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+// 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
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// 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) {
+  CERES_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;
+}