text: // Ceres Solver - A fast non-linear least squares minimizer
  // Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
  // http://code.google.com/p/ceres-solver/
  //
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  // modification, are permitted provided that the following conditions are met:
  //
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  //   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
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  //
  // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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  // 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
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  // POSSIBILITY OF SUCH DAMAGE.
  //
  // Author: keir@google.com (Keir Mierle)
  //
  // Minimize 0.5 (10 - x)^2 using jacobian matrix computed using
  // numeric differentiation.
  
  #include <vector>
  
  #include "ceres/ceres.h"
  
  using ceres::NumericDiffCostFunction;
  using ceres::CENTRAL;
  using ceres::SizedCostFunction;
  using ceres::CostFunction;
  using ceres::Problem;
  using ceres::Solver;
  using ceres::Solve;
  
  class ResidualWithNoDerivative
    : public SizedCostFunction<1 /* number of residuals */,
                               1 /* size of first parameter */> {
   public:
    virtual ~ResidualWithNoDerivative() {}
    virtual bool Evaluate(double const* const* parameters,
                          double* residuals,
                          double** jacobians) const {
      (void) jacobians;  // Ignored; filled in by numeric differentiation.
  
      // f(x) = 10 - x.
      residuals[0] = 10 - parameters[0][0];
      return true;
    }
  };
  
  int main(int argc, char** argv) {
    google::ParseCommandLineFlags(&argc, &argv, true);
    google::InitGoogleLogging(argv[0]);
  
    // The variable to solve for with its initial value.
    double initial_x = 5.0;
    double x = initial_x;
  
    // Set up the only cost function (also known as residual). This uses
    // numeric differentiation to obtain the derivative (jacobian).
    CostFunction* cost =
        new NumericDiffCostFunction<ResidualWithNoDerivative, CENTRAL, 1, 1> (
            new ResidualWithNoDerivative, ceres::TAKE_OWNERSHIP);
  
    // Build the problem.
    Problem problem;
    problem.AddResidualBlock(cost, NULL, &x);
  
    // Run the solver!
    Solver::Options options;
    options.max_num_iterations = 10;
    options.linear_solver_type = ceres::DENSE_QR;
    options.minimizer_progress_to_stdout = true;
    Solver::Summary summary;
    Solve(options, &problem, &summary);
    std::cout << summary.BriefReport() << "\n";
    std::cout << "x : " << initial_x
              << " -> " << x << "\n";
    return 0;
  }
  