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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2022 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: wjr@google.com (William Rucklidge)
//
// This file contains tests for the GradientChecker class.
#include "ceres/gradient_checker.h"
#include <cmath>
#include <random>
#include <utility>
#include <vector>
#include "ceres/cost_function.h"
#include "ceres/problem.h"
#include "ceres/solver.h"
#include "ceres/test_util.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres::internal {
using std::vector;
const double kTolerance = 1e-12;
// We pick a (non-quadratic) function whose derivative are easy:
//
// f = exp(- a' x).
// df = - f a.
//
// where 'a' is a vector of the same size as 'x'. In the block
// version, they are both block vectors, of course.
class GoodTestTerm : public CostFunction {
public:
template <class UniformRandomFunctor>
GoodTestTerm(int arity, int const* dim, UniformRandomFunctor&& randu)
: arity_(arity), return_value_(true) {
std::uniform_real_distribution<double> distribution(-1.0, 1.0);
// Make 'arity' random vectors.
a_.resize(arity_);
for (int j = 0; j < arity_; ++j) {
a_[j].resize(dim[j]);
for (int u = 0; u < dim[j]; ++u) {
a_[j][u] = randu();
}
}
for (int i = 0; i < arity_; i++) {
mutable_parameter_block_sizes()->push_back(dim[i]);
}
set_num_residuals(1);
}
bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const override {
if (!return_value_) {
return false;
}
// Compute a . x.
double ax = 0;
for (int j = 0; j < arity_; ++j) {
for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
ax += a_[j][u] * parameters[j][u];
}
}
// This is the cost, but also appears as a factor
// in the derivatives.
double f = *residuals = exp(-ax);
// Accumulate 1st order derivatives.
if (jacobians) {
for (int j = 0; j < arity_; ++j) {
if (jacobians[j]) {
for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
// See comments before class.
jacobians[j][u] = -f * a_[j][u];
}
}
}
}
return true;
}
void SetReturnValue(bool return_value) { return_value_ = return_value; }
private:
int arity_;
bool return_value_;
vector<vector<double>> a_; // our vectors.
};
class BadTestTerm : public CostFunction {
public:
template <class UniformRandomFunctor>
BadTestTerm(int arity, int const* dim, UniformRandomFunctor&& randu)
: arity_(arity) {
// Make 'arity' random vectors.
a_.resize(arity_);
for (int j = 0; j < arity_; ++j) {
a_[j].resize(dim[j]);
for (int u = 0; u < dim[j]; ++u) {
a_[j][u] = randu();
}
}
for (int i = 0; i < arity_; i++) {
mutable_parameter_block_sizes()->push_back(dim[i]);
}
set_num_residuals(1);
}
bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const override {
// Compute a . x.
double ax = 0;
for (int j = 0; j < arity_; ++j) {
for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
ax += a_[j][u] * parameters[j][u];
}
}
// This is the cost, but also appears as a factor
// in the derivatives.
double f = *residuals = exp(-ax);
// Accumulate 1st order derivatives.
if (jacobians) {
for (int j = 0; j < arity_; ++j) {
if (jacobians[j]) {
for (int u = 0; u < parameter_block_sizes()[j]; ++u) {
// See comments before class.
jacobians[j][u] = -f * a_[j][u] + kTolerance;
}
}
}
}
return true;
}
private:
int arity_;
vector<vector<double>> a_; // our vectors.
};
static void CheckDimensions(const GradientChecker::ProbeResults& results,
const std::vector<int>& parameter_sizes,
const std::vector<int>& local_parameter_sizes,
int residual_size) {
CHECK_EQ(parameter_sizes.size(), local_parameter_sizes.size());
int num_parameters = parameter_sizes.size();
ASSERT_EQ(residual_size, results.residuals.size());
ASSERT_EQ(num_parameters, results.local_jacobians.size());
ASSERT_EQ(num_parameters, results.local_numeric_jacobians.size());
ASSERT_EQ(num_parameters, results.jacobians.size());
ASSERT_EQ(num_parameters, results.numeric_jacobians.size());
for (int i = 0; i < num_parameters; ++i) {
EXPECT_EQ(residual_size, results.local_jacobians.at(i).rows());
EXPECT_EQ(local_parameter_sizes[i], results.local_jacobians.at(i).cols());
EXPECT_EQ(residual_size, results.local_numeric_jacobians.at(i).rows());
EXPECT_EQ(local_parameter_sizes[i],
results.local_numeric_jacobians.at(i).cols());
EXPECT_EQ(residual_size, results.jacobians.at(i).rows());
EXPECT_EQ(parameter_sizes[i], results.jacobians.at(i).cols());
EXPECT_EQ(residual_size, results.numeric_jacobians.at(i).rows());
EXPECT_EQ(parameter_sizes[i], results.numeric_jacobians.at(i).cols());
}
}
TEST(GradientChecker, SmokeTest) {
// Test with 3 blocks of size 2, 3 and 4.
int const num_parameters = 3;
std::vector<int> parameter_sizes(3);
parameter_sizes[0] = 2;
parameter_sizes[1] = 3;
parameter_sizes[2] = 4;
// Make a random set of blocks.
FixedArray<double*> parameters(num_parameters);
std::mt19937 prng;
std::uniform_real_distribution<double> distribution(-1.0, 1.0);
auto randu = [&prng, &distribution] { return distribution(prng); };
for (int j = 0; j < num_parameters; ++j) {
parameters[j] = new double[parameter_sizes[j]];
for (int u = 0; u < parameter_sizes[j]; ++u) {
parameters[j][u] = randu();
}
}
NumericDiffOptions numeric_diff_options;
GradientChecker::ProbeResults results;
// Test that Probe returns true for correct Jacobians.
GoodTestTerm good_term(num_parameters, parameter_sizes.data(), randu);
std::vector<const Manifold*>* manifolds = nullptr;
GradientChecker good_gradient_checker(
&good_term, manifolds, numeric_diff_options);
EXPECT_TRUE(
good_gradient_checker.Probe(parameters.data(), kTolerance, nullptr));
EXPECT_TRUE(
good_gradient_checker.Probe(parameters.data(), kTolerance, &results))
<< results.error_log;
// Check that results contain sensible data.
ASSERT_EQ(results.return_value, true);
ASSERT_EQ(results.residuals.size(), 1);
CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
EXPECT_GE(results.maximum_relative_error, 0.0);
EXPECT_TRUE(results.error_log.empty());
// Test that if the cost function return false, Probe should return false.
good_term.SetReturnValue(false);
EXPECT_FALSE(
good_gradient_checker.Probe(parameters.data(), kTolerance, nullptr));
EXPECT_FALSE(
good_gradient_checker.Probe(parameters.data(), kTolerance, &results))
<< results.error_log;
// Check that results contain sensible data.
ASSERT_EQ(results.return_value, false);
ASSERT_EQ(results.residuals.size(), 1);
CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
for (int i = 0; i < num_parameters; ++i) {
EXPECT_EQ(results.local_jacobians.at(i).norm(), 0);
EXPECT_EQ(results.local_numeric_jacobians.at(i).norm(), 0);
}
EXPECT_EQ(results.maximum_relative_error, 0.0);
EXPECT_FALSE(results.error_log.empty());
// Test that Probe returns false for incorrect Jacobians.
BadTestTerm bad_term(num_parameters, parameter_sizes.data(), randu);
GradientChecker bad_gradient_checker(
&bad_term, manifolds, numeric_diff_options);
EXPECT_FALSE(
bad_gradient_checker.Probe(parameters.data(), kTolerance, nullptr));
EXPECT_FALSE(
bad_gradient_checker.Probe(parameters.data(), kTolerance, &results));
// Check that results contain sensible data.
ASSERT_EQ(results.return_value, true);
ASSERT_EQ(results.residuals.size(), 1);
CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
EXPECT_GT(results.maximum_relative_error, kTolerance);
EXPECT_FALSE(results.error_log.empty());
// Setting a high threshold should make the test pass.
EXPECT_TRUE(bad_gradient_checker.Probe(parameters.data(), 1.0, &results));
// Check that results contain sensible data.
ASSERT_EQ(results.return_value, true);
ASSERT_EQ(results.residuals.size(), 1);
CheckDimensions(results, parameter_sizes, parameter_sizes, 1);
EXPECT_GT(results.maximum_relative_error, 0.0);
EXPECT_TRUE(results.error_log.empty());
for (int j = 0; j < num_parameters; j++) {
delete[] parameters[j];
}
}
/**
* Helper cost function that multiplies the parameters by the given jacobians
* and adds a constant offset.
*/
class LinearCostFunction : public CostFunction {
public:
explicit LinearCostFunction(Vector residuals_offset)
: residuals_offset_(std::move(residuals_offset)) {
set_num_residuals(residuals_offset_.size());
}
bool Evaluate(double const* const* parameter_ptrs,
double* residuals_ptr,
double** residual_J_params) const final {
CHECK_GE(residual_J_params_.size(), 0.0);
VectorRef residuals(residuals_ptr, residual_J_params_[0].rows());
residuals = residuals_offset_;
for (size_t i = 0; i < residual_J_params_.size(); ++i) {
const Matrix& residual_J_param = residual_J_params_[i];
int parameter_size = residual_J_param.cols();
ConstVectorRef param(parameter_ptrs[i], parameter_size);
// Compute residual.
residuals += residual_J_param * param;
// Return Jacobian.
if (residual_J_params != nullptr && residual_J_params[i] != nullptr) {
Eigen::Map<Matrix> residual_J_param_out(residual_J_params[i],
residual_J_param.rows(),
residual_J_param.cols());
if (jacobian_offsets_.count(i) != 0) {
residual_J_param_out = residual_J_param + jacobian_offsets_.at(i);
} else {
residual_J_param_out = residual_J_param;
}
}
}
return true;
}
void AddParameter(const Matrix& residual_J_param) {
CHECK_EQ(num_residuals(), residual_J_param.rows());
residual_J_params_.push_back(residual_J_param);
mutable_parameter_block_sizes()->push_back(residual_J_param.cols());
}
/// Add offset to the given Jacobian before returning it from Evaluate(),
/// thus introducing an error in the computation.
void SetJacobianOffset(size_t index, Matrix offset) {
CHECK_LT(index, residual_J_params_.size());
CHECK_EQ(residual_J_params_[index].rows(), offset.rows());
CHECK_EQ(residual_J_params_[index].cols(), offset.cols());
jacobian_offsets_[index] = offset;
}
private:
std::vector<Matrix> residual_J_params_;
std::map<int, Matrix> jacobian_offsets_;
Vector residuals_offset_;
};
// Helper function to compare two Eigen matrices (used in the test below).
static void ExpectMatricesClose(Matrix p, Matrix q, double tolerance) {
ASSERT_EQ(p.rows(), q.rows());
ASSERT_EQ(p.cols(), q.cols());
ExpectArraysClose(p.size(), p.data(), q.data(), tolerance);
}
// Helper manifold that multiplies the delta vector by the given
// jacobian and adds it to the parameter.
class MatrixManifold : public Manifold {
public:
bool Plus(const double* x,
const double* delta,
double* x_plus_delta) const final {
VectorRef(x_plus_delta, AmbientSize()) =
ConstVectorRef(x, AmbientSize()) +
(global_to_local_ * ConstVectorRef(delta, TangentSize()));
return true;
}
bool PlusJacobian(const double* /*x*/, double* jacobian) const final {
MatrixRef(jacobian, AmbientSize(), TangentSize()) = global_to_local_;
return true;
}
bool Minus(const double* y, const double* x, double* y_minus_x) const final {
LOG(FATAL) << "Should not be called";
return true;
}
bool MinusJacobian(const double* x, double* jacobian) const final {
LOG(FATAL) << "Should not be called";
return true;
}
int AmbientSize() const final { return global_to_local_.rows(); }
int TangentSize() const final { return global_to_local_.cols(); }
Matrix global_to_local_;
};
TEST(GradientChecker, TestCorrectnessWithManifolds) {
// Create cost function.
Eigen::Vector3d residual_offset(100.0, 200.0, 300.0);
LinearCostFunction cost_function(residual_offset);
Eigen::Matrix<double, 3, 3, Eigen::RowMajor> j0;
j0.row(0) << 1.0, 2.0, 3.0;
j0.row(1) << 4.0, 5.0, 6.0;
j0.row(2) << 7.0, 8.0, 9.0;
Eigen::Matrix<double, 3, 2, Eigen::RowMajor> j1;
j1.row(0) << 10.0, 11.0;
j1.row(1) << 12.0, 13.0;
j1.row(2) << 14.0, 15.0;
Eigen::Vector3d param0(1.0, 2.0, 3.0);
Eigen::Vector2d param1(4.0, 5.0);
cost_function.AddParameter(j0);
cost_function.AddParameter(j1);
std::vector<int> parameter_sizes(2);
parameter_sizes[0] = 3;
parameter_sizes[1] = 2;
std::vector<int> tangent_sizes(2);
tangent_sizes[0] = 2;
tangent_sizes[1] = 2;
// Test cost function for correctness.
Eigen::Matrix<double, 3, 3, Eigen::RowMajor> j1_out;
Eigen::Matrix<double, 3, 2, Eigen::RowMajor> j2_out;
Eigen::Vector3d residual;
std::vector<const double*> parameters(2);
parameters[0] = param0.data();
parameters[1] = param1.data();
std::vector<double*> jacobians(2);
jacobians[0] = j1_out.data();
jacobians[1] = j2_out.data();
cost_function.Evaluate(parameters.data(), residual.data(), jacobians.data());
Matrix residual_expected = residual_offset + j0 * param0 + j1 * param1;
ExpectMatricesClose(j1_out, j0, std::numeric_limits<double>::epsilon());
ExpectMatricesClose(j2_out, j1, std::numeric_limits<double>::epsilon());
ExpectMatricesClose(residual, residual_expected, kTolerance);
// Create manifold.
Eigen::Matrix<double, 3, 2, Eigen::RowMajor> global_to_local;
global_to_local.row(0) << 1.5, 2.5;
global_to_local.row(1) << 3.5, 4.5;
global_to_local.row(2) << 5.5, 6.5;
MatrixManifold manifold;
manifold.global_to_local_ = global_to_local;
// Test manifold for correctness.
Eigen::Vector3d x(7.0, 8.0, 9.0);
Eigen::Vector2d delta(10.0, 11.0);
Eigen::Matrix<double, 3, 2, Eigen::RowMajor> global_to_local_out;
manifold.PlusJacobian(x.data(), global_to_local_out.data());
ExpectMatricesClose(global_to_local_out,
global_to_local,
std::numeric_limits<double>::epsilon());
Eigen::Vector3d x_plus_delta;
manifold.Plus(x.data(), delta.data(), x_plus_delta.data());
Eigen::Vector3d x_plus_delta_expected = x + (global_to_local * delta);
ExpectMatricesClose(x_plus_delta, x_plus_delta_expected, kTolerance);
// Now test GradientChecker.
std::vector<const Manifold*> manifolds(2);
manifolds[0] = &manifold;
manifolds[1] = nullptr;
NumericDiffOptions numeric_diff_options;
GradientChecker::ProbeResults results;
GradientChecker gradient_checker(
&cost_function, &manifolds, numeric_diff_options);
Problem::Options problem_options;
problem_options.cost_function_ownership = DO_NOT_TAKE_OWNERSHIP;
problem_options.manifold_ownership = DO_NOT_TAKE_OWNERSHIP;
Problem problem(problem_options);
Eigen::Vector3d param0_solver;
Eigen::Vector2d param1_solver;
problem.AddParameterBlock(param0_solver.data(), 3, &manifold);
problem.AddParameterBlock(param1_solver.data(), 2);
problem.AddResidualBlock(
&cost_function, nullptr, param0_solver.data(), param1_solver.data());
// First test case: everything is correct.
EXPECT_TRUE(gradient_checker.Probe(parameters.data(), kTolerance, nullptr));
EXPECT_TRUE(gradient_checker.Probe(parameters.data(), kTolerance, &results))
<< results.error_log;
// Check that results contain correct data.
ASSERT_EQ(results.return_value, true);
ExpectMatricesClose(
results.residuals, residual, std::numeric_limits<double>::epsilon());
CheckDimensions(results, parameter_sizes, tangent_sizes, 3);
ExpectMatricesClose(
results.local_jacobians.at(0), j0 * global_to_local, kTolerance);
ExpectMatricesClose(results.local_jacobians.at(1),
j1,
std::numeric_limits<double>::epsilon());
ExpectMatricesClose(
results.local_numeric_jacobians.at(0), j0 * global_to_local, kTolerance);
ExpectMatricesClose(results.local_numeric_jacobians.at(1), j1, kTolerance);
ExpectMatricesClose(
results.jacobians.at(0), j0, std::numeric_limits<double>::epsilon());
ExpectMatricesClose(
results.jacobians.at(1), j1, std::numeric_limits<double>::epsilon());
ExpectMatricesClose(results.numeric_jacobians.at(0), j0, kTolerance);
ExpectMatricesClose(results.numeric_jacobians.at(1), j1, kTolerance);
EXPECT_GE(results.maximum_relative_error, 0.0);
EXPECT_TRUE(results.error_log.empty());
// Test interaction with the 'check_gradients' option in Solver.
Solver::Options solver_options;
solver_options.linear_solver_type = DENSE_QR;
solver_options.check_gradients = true;
solver_options.initial_trust_region_radius = 1e10;
Solver solver;
Solver::Summary summary;
param0_solver = param0;
param1_solver = param1;
solver.Solve(solver_options, &problem, &summary);
EXPECT_EQ(CONVERGENCE, summary.termination_type);
EXPECT_LE(summary.final_cost, 1e-12);
// Second test case: Mess up reported derivatives with respect to 3rd
// component of 1st parameter. Check should fail.
Eigen::Matrix<double, 3, 3, Eigen::RowMajor> j0_offset;
j0_offset.setZero();
j0_offset.col(2).setConstant(0.001);
cost_function.SetJacobianOffset(0, j0_offset);
EXPECT_FALSE(gradient_checker.Probe(parameters.data(), kTolerance, nullptr));
EXPECT_FALSE(gradient_checker.Probe(parameters.data(), kTolerance, &results))
<< results.error_log;
// Check that results contain correct data.
ASSERT_EQ(results.return_value, true);
ExpectMatricesClose(
results.residuals, residual, std::numeric_limits<double>::epsilon());
CheckDimensions(results, parameter_sizes, tangent_sizes, 3);
ASSERT_EQ(results.local_jacobians.size(), 2);
ASSERT_EQ(results.local_numeric_jacobians.size(), 2);
ExpectMatricesClose(results.local_jacobians.at(0),
(j0 + j0_offset) * global_to_local,
kTolerance);
ExpectMatricesClose(results.local_jacobians.at(1),
j1,
std::numeric_limits<double>::epsilon());
ExpectMatricesClose(
results.local_numeric_jacobians.at(0), j0 * global_to_local, kTolerance);
ExpectMatricesClose(results.local_numeric_jacobians.at(1), j1, kTolerance);
ExpectMatricesClose(results.jacobians.at(0), j0 + j0_offset, kTolerance);
ExpectMatricesClose(
results.jacobians.at(1), j1, std::numeric_limits<double>::epsilon());
ExpectMatricesClose(results.numeric_jacobians.at(0), j0, kTolerance);
ExpectMatricesClose(results.numeric_jacobians.at(1), j1, kTolerance);
EXPECT_GT(results.maximum_relative_error, 0.0);
EXPECT_FALSE(results.error_log.empty());
// Test interaction with the 'check_gradients' option in Solver.
param0_solver = param0;
param1_solver = param1;
solver.Solve(solver_options, &problem, &summary);
EXPECT_EQ(FAILURE, summary.termination_type);
// Now, zero out the manifold Jacobian with respect to the 3rd component of
// the 1st parameter. This makes the combination of cost function and manifold
// return correct values again.
manifold.global_to_local_.row(2).setZero();
// Verify that the gradient checker does not treat this as an error.
EXPECT_TRUE(gradient_checker.Probe(parameters.data(), kTolerance, &results))
<< results.error_log;
// Check that results contain correct data.
ASSERT_EQ(results.return_value, true);
ExpectMatricesClose(
results.residuals, residual, std::numeric_limits<double>::epsilon());
CheckDimensions(results, parameter_sizes, tangent_sizes, 3);
ASSERT_EQ(results.local_jacobians.size(), 2);
ASSERT_EQ(results.local_numeric_jacobians.size(), 2);
ExpectMatricesClose(results.local_jacobians.at(0),
(j0 + j0_offset) * manifold.global_to_local_,
kTolerance);
ExpectMatricesClose(results.local_jacobians.at(1),
j1,
std::numeric_limits<double>::epsilon());
ExpectMatricesClose(results.local_numeric_jacobians.at(0),
j0 * manifold.global_to_local_,
kTolerance);
ExpectMatricesClose(results.local_numeric_jacobians.at(1), j1, kTolerance);
ExpectMatricesClose(results.jacobians.at(0), j0 + j0_offset, kTolerance);
ExpectMatricesClose(
results.jacobians.at(1), j1, std::numeric_limits<double>::epsilon());
ExpectMatricesClose(results.numeric_jacobians.at(0), j0, kTolerance);
ExpectMatricesClose(results.numeric_jacobians.at(1), j1, kTolerance);
EXPECT_GE(results.maximum_relative_error, 0.0);
EXPECT_TRUE(results.error_log.empty());
// Test interaction with the 'check_gradients' option in Solver.
param0_solver = param0;
param1_solver = param1;
solver.Solve(solver_options, &problem, &summary);
EXPECT_EQ(CONVERGENCE, summary.termination_type);
EXPECT_LE(summary.final_cost, 1e-12);
}
} // namespace ceres::internal