0] = (x2[0] - T(2.0) * x4[0]) * (x2[0] - T(2.0) * x4[0]); 840ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return true; 850ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 860ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong}; 870ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 881d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberlingstruct F4 { 890ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong template <typename T> bool operator()(const T* const x1, 900ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong const T* const x4, 910ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong T* residual) const { 920ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // f4 = sqrt(10) (x1 - x4)^2 930ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong residual[0] = T(sqrt(10.0)) * (x1[0] - x4[0]) * (x1[0] - x4[0]); 940ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return true; 950ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong } 960ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong}; 970ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 981d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha HaeberlingDEFINE_string(minimizer, "trust_region", 991d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling "Minimizer type to use, choices are: line_search & trust_region"); 1001d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling 1010ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongint main(int argc, char** argv) { 1020ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong google::ParseCommandLineFlags(&argc, &argv, true); 1030ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong google::InitGoogleLogging(argv[0]); 1040ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1050ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong double x1 = 3.0; 1060ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong double x2 = -1.0; 1070ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong double x3 = 0.0; 1080ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong double x4 = 1.0; 1090ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1100ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong Problem problem; 1110ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // Add residual terms to the problem using the using the autodiff 1120ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // wrapper to get the derivatives automatically. The parameters, x1 through 1130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong // x4, are modified in place. 1140ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong problem.AddResidualBlock(new AutoDiffCostFunction<F1, 1, 1, 1>(new F1), 1150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong NULL, 1160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong &x1, &x2); 1170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong problem.AddResidualBlock(new AutoDiffCostFunction<F2, 1, 1, 1>(new F2), 1180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong NULL, 1190ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong &x3, &x4); 1200ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong problem.AddResidualBlock(new AutoDiffCostFunction<F3, 1, 1, 1>(new F3), 1210ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong NULL, 1220ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong &x2, &x3); 1230ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong problem.AddResidualBlock(new AutoDiffCostFunction<F4, 1, 1, 1>(new F4), 1240ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong NULL, 1250ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong &x1, &x4); 1260ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1270ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong Solver::Options options; 1281d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling LOG_IF(FATAL, !ceres::StringToMinimizerType(FLAGS_minimizer, 1291d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling &options.minimizer_type)) 1301d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling << "Invalid minimizer: " << FLAGS_minimizer 1311d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling << ", valid options are: trust_region and line_search."; 1321d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling 1331d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling options.max_num_iterations = 100; 1340ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong options.linear_solver_type = ceres::DENSE_QR; 1350ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong options.minimizer_progress_to_stdout = true; 1360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1370ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong std::cout << "Initial x1 = " << x1 1380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << ", x2 = " << x2 1390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << ", x3 = " << x3 1400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << ", x4 = " << x4 1410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << "\n"; 1420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1431d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling // Run the solver! 1441d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling Solver::Summary summary; 1450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong Solve(options, &problem, &summary); 1460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong 1471d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling std::cout << summary.FullReport() << "\n"; 1480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong std::cout << "Final x1 = " << x1 1490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << ", x2 = " << x2 1500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << ", x3 = " << x3 1510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << ", x4 = " << x4 1520ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong << "\n"; 1530ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong return 0; 1540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong} 155