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//
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6// modification, are permitted provided that the following conditions are met:
7//
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12//   and/or other materials provided with the distribution.
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16//
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18// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30
31#include "ceres/ceres.h"
32#include "glog/logging.h"
33
34using ceres::AutoDiffCostFunction;
35using ceres::CostFunction;
36using ceres::Problem;
37using ceres::Solver;
38using 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
50const int kNumObservations = 67;
51const 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
121struct ExponentialResidual {
122  ExponentialResidual(double x, double y)
123      : x_(x), y_(y) {}
124
125  template <typename T> bool operator()(const T* const m,
126                                        const T* const c,
127                                        T* residual) const {
128    residual[0] = T(y_) - exp(m[0] * T(x_) + c[0]);
129    return true;
130  }
131
132 private:
133  const double x_;
134  const double y_;
135};
136
137int main(int argc, char** argv) {
138  google::InitGoogleLogging(argv[0]);
139
140  double m = 0.0;
141  double c = 0.0;
142
143  Problem problem;
144  for (int i = 0; i < kNumObservations; ++i) {
145    problem.AddResidualBlock(
146        new AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>(
147            new ExponentialResidual(data[2 * i], data[2 * i + 1])),
148        NULL,
149        &m, &c);
150  }
151
152  Solver::Options options;
153  options.max_num_iterations = 25;
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