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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 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
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//
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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
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: keir@google.com (Keir Mierle)
// tbennun@gmail.com (Tal Ben-Nun)
#include "ceres/numeric_diff_cost_function.h"
#include <algorithm>
#include <array>
#include <cmath>
#include <memory>
#include <random>
#include <string>
#include <vector>
#include "ceres/array_utils.h"
#include "ceres/numeric_diff_test_utils.h"
#include "ceres/test_util.h"
#include "ceres/types.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
TEST(NumericDiffCostFunction, EasyCaseFunctorCentralDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<EasyFunctor,
CENTRAL,
3, // number of residuals
5, // size of x1
5 // size of x2
>>(new EasyFunctor);
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction, EasyCaseFunctorForwardDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<EasyFunctor,
FORWARD,
3, // number of residuals
5, // size of x1
5 // size of x2
>>(new EasyFunctor);
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction, EasyCaseFunctorRidders) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<EasyFunctor,
RIDDERS,
3, // number of residuals
5, // size of x1
5 // size of x2
>>(new EasyFunctor);
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
TEST(NumericDiffCostFunction, EasyCaseCostFunctionCentralDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<EasyCostFunction,
CENTRAL,
3, // number of residuals
5, // size of x1
5 // size of x2
>>(new EasyCostFunction,
TAKE_OWNERSHIP);
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction, EasyCaseCostFunctionForwardDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<EasyCostFunction,
FORWARD,
3, // number of residuals
5, // size of x1
5 // size of x2
>>(new EasyCostFunction,
TAKE_OWNERSHIP);
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction, EasyCaseCostFunctionRidders) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<EasyCostFunction,
RIDDERS,
3, // number of residuals
5, // size of x1
5 // size of x2
>>(new EasyCostFunction,
TAKE_OWNERSHIP);
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
TEST(NumericDiffCostFunction, TranscendentalCaseFunctorCentralDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<TranscendentalFunctor,
CENTRAL,
2, // number of residuals
5, // size of x1
5 // size of x2
>>(new TranscendentalFunctor);
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction, TranscendentalCaseFunctorForwardDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<TranscendentalFunctor,
FORWARD,
2, // number of residuals
5, // size of x1
5 // size of x2
>>(new TranscendentalFunctor);
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction, TranscendentalCaseFunctorRidders) {
NumericDiffOptions options;
// Using a smaller initial step size to overcome oscillatory function
// behavior.
options.ridders_relative_initial_step_size = 1e-3;
auto cost_function =
std::make_unique<NumericDiffCostFunction<TranscendentalFunctor,
RIDDERS,
2, // number of residuals
5, // size of x1
5 // size of x2
>>(
new TranscendentalFunctor, TAKE_OWNERSHIP, 2, options);
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
TEST(NumericDiffCostFunction,
TranscendentalCaseCostFunctionCentralDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<TranscendentalCostFunction,
CENTRAL,
2, // number of residuals
5, // size of x1
5 // size of x2
>>(
new TranscendentalCostFunction, TAKE_OWNERSHIP);
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction,
TranscendentalCaseCostFunctionForwardDifferences) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<TranscendentalCostFunction,
FORWARD,
2, // number of residuals
5, // size of x1
5 // size of x2
>>(
new TranscendentalCostFunction, TAKE_OWNERSHIP);
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction, TranscendentalCaseCostFunctionRidders) {
NumericDiffOptions options;
// Using a smaller initial step size to overcome oscillatory function
// behavior.
options.ridders_relative_initial_step_size = 1e-3;
auto cost_function =
std::make_unique<NumericDiffCostFunction<TranscendentalCostFunction,
RIDDERS,
2, // number of residuals
5, // size of x1
5 // size of x2
>>(
new TranscendentalCostFunction, TAKE_OWNERSHIP, 2, options);
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
template <int num_rows, int num_cols>
class SizeTestingCostFunction : public SizedCostFunction<num_rows, num_cols> {
public:
bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const final {
return true;
}
};
// As described in
// http://forum.kde.org/viewtopic.php?f=74&t=98536#p210774
// Eigen3 has restrictions on the Row/Column major storage of vectors,
// depending on their dimensions. This test ensures that the correct
// templates are instantiated for various shapes of the Jacobian
// matrix.
TEST(NumericDiffCostFunction, EigenRowMajorColMajorTest) {
std::unique_ptr<CostFunction> cost_function = std::make_unique<
NumericDiffCostFunction<SizeTestingCostFunction<1, 1>, CENTRAL, 1, 1>>(
new SizeTestingCostFunction<1, 1>, ceres::TAKE_OWNERSHIP);
cost_function = std::make_unique<
NumericDiffCostFunction<SizeTestingCostFunction<2, 1>, CENTRAL, 2, 1>>(
new SizeTestingCostFunction<2, 1>, ceres::TAKE_OWNERSHIP);
cost_function = std::make_unique<
NumericDiffCostFunction<SizeTestingCostFunction<1, 2>, CENTRAL, 1, 2>>(
new SizeTestingCostFunction<1, 2>, ceres::TAKE_OWNERSHIP);
cost_function = std::make_unique<
NumericDiffCostFunction<SizeTestingCostFunction<2, 2>, CENTRAL, 2, 2>>(
new SizeTestingCostFunction<2, 2>, ceres::TAKE_OWNERSHIP);
cost_function = std::make_unique<
NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 1>>(
new EasyFunctor, TAKE_OWNERSHIP, 1);
cost_function = std::make_unique<
NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 1>>(
new EasyFunctor, TAKE_OWNERSHIP, 2);
cost_function = std::make_unique<
NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 2>>(
new EasyFunctor, TAKE_OWNERSHIP, 1);
cost_function = std::make_unique<
NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 2>>(
new EasyFunctor, TAKE_OWNERSHIP, 2);
cost_function = std::make_unique<
NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 2, 1>>(
new EasyFunctor, TAKE_OWNERSHIP, 1);
cost_function = std::make_unique<
NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 2, 1>>(
new EasyFunctor, TAKE_OWNERSHIP, 2);
}
TEST(NumericDiffCostFunction,
EasyCaseFunctorCentralDifferencesAndDynamicNumResiduals) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<EasyFunctor,
CENTRAL,
ceres::DYNAMIC,
5, // size of x1
5 // size of x2
>>(
new EasyFunctor, TAKE_OWNERSHIP, 3);
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction, ExponentialFunctorRidders) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<ExponentialFunctor,
RIDDERS,
1, // number of residuals
1 // size of x1
>>(new ExponentialFunctor);
ExponentialFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
TEST(NumericDiffCostFunction, ExponentialCostFunctionRidders) {
auto cost_function =
std::make_unique<NumericDiffCostFunction<ExponentialCostFunction,
RIDDERS,
1, // number of residuals
1 // size of x1
>>(new ExponentialCostFunction);
ExponentialFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
TEST(NumericDiffCostFunction, RandomizedFunctorRidders) {
std::mt19937 prng;
NumericDiffOptions options;
// Larger initial step size is chosen to produce robust results in the
// presence of random noise.
options.ridders_relative_initial_step_size = 10.0;
auto cost_function =
std::make_unique<NumericDiffCostFunction<RandomizedFunctor,
RIDDERS,
1, // number of residuals
1 // size of x1
>>(
new RandomizedFunctor(kNoiseFactor, prng),
TAKE_OWNERSHIP,
1,
options);
RandomizedFunctor functor(kNoiseFactor, prng);
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
TEST(NumericDiffCostFunction, RandomizedCostFunctionRidders) {
std::mt19937 prng;
NumericDiffOptions options;
// Larger initial step size is chosen to produce robust results in the
// presence of random noise.
options.ridders_relative_initial_step_size = 10.0;
auto cost_function =
std::make_unique<NumericDiffCostFunction<RandomizedCostFunction,
RIDDERS,
1, // number of residuals
1 // size of x1
>>(
new RandomizedCostFunction(kNoiseFactor, prng),
TAKE_OWNERSHIP,
1,
options);
RandomizedFunctor functor(kNoiseFactor, prng);
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
struct OnlyFillsOneOutputFunctor {
bool operator()(const double* x, double* output) const {
output[0] = x[0];
return true;
}
};
TEST(NumericDiffCostFunction, PartiallyFilledResidualShouldFailEvaluation) {
double parameter = 1.0;
double jacobian[2];
double residuals[2];
double* parameters[] = {&parameter};
double* jacobians[] = {jacobian};
auto cost_function = std::make_unique<
NumericDiffCostFunction<OnlyFillsOneOutputFunctor, CENTRAL, 2, 1>>(
new OnlyFillsOneOutputFunctor);
InvalidateArray(2, jacobian);
InvalidateArray(2, residuals);
EXPECT_TRUE(cost_function->Evaluate(parameters, residuals, jacobians));
EXPECT_FALSE(IsArrayValid(2, residuals));
InvalidateArray(2, residuals);
EXPECT_TRUE(cost_function->Evaluate(parameters, residuals, nullptr));
// We are only testing residuals here, because the Jacobians are
// computed using finite differencing from the residuals, so unless
// we introduce a validation step after every evaluation of
// residuals inside NumericDiffCostFunction, there is no way of
// ensuring that the Jacobian array is invalid.
EXPECT_FALSE(IsArrayValid(2, residuals));
}
TEST(NumericDiffCostFunction, ParameterBlockConstant) {
constexpr int kNumResiduals = 3;
constexpr int kX1 = 5;
constexpr int kX2 = 5;
auto cost_function = std::make_unique<
NumericDiffCostFunction<EasyFunctor, CENTRAL, kNumResiduals, kX1, kX2>>(
new EasyFunctor);
// Prepare the parameters and residuals.
std::array<double, kX1> x1{1e-64, 2.0, 3.0, 4.0, 5.0};
std::array<double, kX2> x2{9.0, 9.0, 5.0, 5.0, 1.0};
std::array<double*, 2> parameter_blocks{x1.data(), x2.data()};
std::vector<double> residuals(kNumResiduals, -100000);
// Evaluate the full jacobian.
std::vector<std::vector<double>> jacobian_full_vect(2);
jacobian_full_vect[0].resize(kNumResiduals * kX1, -100000);
jacobian_full_vect[1].resize(kNumResiduals * kX2, -100000);
{
std::array<double*, 2> jacobian{jacobian_full_vect[0].data(),
jacobian_full_vect[1].data()};
ASSERT_TRUE(cost_function->Evaluate(
parameter_blocks.data(), residuals.data(), jacobian.data()));
}
// Evaluate and check jacobian when first parameter block is constant.
{
std::vector<double> jacobian_vect(kNumResiduals * kX2, -100000);
std::array<double*, 2> jacobian{nullptr, jacobian_vect.data()};
ASSERT_TRUE(cost_function->Evaluate(
parameter_blocks.data(), residuals.data(), jacobian.data()));
for (int i = 0; i < kNumResiduals * kX2; ++i) {
EXPECT_DOUBLE_EQ(jacobian_full_vect[1][i], jacobian_vect[i]);
}
}
// Evaluate and check jacobian when second parameter block is constant.
{
std::vector<double> jacobian_vect(kNumResiduals * kX1, -100000);
std::array<double*, 2> jacobian{jacobian_vect.data(), nullptr};
ASSERT_TRUE(cost_function->Evaluate(
parameter_blocks.data(), residuals.data(), jacobian.data()));
for (int i = 0; i < kNumResiduals * kX1; ++i) {
EXPECT_DOUBLE_EQ(jacobian_full_vect[0][i], jacobian_vect[i]);
}
}
}
} // namespace internal
} // namespace ceres