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.
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14 // used to endorse or promote products derived from this software without
15 // specific prior written permission.
16 //
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28 //
29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30 //
31 // An example program that minimizes Powell's singular function.
32 //
33 // F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2)
34 //
35 // f1 = x1 + 10*x2;
36 // f2 = sqrt(5) * (x3 - x4)
37 // f3 = (x2 - 2*x3)^2
38 // f4 = sqrt(10) * (x1 - x4)^2
39 //
40 // The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1.
41 // The minimum is 0 at (x1, x2, x3, x4) = 0.
42 //
43 // From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S.
44 // Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software,
45 // Vol 7(1), March 1981.
46
47 #include <vector>
48 #include "ceres/ceres.h"
49 #include "gflags/gflags.h"
50 #include "glog/logging.h"
51
52 using ceres::AutoDiffCostFunction;
53 using ceres::CostFunction;
54 using ceres::Problem;
55 using ceres::Solver;
56 using ceres::Solve;
57
58 struct F1 {
operator ()F159 template <typename T> bool operator()(const T* const x1,
60 const T* const x2,
61 T* residual) const {
62 // f1 = x1 + 10 * x2;
63 residual[0] = x1[0] + T(10.0) * x2[0];
64 return true;
65 }
66 };
67
68 struct F2 {
operator ()F269 template <typename T> bool operator()(const T* const x3,
70 const T* const x4,
71 T* residual) const {
72 // f2 = sqrt(5) (x3 - x4)
73 residual[0] = T(sqrt(5.0)) * (x3[0] - x4[0]);
74 return true;
75 }
76 };
77
78 struct F3 {
operator ()F379 template <typename T> bool operator()(const T* const x2,
80 const T* const x4,
81 T* residual) const {
82 // f3 = (x2 - 2 x3)^2
83 residual[0] = (x2[0] - T(2.0) * x4[0]) * (x2[0] - T(2.0) * x4[0]);
84 return true;
85 }
86 };
87
88 struct F4 {
operator ()F489 template <typename T> bool operator()(const T* const x1,
90 const T* const x4,
91 T* residual) const {
92 // f4 = sqrt(10) (x1 - x4)^2
93 residual[0] = T(sqrt(10.0)) * (x1[0] - x4[0]) * (x1[0] - x4[0]);
94 return true;
95 }
96 };
97
98 DEFINE_string(minimizer, "trust_region",
99 "Minimizer type to use, choices are: line_search & trust_region");
100
main(int argc,char ** argv)101 int main(int argc, char** argv) {
102 google::ParseCommandLineFlags(&argc, &argv, true);
103 google::InitGoogleLogging(argv[0]);
104
105 double x1 = 3.0;
106 double x2 = -1.0;
107 double x3 = 0.0;
108 double x4 = 1.0;
109
110 Problem problem;
111 // Add residual terms to the problem using the using the autodiff
112 // wrapper to get the derivatives automatically. The parameters, x1 through
113 // x4, are modified in place.
114 problem.AddResidualBlock(new AutoDiffCostFunction<F1, 1, 1, 1>(new F1),
115 NULL,
116 &x1, &x2);
117 problem.AddResidualBlock(new AutoDiffCostFunction<F2, 1, 1, 1>(new F2),
118 NULL,
119 &x3, &x4);
120 problem.AddResidualBlock(new AutoDiffCostFunction<F3, 1, 1, 1>(new F3),
121 NULL,
122 &x2, &x3);
123 problem.AddResidualBlock(new AutoDiffCostFunction<F4, 1, 1, 1>(new F4),
124 NULL,
125 &x1, &x4);
126
127 Solver::Options options;
128 LOG_IF(FATAL, !ceres::StringToMinimizerType(FLAGS_minimizer,
129 &options.minimizer_type))
130 << "Invalid minimizer: " << FLAGS_minimizer
131 << ", valid options are: trust_region and line_search.";
132
133 options.max_num_iterations = 100;
134 options.linear_solver_type = ceres::DENSE_QR;
135 options.minimizer_progress_to_stdout = true;
136
137 std::cout << "Initial x1 = " << x1
138 << ", x2 = " << x2
139 << ", x3 = " << x3
140 << ", x4 = " << x4
141 << "\n";
142
143 // Run the solver!
144 Solver::Summary summary;
145 Solve(options, &problem, &summary);
146
147 std::cout << summary.FullReport() << "\n";
148 std::cout << "Final x1 = " << x1
149 << ", x2 = " << x2
150 << ", x3 = " << x3
151 << ", x4 = " << x4
152 << "\n";
153 return 0;
154 }
155