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

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

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// Author: keir@google.com (Keir Mierle)

//         sameeragarwal@google.com (Sameer Agarwal)

//

// End-to-end tests for Ceres using Powell's function.

#include <cmath>

#include <cstdlib>

#include "ceres/autodiff_cost_function.h"

#include "ceres/problem.h"

#include "ceres/solver.h"

#include "ceres/test_util.h"

#include "ceres/types.h"

#include "glog/logging.h"

#include "gtest/gtest.h"

namespace ceres {

namespace internal {

// This class implements the SystemTestProblem interface and provides

// access to an implementation of 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.

class PowellsFunction {

 public:

  PowellsFunction() {

    x_[0] =  3.0;

    x_[1] = -1.0;

    x_[2] =  0.0;

    x_[3] =  1.0;

    problem_.AddResidualBlock(

        new AutoDiffCostFunction<F1, 1, 1, 1>(new F1), NULL, &x_[0], &x_[1]);

    problem_.AddResidualBlock(

        new AutoDiffCostFunction<F2, 1, 1, 1>(new F2), NULL, &x_[2], &x_[3]);

    problem_.AddResidualBlock(

        new AutoDiffCostFunction<F3, 1, 1, 1>(new F3), NULL, &x_[1], &x_[2]);

    problem_.AddResidualBlock(

        new AutoDiffCostFunction<F4, 1, 1, 1>(new F4), NULL, &x_[0], &x_[3]);

    // Settings for the reference solution.

    options_.linear_solver_type = ceres::DENSE_QR;

    options_.max_num_iterations = 10;

    options_.num_threads = 1;

  }

  Problem* mutable_problem() { return &problem_; }

  Solver::Options* mutable_solver_options() { return &options_; }

  static double kResidualTolerance;

 private:

  // Templated functions used for automatically differentiated cost

  // functions.

  class F1 {

   public:

    template <typename T> bool operator()(const T* const x1,

                                          const T* const x2,

                                          T* residual) const {

      // f1 = x1 + 10 * x2;

      *residual = *x1 + 10.0 * *x2;

      return true;

    }

  };

  class F2 {

   public:

    template <typename T> bool operator()(const T* const x3,

                                          const T* const x4,

                                          T* residual) const {

      // f2 = sqrt(5) (x3 - x4)

      *residual = sqrt(5.0) * (*x3 - *x4);

      return true;

    }

  };

  class F3 {

   public:

    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;

    }

  };

  class F4 {

   public:

    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;

    }

  };

  double x_[4];

  Problem problem_;

  Solver::Options options_;

};

double PowellsFunction::kResidualTolerance = 1e-8;

typedef SystemTest<PowellsFunction> PowellTest;

const bool kAutomaticOrdering = true;

TEST_F(PowellTest, DenseQR) {

  RunSolverForConfigAndExpectResidualsMatch(

      SolverConfig(DENSE_QR, NO_SPARSE));

}

TEST_F(PowellTest, DenseNormalCholesky) {

  RunSolverForConfigAndExpectResidualsMatch(

      SolverConfig(DENSE_NORMAL_CHOLESKY));

}

TEST_F(PowellTest, DenseSchur) {

  RunSolverForConfigAndExpectResidualsMatch(

      SolverConfig(DENSE_SCHUR));

}

TEST_F(PowellTest, IterativeSchurWithJacobi) {

  RunSolverForConfigAndExpectResidualsMatch(

      SolverConfig(ITERATIVE_SCHUR, NO_SPARSE, kAutomaticOrdering, JACOBI));

}

#ifndef CERES_NO_SUITESPARSE

TEST_F(PowellTest, SparseNormalCholeskyUsingSuiteSparse) {

  RunSolverForConfigAndExpectResidualsMatch(

      SolverConfig(SPARSE_NORMAL_CHOLESKY, SUITE_SPARSE, kAutomaticOrdering));

}

#endif  // CERES_NO_SUITESPARSE

#ifndef CERES_NO_CXSPARSE

TEST_F(PowellTest, SparseNormalCholeskyUsingCXSparse) {

  RunSolverForConfigAndExpectResidualsMatch(

      SolverConfig(SPARSE_NORMAL_CHOLESKY, CX_SPARSE, kAutomaticOrdering));

}

#endif  // CERES_NO_CXSPARSE

#ifdef CERES_USE_EIGEN_SPARSE

TEST_F(PowellTest, SparseNormalCholeskyUsingEigenSparse) {

  RunSolverForConfigAndExpectResidualsMatch(

      SolverConfig(SPARSE_NORMAL_CHOLESKY, EIGEN_SPARSE, kAutomaticOrdering));

}

#endif  // CERES_USE_EIGEN_SPARSE

}  // namespace internal

}  // namespace ceres