internal/ceres/system_test.cc

// 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 "ceres/autodiff_cost_function.h"
#include "ceres/internal/config.h"
#include "ceres/jet.h"
#include "ceres/problem.h"
#include "ceres/solver.h"
#include "ceres/test_util.h"
#include "ceres/types.h"
#include "gtest/gtest.h"

namespace ceres::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), nullptr, &x_[0], &x_[1]);
    problem_.AddResidualBlock(
        new AutoDiffCostFunction<F2, 1, 1, 1>(new F2), nullptr, &x_[2], &x_[3]);
    problem_.AddResidualBlock(
        new AutoDiffCostFunction<F3, 1, 1, 1>(new F3), nullptr, &x_[1], &x_[2]);
    problem_.AddResidualBlock(
        new AutoDiffCostFunction<F4, 1, 1, 1>(new F4), nullptr, &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 constexpr double kResidualTolerance = 1e-8;

 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[0] + 10.0 * x2[0];
      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[0] - x4[0]);
      return true;
    }
  };

  class F3 {
   public:
    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;
    }
  };

  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_;
};

using PowellTest = SystemTest<PowellsFunction>;

TEST_F(PowellTest, DenseQR) {
  PowellsFunction powells_function;
  Solver::Options* options = powells_function.mutable_solver_options();
  options->linear_solver_type = DENSE_QR;
  RunSolverForConfigAndExpectResidualsMatch(*options,
                                            powells_function.mutable_problem());
}

TEST_F(PowellTest, DenseNormalCholesky) {
  PowellsFunction powells_function;
  Solver::Options* options = powells_function.mutable_solver_options();
  options->linear_solver_type = DENSE_NORMAL_CHOLESKY;
  RunSolverForConfigAndExpectResidualsMatch(*options,
                                            powells_function.mutable_problem());
}

TEST_F(PowellTest, DenseSchur) {
  PowellsFunction powells_function;
  Solver::Options* options = powells_function.mutable_solver_options();
  options->linear_solver_type = DENSE_SCHUR;
  RunSolverForConfigAndExpectResidualsMatch(*options,
                                            powells_function.mutable_problem());
}

TEST_F(PowellTest, IterativeSchurWithJacobi) {
  PowellsFunction powells_function;
  Solver::Options* options = powells_function.mutable_solver_options();
  options->linear_solver_type = ITERATIVE_SCHUR;
  options->sparse_linear_algebra_library_type = NO_SPARSE;
  options->preconditioner_type = JACOBI;
  RunSolverForConfigAndExpectResidualsMatch(*options,
                                            powells_function.mutable_problem());
}

#ifndef CERES_NO_SUITESPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingSuiteSparse) {
  PowellsFunction powells_function;
  Solver::Options* options = powells_function.mutable_solver_options();
  options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  options->sparse_linear_algebra_library_type = SUITE_SPARSE;
  RunSolverForConfigAndExpectResidualsMatch(*options,
                                            powells_function.mutable_problem());
}
#endif  // CERES_NO_SUITESPARSE

#ifndef CERES_NO_ACCELERATE_SPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingAccelerateSparse) {
  PowellsFunction powells_function;
  Solver::Options* options = powells_function.mutable_solver_options();
  options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  options->sparse_linear_algebra_library_type = ACCELERATE_SPARSE;
  RunSolverForConfigAndExpectResidualsMatch(*options,
                                            powells_function.mutable_problem());
}
#endif  // CERES_NO_ACCELERATE_SPARSE

#ifdef CERES_USE_EIGEN_SPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingEigenSparse) {
  PowellsFunction powells_function;
  Solver::Options* options = powells_function.mutable_solver_options();
  options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  options->sparse_linear_algebra_library_type = EIGEN_SPARSE;
  RunSolverForConfigAndExpectResidualsMatch(*options,
                                            powells_function.mutable_problem());
}
#endif  // CERES_USE_EIGEN_SPARSE

}  // namespace ceres::internal