internal/ceres/solver_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2019 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
//   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.
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//   used to endorse or promote products derived from this software without
//   specific prior written permission.
//
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/solver.h"

#include <cmath>
#include <limits>
#include <memory>
#include <vector>

#include "ceres/autodiff_cost_function.h"
#include "ceres/evaluation_callback.h"
#include "ceres/local_parameterization.h"
#include "ceres/problem.h"
#include "ceres/problem_impl.h"
#include "ceres/sized_cost_function.h"
#include "gtest/gtest.h"

namespace ceres {
namespace internal {

using std::string;

TEST(SolverOptions, DefaultTrustRegionOptionsAreValid) {
  Solver::Options options;
  options.minimizer_type = TRUST_REGION;
  string error;
  EXPECT_TRUE(options.IsValid(&error)) << error;
}

TEST(SolverOptions, DefaultLineSearchOptionsAreValid) {
  Solver::Options options;
  options.minimizer_type = LINE_SEARCH;
  string error;
  EXPECT_TRUE(options.IsValid(&error)) << error;
}

struct QuadraticCostFunctor {
  template <typename T>
  bool operator()(const T* const x, T* residual) const {
    residual[0] = T(5.0) - *x;
    return true;
  }

  static CostFunction* Create() {
    return new AutoDiffCostFunction<QuadraticCostFunctor, 1, 1>(
        new QuadraticCostFunctor);
  }
};

struct RememberingCallback : public IterationCallback {
  explicit RememberingCallback(double* x) : calls(0), x(x) {}
  virtual ~RememberingCallback() {}
  CallbackReturnType operator()(const IterationSummary& summary) final {
    x_values.push_back(*x);
    return SOLVER_CONTINUE;
  }
  int calls;
  double* x;
  std::vector<double> x_values;
};

struct NoOpEvaluationCallback : EvaluationCallback {
  virtual ~NoOpEvaluationCallback() {}
  void PrepareForEvaluation(bool evaluate_jacobians,
                            bool new_evaluation_point) final {
    (void)evaluate_jacobians;
    (void)new_evaluation_point;
  }
};

TEST(Solver, UpdateStateEveryIterationOptionNoEvaluationCallback) {
  double x = 50.0;
  const double original_x = x;

  Problem::Options problem_options;
  Problem problem(problem_options);
  problem.AddResidualBlock(QuadraticCostFunctor::Create(), nullptr, &x);

  Solver::Options options;
  options.linear_solver_type = DENSE_QR;

  RememberingCallback callback(&x);
  options.callbacks.push_back(&callback);

  Solver::Summary summary;

  int num_iterations;

  // First: update_state_every_iteration=false, evaluation_callback=nullptr.
  Solve(options, &problem, &summary);
  num_iterations =
      summary.num_successful_steps + summary.num_unsuccessful_steps;
  EXPECT_GT(num_iterations, 1);
  for (int i = 0; i < callback.x_values.size(); ++i) {
    EXPECT_EQ(50.0, callback.x_values[i]);
  }

  // Second: update_state_every_iteration=true, evaluation_callback=nullptr.
  x = 50.0;
  options.update_state_every_iteration = true;
  callback.x_values.clear();
  Solve(options, &problem, &summary);
  num_iterations =
      summary.num_successful_steps + summary.num_unsuccessful_steps;
  EXPECT_GT(num_iterations, 1);
  EXPECT_EQ(original_x, callback.x_values[0]);
  EXPECT_NE(original_x, callback.x_values[1]);
}

TEST(Solver, UpdateStateEveryIterationOptionWithEvaluationCallback) {
  double x = 50.0;
  const double original_x = x;

  Problem::Options problem_options;
  NoOpEvaluationCallback evaluation_callback;
  problem_options.evaluation_callback = &evaluation_callback;

  Problem problem(problem_options);
  problem.AddResidualBlock(QuadraticCostFunctor::Create(), nullptr, &x);

  Solver::Options options;
  options.linear_solver_type = DENSE_QR;
  RememberingCallback callback(&x);
  options.callbacks.push_back(&callback);

  Solver::Summary summary;

  int num_iterations;

  // First: update_state_every_iteration=true, evaluation_callback=!nullptr.
  x = 50.0;
  options.update_state_every_iteration = true;
  callback.x_values.clear();
  Solve(options, &problem, &summary);
  num_iterations =
      summary.num_successful_steps + summary.num_unsuccessful_steps;
  EXPECT_GT(num_iterations, 1);
  EXPECT_EQ(original_x, callback.x_values[0]);
  EXPECT_NE(original_x, callback.x_values[1]);

  // Second: update_state_every_iteration=false, evaluation_callback=!nullptr.
  x = 50.0;
  options.update_state_every_iteration = false;
  callback.x_values.clear();
  Solve(options, &problem, &summary);
  num_iterations =
      summary.num_successful_steps + summary.num_unsuccessful_steps;
  EXPECT_GT(num_iterations, 1);
  EXPECT_EQ(original_x, callback.x_values[0]);
  EXPECT_NE(original_x, callback.x_values[1]);
}

TEST(Solver, CantMixEvaluationCallbackWithInnerIterations) {
  double x = 50.0;
  double y = 60.0;

  Problem::Options problem_options;
  NoOpEvaluationCallback evaluation_callback;
  problem_options.evaluation_callback = &evaluation_callback;

  Problem problem(problem_options);
  problem.AddResidualBlock(QuadraticCostFunctor::Create(), nullptr, &x);
  problem.AddResidualBlock(QuadraticCostFunctor::Create(), nullptr, &y);

  Solver::Options options;
  options.use_inner_iterations = true;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, FAILURE);

  options.use_inner_iterations = false;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, CONVERGENCE);
}

// The parameters must be in separate blocks so that they can be individually
// set constant or not.
struct Quadratic4DCostFunction {
  template <typename T>
  bool operator()(const T* const x,
                  const T* const y,
                  const T* const z,
                  const T* const w,
                  T* residual) const {
    // A 4-dimension axis-aligned quadratic.
    residual[0] = T(10.0) - *x + T(20.0) - *y + T(30.0) - *z + T(40.0) - *w;
    return true;
  }

  static CostFunction* Create() {
    return new AutoDiffCostFunction<Quadratic4DCostFunction, 1, 1, 1, 1, 1>(
        new Quadratic4DCostFunction);
  }
};

// A cost function that simply returns its argument.
class UnaryIdentityCostFunction : public SizedCostFunction<1, 1> {
 public:
  bool Evaluate(double const* const* parameters,
                double* residuals,
                double** jacobians) const final {
    residuals[0] = parameters[0][0];
    if (jacobians != nullptr && jacobians[0] != nullptr) {
      jacobians[0][0] = 1.0;
    }
    return true;
  }
};

TEST(Solver, TrustRegionProblemHasNoParameterBlocks) {
  Problem problem;
  Solver::Options options;
  options.minimizer_type = TRUST_REGION;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, CONVERGENCE);
  EXPECT_EQ(summary.message,
            "Function tolerance reached. "
            "No non-constant parameter blocks found.");
}

TEST(Solver, LineSearchProblemHasNoParameterBlocks) {
  Problem problem;
  Solver::Options options;
  options.minimizer_type = LINE_SEARCH;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, CONVERGENCE);
  EXPECT_EQ(summary.message,
            "Function tolerance reached. "
            "No non-constant parameter blocks found.");
}

TEST(Solver, TrustRegionProblemHasZeroResiduals) {
  Problem problem;
  double x = 1;
  problem.AddParameterBlock(&x, 1);
  Solver::Options options;
  options.minimizer_type = TRUST_REGION;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, CONVERGENCE);
  EXPECT_EQ(summary.message,
            "Function tolerance reached. "
            "No non-constant parameter blocks found.");
}

TEST(Solver, LineSearchProblemHasZeroResiduals) {
  Problem problem;
  double x = 1;
  problem.AddParameterBlock(&x, 1);
  Solver::Options options;
  options.minimizer_type = LINE_SEARCH;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, CONVERGENCE);
  EXPECT_EQ(summary.message,
            "Function tolerance reached. "
            "No non-constant parameter blocks found.");
}

TEST(Solver, TrustRegionProblemIsConstant) {
  Problem problem;
  double x = 1;
  problem.AddResidualBlock(new UnaryIdentityCostFunction, nullptr, &x);
  problem.SetParameterBlockConstant(&x);
  Solver::Options options;
  options.minimizer_type = TRUST_REGION;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, CONVERGENCE);
  EXPECT_EQ(summary.initial_cost, 1.0 / 2.0);
  EXPECT_EQ(summary.final_cost, 1.0 / 2.0);
}

TEST(Solver, LineSearchProblemIsConstant) {
  Problem problem;
  double x = 1;
  problem.AddResidualBlock(new UnaryIdentityCostFunction, nullptr, &x);
  problem.SetParameterBlockConstant(&x);
  Solver::Options options;
  options.minimizer_type = LINE_SEARCH;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_EQ(summary.termination_type, CONVERGENCE);
  EXPECT_EQ(summary.initial_cost, 1.0 / 2.0);
  EXPECT_EQ(summary.final_cost, 1.0 / 2.0);
}

#if defined(CERES_NO_SUITESPARSE)
TEST(Solver, SparseNormalCholeskyNoSuiteSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = SUITE_SPARSE;
  options.linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, SparseSchurNoSuiteSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = SUITE_SPARSE;
  options.linear_solver_type = SPARSE_SCHUR;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}
#endif

#if defined(CERES_NO_CXSPARSE)
TEST(Solver, SparseNormalCholeskyNoCXSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = CX_SPARSE;
  options.linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, SparseSchurNoCXSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = CX_SPARSE;
  options.linear_solver_type = SPARSE_SCHUR;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}
#endif

#if defined(CERES_NO_ACCELERATE_SPARSE)
TEST(Solver, SparseNormalCholeskyNoAccelerateSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = ACCELERATE_SPARSE;
  options.linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, SparseSchurNoAccelerateSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = ACCELERATE_SPARSE;
  options.linear_solver_type = SPARSE_SCHUR;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}
#else
TEST(Solver, DynamicSparseNormalCholeskyUnsupportedWithAccelerateSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = ACCELERATE_SPARSE;
  options.linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  options.dynamic_sparsity = true;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}
#endif

#if !defined(CERES_USE_EIGEN_SPARSE)
TEST(Solver, SparseNormalCholeskyNoEigenSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = EIGEN_SPARSE;
  options.linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, SparseSchurNoEigenSparse) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = EIGEN_SPARSE;
  options.linear_solver_type = SPARSE_SCHUR;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}
#endif

TEST(Solver, SparseNormalCholeskyNoSparseLibrary) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = NO_SPARSE;
  options.linear_solver_type = SPARSE_NORMAL_CHOLESKY;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, SparseSchurNoSparseLibrary) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = NO_SPARSE;
  options.linear_solver_type = SPARSE_SCHUR;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, IterativeSchurWithClusterJacobiPerconditionerNoSparseLibrary) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = NO_SPARSE;
  options.linear_solver_type = ITERATIVE_SCHUR;
  // Requires SuiteSparse.
  options.preconditioner_type = CLUSTER_JACOBI;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver,
     IterativeSchurWithClusterTridiagonalPerconditionerNoSparseLibrary) {
  Solver::Options options;
  options.sparse_linear_algebra_library_type = NO_SPARSE;
  options.linear_solver_type = ITERATIVE_SCHUR;
  // Requires SuiteSparse.
  options.preconditioner_type = CLUSTER_TRIDIAGONAL;
  string message;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, IterativeLinearSolverForDogleg) {
  Solver::Options options;
  options.trust_region_strategy_type = DOGLEG;
  string message;
  options.linear_solver_type = ITERATIVE_SCHUR;
  EXPECT_FALSE(options.IsValid(&message));

  options.linear_solver_type = CGNR;
  EXPECT_FALSE(options.IsValid(&message));
}

TEST(Solver, LinearSolverTypeNormalOperation) {
  Solver::Options options;
  options.linear_solver_type = DENSE_QR;

  string message;
  EXPECT_TRUE(options.IsValid(&message));

  options.linear_solver_type = DENSE_NORMAL_CHOLESKY;
  EXPECT_TRUE(options.IsValid(&message));

  options.linear_solver_type = DENSE_SCHUR;
  EXPECT_TRUE(options.IsValid(&message));

  options.linear_solver_type = SPARSE_SCHUR;
#if defined(CERES_NO_SUITESPARSE) && defined(CERES_NO_CXSPARSE) && \
    !defined(CERES_USE_EIGEN_SPARSE)
  EXPECT_FALSE(options.IsValid(&message));
#else
  EXPECT_TRUE(options.IsValid(&message));
#endif

  options.linear_solver_type = ITERATIVE_SCHUR;
  EXPECT_TRUE(options.IsValid(&message));
}

template <int kNumResiduals, int... Ns>
class DummyCostFunction : public SizedCostFunction<kNumResiduals, Ns...> {
 public:
  bool Evaluate(double const* const* parameters,
                double* residuals,
                double** jacobians) const {
    for (int i = 0; i < kNumResiduals; ++i) {
      residuals[i] = kNumResiduals * kNumResiduals + i;
    }

    return true;
  }
};

TEST(Solver, FixedCostForConstantProblem) {
  double x = 1.0;
  Problem problem;
  problem.AddResidualBlock(new DummyCostFunction<2, 1>(), nullptr, &x);
  problem.SetParameterBlockConstant(&x);
  const double expected_cost = 41.0 / 2.0;  // 1/2 * ((4 + 0)^2 + (4 + 1)^2)
  Solver::Options options;
  Solver::Summary summary;
  Solve(options, &problem, &summary);
  EXPECT_TRUE(summary.IsSolutionUsable());
  EXPECT_EQ(summary.fixed_cost, expected_cost);
  EXPECT_EQ(summary.initial_cost, expected_cost);
  EXPECT_EQ(summary.final_cost, expected_cost);
  EXPECT_EQ(summary.iterations.size(), 0);
}

struct LinearCostFunction {
  template <typename T>
  bool operator()(const T* x, const T* y, T* residual) const {
    residual[0] = T(10.0) - *x;
    residual[1] = T(5.0) - *y;
    return true;
  }
  static CostFunction* Create() {
    return new AutoDiffCostFunction<LinearCostFunction, 2, 1, 1>(
        new LinearCostFunction);
  }
};

TEST(Solver, ZeroSizedLocalParameterizationHoldsParameterBlockConstant) {
  double x = 0.0;
  double y = 1.0;
  Problem problem;
  problem.AddResidualBlock(LinearCostFunction::Create(), nullptr, &x, &y);
  problem.SetParameterization(&y, new SubsetParameterization(1, {0}));
  EXPECT_TRUE(problem.IsParameterBlockConstant(&y));

  Solver::Options options;
  options.function_tolerance = 0.0;
  options.gradient_tolerance = 0.0;
  options.parameter_tolerance = 0.0;
  Solver::Summary summary;
  Solve(options, &problem, &summary);

  EXPECT_EQ(summary.termination_type, CONVERGENCE);
  EXPECT_NEAR(x, 10.0, 1e-7);
  EXPECT_EQ(y, 1.0);
}

}  // namespace internal
}  // namespace ceres