// Ceres Solver - A fast non-linear least squares minimizer

// Copyright 2015 Google Inc. All rights reserved.

// http://ceres-solver.org/

//

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// 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 x4,

                                        T* residual) const {

    // f3 = (x2 - 2 x3)^2

    residual[0] = (x2[0] - 2.0 * x4[0]) * (x2[0] - 2.0 * x4[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;

}