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 #include "ceres/ceres.h" 32 #include "gflags/gflags.h" 33 34 using ceres::AutoDiffCostFunction; 35 using ceres::CostFunction; 36 using ceres::Problem; 37 using ceres::Solver; 38 using ceres::Solve; 39 40 // Data generated using the following octave code. 41 // randn('seed', 23497); 42 // m = 0.3; 43 // c = 0.1; 44 // x=[0:0.075:5]; 45 // y = exp(m * x + c); 46 // noise = randn(size(x)) * 0.2; 47 // y_observed = y + noise; 48 // data = [x', y_observed']; 49 50 const int kNumObservations = 67; 51 const double data[] = { 52 0.000000e+00, 1.133898e+00, 53 7.500000e-02, 1.334902e+00, 54 1.500000e-01, 1.213546e+00, 55 2.250000e-01, 1.252016e+00, 56 3.000000e-01, 1.392265e+00, 57 3.750000e-01, 1.314458e+00, 58 4.500000e-01, 1.472541e+00, 59 5.250000e-01, 1.536218e+00, 60 6.000000e-01, 1.355679e+00, 61 6.750000e-01, 1.463566e+00, 62 7.500000e-01, 1.490201e+00, 63 8.250000e-01, 1.658699e+00, 64 9.000000e-01, 1.067574e+00, 65 9.750000e-01, 1.464629e+00, 66 1.050000e+00, 1.402653e+00, 67 1.125000e+00, 1.713141e+00, 68 1.200000e+00, 1.527021e+00, 69 1.275000e+00, 1.702632e+00, 70 1.350000e+00, 1.423899e+00, 71 1.425000e+00, 1.543078e+00, 72 1.500000e+00, 1.664015e+00, 73 1.575000e+00, 1.732484e+00, 74 1.650000e+00, 1.543296e+00, 75 1.725000e+00, 1.959523e+00, 76 1.800000e+00, 1.685132e+00, 77 1.875000e+00, 1.951791e+00, 78 1.950000e+00, 2.095346e+00, 79 2.025000e+00, 2.361460e+00, 80 2.100000e+00, 2.169119e+00, 81 2.175000e+00, 2.061745e+00, 82 2.250000e+00, 2.178641e+00, 83 2.325000e+00, 2.104346e+00, 84 2.400000e+00, 2.584470e+00, 85 2.475000e+00, 1.914158e+00, 86 2.550000e+00, 2.368375e+00, 87 2.625000e+00, 2.686125e+00, 88 2.700000e+00, 2.712395e+00, 89 2.775000e+00, 2.499511e+00, 90 2.850000e+00, 2.558897e+00, 91 2.925000e+00, 2.309154e+00, 92 3.000000e+00, 2.869503e+00, 93 3.075000e+00, 3.116645e+00, 94 3.150000e+00, 3.094907e+00, 95 3.225000e+00, 2.471759e+00, 96 3.300000e+00, 3.017131e+00, 97 3.375000e+00, 3.232381e+00, 98 3.450000e+00, 2.944596e+00, 99 3.525000e+00, 3.385343e+00, 100 3.600000e+00, 3.199826e+00, 101 3.675000e+00, 3.423039e+00, 102 3.750000e+00, 3.621552e+00, 103 3.825000e+00, 3.559255e+00, 104 3.900000e+00, 3.530713e+00, 105 3.975000e+00, 3.561766e+00, 106 4.050000e+00, 3.544574e+00, 107 4.125000e+00, 3.867945e+00, 108 4.200000e+00, 4.049776e+00, 109 4.275000e+00, 3.885601e+00, 110 4.350000e+00, 4.110505e+00, 111 4.425000e+00, 4.345320e+00, 112 4.500000e+00, 4.161241e+00, 113 4.575000e+00, 4.363407e+00, 114 4.650000e+00, 4.161576e+00, 115 4.725000e+00, 4.619728e+00, 116 4.800000e+00, 4.737410e+00, 117 4.875000e+00, 4.727863e+00, 118 4.950000e+00, 4.669206e+00, 119 }; 120 121 class ExponentialResidual { 122 public: 123 ExponentialResidual(double x, double y) 124 : x_(x), y_(y) {} 125 126 template <typename T> bool operator()(const T* const m, 127 const T* const c, 128 T* residual) const { 129 residual[0] = T(y_) - exp(m[0] * T(x_) + c[0]); 130 return true; 131 } 132 133 private: 134 const double x_; 135 const double y_; 136 }; 137 138 int main(int argc, char** argv) { 139 google::ParseCommandLineFlags(&argc, &argv, true); 140 google::InitGoogleLogging(argv[0]); 141 142 double m = 0.0; 143 double c = 0.0; 144 145 Problem problem; 146 for (int i = 0; i < kNumObservations; ++i) { 147 problem.AddResidualBlock( 148 new AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>( 149 new ExponentialResidual(data[2 * i], data[2 * i + 1])), 150 NULL, 151 &m, &c); 152 } 153 154 Solver::Options options; 155 options.max_num_iterations = 25; 156 options.linear_solver_type = ceres::DENSE_QR; 157 options.minimizer_progress_to_stdout = true; 158 159 Solver::Summary summary; 160 Solve(options, &problem, &summary); 161 std::cout << summary.BriefReport() << "\n"; 162 std::cout << "Initial m: " << 0.0 << " c: " << 0.0 << "\n"; 163 std::cout << "Final m: " << m << " c: " << c << "\n"; 164 return 0; 165 } 166
