| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| // |
| // An example program that minimizes Powell's singular function. |
| // |
| // F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2) |
| // |
| // f1 = x1 + 10*x2; |
| // f2 = sqrt(5) * (x3 - x4) |
| // f3 = (x2 - 2*x3)^2 |
| // f4 = sqrt(10) * (x1 - x4)^2 |
| // |
| // The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1. |
| // The minimum is 0 at (x1, x2, x3, x4) = 0. |
| // |
| // From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S. |
| // Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software, |
| // Vol 7(1), March 1981. |
| |
| #include <vector> |
| #include "ceres/ceres.h" |
| #include "gflags/gflags.h" |
| #include "glog/logging.h" |
| |
| using ceres::AutoDiffCostFunction; |
| using ceres::CostFunction; |
| using ceres::Problem; |
| using ceres::Solver; |
| using ceres::Solve; |
| |
| struct F1 { |
| template <typename T> bool operator()(const T* const x1, |
| const T* const x2, |
| T* residual) const { |
| // f1 = x1 + 10 * x2; |
| residual[0] = x1[0] + 10.0 * x2[0]; |
| return true; |
| } |
| }; |
| |
| struct F2 { |
| template <typename T> bool operator()(const T* const x3, |
| const T* const x4, |
| T* residual) const { |
| // f2 = sqrt(5) (x3 - x4) |
| residual[0] = sqrt(5.0) * (x3[0] - x4[0]); |
| return true; |
| } |
| }; |
| |
| struct F3 { |
| template <typename T> bool operator()(const T* const x2, |
| const T* const x3, |
| T* residual) const { |
| // f3 = (x2 - 2 x3)^2 |
| residual[0] = (x2[0] - 2.0 * x3[0]) * (x2[0] - 2.0 * x3[0]); |
| return true; |
| } |
| }; |
| |
| struct F4 { |
| template <typename T> bool operator()(const T* const x1, |
| const T* const x4, |
| T* residual) const { |
| // f4 = sqrt(10) (x1 - x4)^2 |
| residual[0] = sqrt(10.0) * (x1[0] - x4[0]) * (x1[0] - x4[0]); |
| return true; |
| } |
| }; |
| |
| DEFINE_string(minimizer, "trust_region", |
| "Minimizer type to use, choices are: line_search & trust_region"); |
| |
| int main(int argc, char** argv) { |
| GFLAGS_NAMESPACE::ParseCommandLineFlags(&argc, &argv, true); |
| google::InitGoogleLogging(argv[0]); |
| |
| double x1 = 3.0; |
| double x2 = -1.0; |
| double x3 = 0.0; |
| double x4 = 1.0; |
| |
| Problem problem; |
| // Add residual terms to the problem using the using the autodiff |
| // wrapper to get the derivatives automatically. The parameters, x1 through |
| // x4, are modified in place. |
| problem.AddResidualBlock(new AutoDiffCostFunction<F1, 1, 1, 1>(new F1), |
| NULL, |
| &x1, &x2); |
| problem.AddResidualBlock(new AutoDiffCostFunction<F2, 1, 1, 1>(new F2), |
| NULL, |
| &x3, &x4); |
| problem.AddResidualBlock(new AutoDiffCostFunction<F3, 1, 1, 1>(new F3), |
| NULL, |
| &x2, &x3); |
| problem.AddResidualBlock(new AutoDiffCostFunction<F4, 1, 1, 1>(new F4), |
| NULL, |
| &x1, &x4); |
| |
| Solver::Options options; |
| LOG_IF(FATAL, !ceres::StringToMinimizerType(FLAGS_minimizer, |
| &options.minimizer_type)) |
| << "Invalid minimizer: " << FLAGS_minimizer |
| << ", valid options are: trust_region and line_search."; |
| |
| options.max_num_iterations = 100; |
| options.linear_solver_type = ceres::DENSE_QR; |
| options.minimizer_progress_to_stdout = true; |
| |
| std::cout << "Initial x1 = " << x1 |
| << ", x2 = " << x2 |
| << ", x3 = " << x3 |
| << ", x4 = " << x4 |
| << "\n"; |
| |
| // Run the solver! |
| Solver::Summary summary; |
| Solve(options, &problem, &summary); |
| |
| std::cout << summary.FullReport() << "\n"; |
| std::cout << "Final x1 = " << x1 |
| << ", x2 = " << x2 |
| << ", x3 = " << x3 |
| << ", x4 = " << x4 |
| << "\n"; |
| return 0; |
| } |