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//
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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
52using ceres::AutoDiffCostFunction;
53using ceres::CostFunction;
54using ceres::Problem;
55using ceres::Solver;
56using ceres::Solve;
57
58struct F1 {
59  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
68struct F2 {
69  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
78struct F3 {
79  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
88struct F4 {
89  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
98DEFINE_string(minimizer, "trust_region",
99              "Minimizer type to use, choices are: line_search & trust_region");
100
101int 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