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@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
45const int kNumObservations = 67;
46const double data[] = {
470.000000e+00, 1.133898e+00,
487.500000e-02, 1.334902e+00,
491.500000e-01, 1.213546e+00,
502.250000e-01, 1.252016e+00,
513.000000e-01, 1.392265e+00,
523.750000e-01, 1.314458e+00,
534.500000e-01, 1.472541e+00,
545.250000e-01, 1.536218e+00,
556.000000e-01, 1.355679e+00,
566.750000e-01, 1.463566e+00,
577.500000e-01, 1.490201e+00,
588.250000e-01, 1.658699e+00,
599.000000e-01, 1.067574e+00,
609.750000e-01, 1.464629e+00,
611.050000e+00, 1.402653e+00,
621.125000e+00, 1.713141e+00,
631.200000e+00, 1.527021e+00,
641.275000e+00, 1.702632e+00,
651.350000e+00, 1.423899e+00,
661.425000e+00, 5.543078e+00, // Outlier point
671.500000e+00, 5.664015e+00, // Outlier point
681.575000e+00, 1.732484e+00,
691.650000e+00, 1.543296e+00,
701.725000e+00, 1.959523e+00,
711.800000e+00, 1.685132e+00,
721.875000e+00, 1.951791e+00,
731.950000e+00, 2.095346e+00,
742.025000e+00, 2.361460e+00,
752.100000e+00, 2.169119e+00,
762.175000e+00, 2.061745e+00,
772.250000e+00, 2.178641e+00,
782.325000e+00, 2.104346e+00,
792.400000e+00, 2.584470e+00,
802.475000e+00, 1.914158e+00,
812.550000e+00, 2.368375e+00,
822.625000e+00, 2.686125e+00,
832.700000e+00, 2.712395e+00,
842.775000e+00, 2.499511e+00,
852.850000e+00, 2.558897e+00,
862.925000e+00, 2.309154e+00,
873.000000e+00, 2.869503e+00,
883.075000e+00, 3.116645e+00,
893.150000e+00, 3.094907e+00,
903.225000e+00, 2.471759e+00,
913.300000e+00, 3.017131e+00,
923.375000e+00, 3.232381e+00,
933.450000e+00, 2.944596e+00,
943.525000e+00, 3.385343e+00,
953.600000e+00, 3.199826e+00,
963.675000e+00, 3.423039e+00,
973.750000e+00, 3.621552e+00,
983.825000e+00, 3.559255e+00,
993.900000e+00, 3.530713e+00,
1003.975000e+00, 3.561766e+00,
1014.050000e+00, 3.544574e+00,
1024.125000e+00, 3.867945e+00,
1034.200000e+00, 4.049776e+00,
1044.275000e+00, 3.885601e+00,
1054.350000e+00, 4.110505e+00,
1064.425000e+00, 4.345320e+00,
1074.500000e+00, 4.161241e+00,
1084.575000e+00, 4.363407e+00,
1094.650000e+00, 4.161576e+00,
1104.725000e+00, 4.619728e+00,
1114.800000e+00, 4.737410e+00,
1124.875000e+00, 4.727863e+00,
1134.950000e+00, 4.669206e+00
114};
115
116using ceres::AutoDiffCostFunction;
117using ceres::CostFunction;
118using ceres::CauchyLoss;
119using ceres::Problem;
120using ceres::Solve;
121using ceres::Solver;
122
123struct 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
139int 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