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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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.
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14 // used to endorse or promote products derived from this software without
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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
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24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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28 //
29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30
31 #include "ceres/ceres.h"
32 #include "glog/logging.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 struct ExponentialResidual {
ExponentialResidualExponentialResidual122 ExponentialResidual(double x, double y)
123 : x_(x), y_(y) {}
124
operator ()ExponentialResidual125 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
main(int argc,char ** argv)137 int 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