examples/quadratic_auto_diff.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: keir@google.com (Keir Mierle)
//
// A simple example of using the Ceres minimizer.
//
// Minimize 0.5 (10 - x)^2 using jacobian matrix computed using
// automatic differentiation.

#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;

// A templated cost function that implements the residual r = 10 - x. The method
// Map is templated so that we can then use an automatic differentiation wrapper
// around it to generate its derivatives.
class QuadraticCostFunction {
 public:
  template <typename T> bool operator()(const T* const x, T* residual) const {
    residual[0] = T(10.0) - x[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;

  // Build the problem.
  Problem problem;

  // Set up the only cost function (also known as residual). This uses
  // auto-differentiation to obtain the derivative (jacobian).
  problem.AddResidualBlock(
      new AutoDiffCostFunction<QuadraticCostFunction, 1, 1>(
          new QuadraticCostFunction),
      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;
}