1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2010, 2011, 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 // An example program that minimizes Powell's singular function. 32 // 33 // F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2) 34 // 35 // f1 = x1 + 10*x2; 36 // f2 = sqrt(5) * (x3 - x4) 37 // f3 = (x2 - 2*x3)^2 38 // f4 = sqrt(10) * (x1 - x4)^2 39 // 40 // The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1. 41 // The minimum is 0 at (x1, x2, x3, x4) = 0. 42 // 43 // From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S. 44 // Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software, 45 // Vol 7(1), March 1981. 46 47 #include <vector> 48 #include "ceres/ceres.h" 49 #include "gflags/gflags.h" 50 #include "glog/logging.h" 51 52 using ceres::AutoDiffCostFunction; 53 using ceres::CostFunction; 54 using ceres::Problem; 55 using ceres::Solver; 56 using ceres::Solve; 57 58 struct F1 { 59 template <typename T> bool operator()(const T* const x1, 60 const T* const x2, 61 T* residual) const { 62 // f1 = x1 + 10 * x2; 63 residual[0] = x1[0] + T(10.0) * x2[0]; 64 return true; 65 } 66 }; 67 68 struct F2 { 69 template <typename T> bool operator()(const T* const x3, 70 const T* const x4, 71 T* residual) const { 72 // f2 = sqrt(5) (x3 - x4) 73 residual[0] = T(sqrt(5.0)) * (x3[0] - x4[0]); 74 return true; 75 } 76 }; 77 78 struct F3 { 79 template <typename T> bool operator()(const T* const x2, 80 const T* const x4, 81 T* residual) const { 82 // f3 = (x2 - 2 x3)^2 83 residual[0] = (x2[0] - T(2.0) * x4[0]) * (x2[0] - T(2.0) * x4[0]); 84 return true; 85 } 86 }; 87 88 struct F4 { 89 template <typename T> bool operator()(const T* const x1, 90 const T* const x4, 91 T* residual) const { 92 // f4 = sqrt(10) (x1 - x4)^2 93 residual[0] = T(sqrt(10.0)) * (x1[0] - x4[0]) * (x1[0] - x4[0]); 94 return true; 95 } 96 }; 97 98 DEFINE_string(minimizer, "trust_region", 99 "Minimizer type to use, choices are: line_search & trust_region"); 100 101 int main(int argc, char** argv) { 102 google::ParseCommandLineFlags(&argc, &argv, true); 103 google::InitGoogleLogging(argv[0]); 104 105 double x1 = 3.0; 106 double x2 = -1.0; 107 double x3 = 0.0; 108 double x4 = 1.0; 109 110 Problem problem; 111 // Add residual terms to the problem using the using the autodiff 112 // wrapper to get the derivatives automatically. The parameters, x1 through 113 // x4, are modified in place. 114 problem.AddResidualBlock(new AutoDiffCostFunction<F1, 1, 1, 1>(new F1), 115 NULL, 116 &x1, &x2); 117 problem.AddResidualBlock(new AutoDiffCostFunction<F2, 1, 1, 1>(new F2), 118 NULL, 119 &x3, &x4); 120 problem.AddResidualBlock(new AutoDiffCostFunction<F3, 1, 1, 1>(new F3), 121 NULL, 122 &x2, &x3); 123 problem.AddResidualBlock(new AutoDiffCostFunction<F4, 1, 1, 1>(new F4), 124 NULL, 125 &x1, &x4); 126 127 Solver::Options options; 128 LOG_IF(FATAL, !ceres::StringToMinimizerType(FLAGS_minimizer, 129 &options.minimizer_type)) 130 << "Invalid minimizer: " << FLAGS_minimizer 131 << ", valid options are: trust_region and line_search."; 132 133 options.max_num_iterations = 100; 134 options.linear_solver_type = ceres::DENSE_QR; 135 options.minimizer_progress_to_stdout = true; 136 137 std::cout << "Initial x1 = " << x1 138 << ", x2 = " << x2 139 << ", x3 = " << x3 140 << ", x4 = " << x4 141 << "\n"; 142 143 // Run the solver! 144 Solver::Summary summary; 145 Solve(options, &problem, &summary); 146 147 std::cout << summary.FullReport() << "\n"; 148 std::cout << "Final x1 = " << x1 149 << ", x2 = " << x2 150 << ", x3 = " << x3 151 << ", x4 = " << x4 152 << "\n"; 153 return 0; 154 } 155
