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 "glog/logging.h" 33 34 // Data generated using the following octave code. 35 // randn('seed', 23497); 36 // m = 0.3; 37 // c = 0.1; 38 // x=[0:0.075:5]; 39 // y = exp(m * x + c); 40 // noise = randn(size(x)) * 0.2; 41 // outlier_noise = rand(size(x)) < 0.05; 42 // y_observed = y + noise + outlier_noise; 43 // data = [x', y_observed']; 44 45 const int kNumObservations = 67; 46 const double data[] = { 47 0.000000e+00, 1.133898e+00, 48 7.500000e-02, 1.334902e+00, 49 1.500000e-01, 1.213546e+00, 50 2.250000e-01, 1.252016e+00, 51 3.000000e-01, 1.392265e+00, 52 3.750000e-01, 1.314458e+00, 53 4.500000e-01, 1.472541e+00, 54 5.250000e-01, 1.536218e+00, 55 6.000000e-01, 1.355679e+00, 56 6.750000e-01, 1.463566e+00, 57 7.500000e-01, 1.490201e+00, 58 8.250000e-01, 1.658699e+00, 59 9.000000e-01, 1.067574e+00, 60 9.750000e-01, 1.464629e+00, 61 1.050000e+00, 1.402653e+00, 62 1.125000e+00, 1.713141e+00, 63 1.200000e+00, 1.527021e+00, 64 1.275000e+00, 1.702632e+00, 65 1.350000e+00, 1.423899e+00, 66 1.425000e+00, 5.543078e+00, // Outlier point 67 1.500000e+00, 5.664015e+00, // Outlier point 68 1.575000e+00, 1.732484e+00, 69 1.650000e+00, 1.543296e+00, 70 1.725000e+00, 1.959523e+00, 71 1.800000e+00, 1.685132e+00, 72 1.875000e+00, 1.951791e+00, 73 1.950000e+00, 2.095346e+00, 74 2.025000e+00, 2.361460e+00, 75 2.100000e+00, 2.169119e+00, 76 2.175000e+00, 2.061745e+00, 77 2.250000e+00, 2.178641e+00, 78 2.325000e+00, 2.104346e+00, 79 2.400000e+00, 2.584470e+00, 80 2.475000e+00, 1.914158e+00, 81 2.550000e+00, 2.368375e+00, 82 2.625000e+00, 2.686125e+00, 83 2.700000e+00, 2.712395e+00, 84 2.775000e+00, 2.499511e+00, 85 2.850000e+00, 2.558897e+00, 86 2.925000e+00, 2.309154e+00, 87 3.000000e+00, 2.869503e+00, 88 3.075000e+00, 3.116645e+00, 89 3.150000e+00, 3.094907e+00, 90 3.225000e+00, 2.471759e+00, 91 3.300000e+00, 3.017131e+00, 92 3.375000e+00, 3.232381e+00, 93 3.450000e+00, 2.944596e+00, 94 3.525000e+00, 3.385343e+00, 95 3.600000e+00, 3.199826e+00, 96 3.675000e+00, 3.423039e+00, 97 3.750000e+00, 3.621552e+00, 98 3.825000e+00, 3.559255e+00, 99 3.900000e+00, 3.530713e+00, 100 3.975000e+00, 3.561766e+00, 101 4.050000e+00, 3.544574e+00, 102 4.125000e+00, 3.867945e+00, 103 4.200000e+00, 4.049776e+00, 104 4.275000e+00, 3.885601e+00, 105 4.350000e+00, 4.110505e+00, 106 4.425000e+00, 4.345320e+00, 107 4.500000e+00, 4.161241e+00, 108 4.575000e+00, 4.363407e+00, 109 4.650000e+00, 4.161576e+00, 110 4.725000e+00, 4.619728e+00, 111 4.800000e+00, 4.737410e+00, 112 4.875000e+00, 4.727863e+00, 113 4.950000e+00, 4.669206e+00 114 }; 115 116 using ceres::AutoDiffCostFunction; 117 using ceres::CostFunction; 118 using ceres::CauchyLoss; 119 using ceres::Problem; 120 using ceres::Solve; 121 using ceres::Solver; 122 123 struct ExponentialResidual { 124 ExponentialResidual(double x, double y) 125 : x_(x), y_(y) {} 126 127 template <typename T> bool operator()(const T* const m, 128 const T* const c, 129 T* residual) const { 130 residual[0] = T(y_) - exp(m[0] * T(x_) + c[0]); 131 return true; 132 } 133 134 private: 135 const double x_; 136 const double y_; 137 }; 138 139 int main(int argc, char** argv) { 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 CostFunction* cost_function = 148 new AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>( 149 new ExponentialResidual(data[2 * i], data[2 * i + 1])); 150 problem.AddResidualBlock(cost_function, NULL, &m, &c); 151 } 152 153 Solver::Options options; 154 options.linear_solver_type = ceres::DENSE_QR; 155 options.minimizer_progress_to_stdout = true; 156 157 Solver::Summary summary; 158 Solve(options, &problem, &summary); 159 std::cout << summary.BriefReport() << "\n"; 160 std::cout << "Initial m: " << 0.0 << " c: " << 0.0 << "\n"; 161 std::cout << "Final m: " << m << " c: " << c << "\n"; 162 return 0; 163 } 164
