| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2023 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| // |
| // This example fits the curve f(x;m,c) = e^(m * x + c) to data, minimizing the |
| // sum squared loss. |
| |
| #include "ceres/ceres.h" |
| #include "glog/logging.h" |
| |
| // Data generated using the following octave code. |
| // randn('seed', 23497); |
| // m = 0.3; |
| // c = 0.1; |
| // x=[0:0.075:5]; |
| // y = exp(m * x + c); |
| // noise = randn(size(x)) * 0.2; |
| // y_observed = y + noise; |
| // data = [x', y_observed']; |
| |
| const int kNumObservations = 67; |
| // clang-format off |
| const double data[] = { |
| 0.000000e+00, 1.133898e+00, |
| 7.500000e-02, 1.334902e+00, |
| 1.500000e-01, 1.213546e+00, |
| 2.250000e-01, 1.252016e+00, |
| 3.000000e-01, 1.392265e+00, |
| 3.750000e-01, 1.314458e+00, |
| 4.500000e-01, 1.472541e+00, |
| 5.250000e-01, 1.536218e+00, |
| 6.000000e-01, 1.355679e+00, |
| 6.750000e-01, 1.463566e+00, |
| 7.500000e-01, 1.490201e+00, |
| 8.250000e-01, 1.658699e+00, |
| 9.000000e-01, 1.067574e+00, |
| 9.750000e-01, 1.464629e+00, |
| 1.050000e+00, 1.402653e+00, |
| 1.125000e+00, 1.713141e+00, |
| 1.200000e+00, 1.527021e+00, |
| 1.275000e+00, 1.702632e+00, |
| 1.350000e+00, 1.423899e+00, |
| 1.425000e+00, 1.543078e+00, |
| 1.500000e+00, 1.664015e+00, |
| 1.575000e+00, 1.732484e+00, |
| 1.650000e+00, 1.543296e+00, |
| 1.725000e+00, 1.959523e+00, |
| 1.800000e+00, 1.685132e+00, |
| 1.875000e+00, 1.951791e+00, |
| 1.950000e+00, 2.095346e+00, |
| 2.025000e+00, 2.361460e+00, |
| 2.100000e+00, 2.169119e+00, |
| 2.175000e+00, 2.061745e+00, |
| 2.250000e+00, 2.178641e+00, |
| 2.325000e+00, 2.104346e+00, |
| 2.400000e+00, 2.584470e+00, |
| 2.475000e+00, 1.914158e+00, |
| 2.550000e+00, 2.368375e+00, |
| 2.625000e+00, 2.686125e+00, |
| 2.700000e+00, 2.712395e+00, |
| 2.775000e+00, 2.499511e+00, |
| 2.850000e+00, 2.558897e+00, |
| 2.925000e+00, 2.309154e+00, |
| 3.000000e+00, 2.869503e+00, |
| 3.075000e+00, 3.116645e+00, |
| 3.150000e+00, 3.094907e+00, |
| 3.225000e+00, 2.471759e+00, |
| 3.300000e+00, 3.017131e+00, |
| 3.375000e+00, 3.232381e+00, |
| 3.450000e+00, 2.944596e+00, |
| 3.525000e+00, 3.385343e+00, |
| 3.600000e+00, 3.199826e+00, |
| 3.675000e+00, 3.423039e+00, |
| 3.750000e+00, 3.621552e+00, |
| 3.825000e+00, 3.559255e+00, |
| 3.900000e+00, 3.530713e+00, |
| 3.975000e+00, 3.561766e+00, |
| 4.050000e+00, 3.544574e+00, |
| 4.125000e+00, 3.867945e+00, |
| 4.200000e+00, 4.049776e+00, |
| 4.275000e+00, 3.885601e+00, |
| 4.350000e+00, 4.110505e+00, |
| 4.425000e+00, 4.345320e+00, |
| 4.500000e+00, 4.161241e+00, |
| 4.575000e+00, 4.363407e+00, |
| 4.650000e+00, 4.161576e+00, |
| 4.725000e+00, 4.619728e+00, |
| 4.800000e+00, 4.737410e+00, |
| 4.875000e+00, 4.727863e+00, |
| 4.950000e+00, 4.669206e+00, |
| }; |
| // clang-format on |
| |
| struct ExponentialResidual { |
| ExponentialResidual(double x, double y) : x_(x), y_(y) {} |
| |
| template <typename T> |
| bool operator()(const T* const m, const T* const c, T* residual) const { |
| residual[0] = y_ - exp(m[0] * x_ + c[0]); |
| return true; |
| } |
| |
| private: |
| const double x_; |
| const double y_; |
| }; |
| |
| int main(int argc, char** argv) { |
| google::InitGoogleLogging(argv[0]); |
| |
| const double initial_m = 0.0; |
| const double initial_c = 0.0; |
| double m = initial_m; |
| double c = initial_c; |
| |
| ceres::Problem problem; |
| for (int i = 0; i < kNumObservations; ++i) { |
| problem.AddResidualBlock( |
| new ceres::AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>( |
| data[2 * i], data[2 * i + 1]), |
| nullptr, |
| &m, |
| &c); |
| } |
| |
| ceres::Solver::Options options; |
| options.max_num_iterations = 25; |
| options.linear_solver_type = ceres::DENSE_QR; |
| options.minimizer_progress_to_stdout = true; |
| |
| ceres::Solver::Summary summary; |
| ceres::Solve(options, &problem, &summary); |
| std::cout << summary.BriefReport() << "\n"; |
| std::cout << "Initial m: " << initial_m << " c: " << initial_c << "\n"; |
| std::cout << "Final m: " << m << " c: " << c << "\n"; |
| return 0; |
| } |