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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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// 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
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/dense_cholesky.h"
#include <memory>
#include <numeric>
#include <sstream>
#include <string>
#include <utility>
#include <vector>
#include "Eigen/Dense"
#include "ceres/internal/config.h"
#include "ceres/internal/eigen.h"
#include "ceres/iterative_refiner.h"
#include "ceres/linear_solver.h"
#include "glog/logging.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"
namespace ceres::internal {
using Param = ::testing::tuple<DenseLinearAlgebraLibraryType, bool>;
constexpr bool kMixedPrecision = true;
constexpr bool kFullPrecision = false;
namespace {
std::string ParamInfoToString(testing::TestParamInfo<Param> info) {
Param param = info.param;
std::stringstream ss;
ss << DenseLinearAlgebraLibraryTypeToString(::testing::get<0>(param)) << "_"
<< (::testing::get<1>(param) ? "MixedPrecision" : "FullPrecision");
return ss.str();
}
} // namespace
class DenseCholeskyTest : public ::testing::TestWithParam<Param> {};
TEST_P(DenseCholeskyTest, FactorAndSolve) {
// TODO(sameeragarwal): Convert these tests into type parameterized tests so
// that we can test the single and double precision solvers.
using Scalar = double;
using MatrixType = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
using VectorType = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
LinearSolver::Options options;
ContextImpl context;
#ifndef CERES_NO_CUDA
options.context = &context;
std::string error;
CHECK(context.InitCuda(&error)) << error;
#endif // CERES_NO_CUDA
options.dense_linear_algebra_library_type = ::testing::get<0>(GetParam());
options.use_mixed_precision_solves = ::testing::get<1>(GetParam());
const int kNumRefinementSteps = 4;
if (options.use_mixed_precision_solves) {
options.max_num_refinement_iterations = kNumRefinementSteps;
}
auto dense_cholesky = DenseCholesky::Create(options);
const int kNumTrials = 10;
const int kMinNumCols = 1;
const int kMaxNumCols = 10;
for (int num_cols = kMinNumCols; num_cols < kMaxNumCols; ++num_cols) {
for (int trial = 0; trial < kNumTrials; ++trial) {
const MatrixType a = MatrixType::Random(num_cols, num_cols);
MatrixType lhs = a.transpose() * a;
lhs += VectorType::Ones(num_cols).asDiagonal();
Vector x = VectorType::Random(num_cols);
Vector rhs = lhs * x;
Vector actual = Vector::Random(num_cols);
LinearSolver::Summary summary;
summary.termination_type = dense_cholesky->FactorAndSolve(
num_cols, lhs.data(), rhs.data(), actual.data(), &summary.message);
EXPECT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
EXPECT_NEAR((x - actual).norm() / x.norm(),
0.0,
std::numeric_limits<double>::epsilon() * 10)
<< "\nexpected: " << x.transpose()
<< "\nactual : " << actual.transpose();
}
}
}
INSTANTIATE_TEST_SUITE_P(EigenCholesky,
DenseCholeskyTest,
::testing::Combine(::testing::Values(EIGEN),
::testing::Values(kMixedPrecision,
kFullPrecision)),
ParamInfoToString);
#ifndef CERES_NO_LAPACK
INSTANTIATE_TEST_SUITE_P(LapackCholesky,
DenseCholeskyTest,
::testing::Combine(::testing::Values(LAPACK),
::testing::Values(kMixedPrecision,
kFullPrecision)),
ParamInfoToString);
#endif
#ifndef CERES_NO_CUDA
INSTANTIATE_TEST_SUITE_P(CudaCholesky,
DenseCholeskyTest,
::testing::Combine(::testing::Values(CUDA),
::testing::Values(kMixedPrecision,
kFullPrecision)),
ParamInfoToString);
#endif
class MockDenseCholesky : public DenseCholesky {
public:
MOCK_METHOD3(Factorize,
LinearSolverTerminationType(int num_cols,
double* lhs,
std::string* message));
MOCK_METHOD3(Solve,
LinearSolverTerminationType(const double* rhs,
double* solution,
std::string* message));
};
class MockDenseIterativeRefiner : public DenseIterativeRefiner {
public:
MockDenseIterativeRefiner() : DenseIterativeRefiner(1) {}
MOCK_METHOD5(Refine,
void(int num_cols,
const double* lhs,
const double* rhs,
DenseCholesky* dense_cholesky,
double* solution));
};
using testing::_;
using testing::Return;
TEST(RefinedDenseCholesky, Factorize) {
auto dense_cholesky = std::make_unique<MockDenseCholesky>();
auto iterative_refiner = std::make_unique<MockDenseIterativeRefiner>();
EXPECT_CALL(*dense_cholesky, Factorize(_, _, _))
.Times(1)
.WillRepeatedly(Return(LinearSolverTerminationType::SUCCESS));
EXPECT_CALL(*iterative_refiner, Refine(_, _, _, _, _)).Times(0);
RefinedDenseCholesky refined_dense_cholesky(std::move(dense_cholesky),
std::move(iterative_refiner));
double lhs;
std::string message;
EXPECT_EQ(refined_dense_cholesky.Factorize(1, &lhs, &message),
LinearSolverTerminationType::SUCCESS);
};
TEST(RefinedDenseCholesky, FactorAndSolveWithUnsuccessfulFactorization) {
auto dense_cholesky = std::make_unique<MockDenseCholesky>();
auto iterative_refiner = std::make_unique<MockDenseIterativeRefiner>();
EXPECT_CALL(*dense_cholesky, Factorize(_, _, _))
.Times(1)
.WillRepeatedly(Return(LinearSolverTerminationType::FAILURE));
EXPECT_CALL(*dense_cholesky, Solve(_, _, _)).Times(0);
EXPECT_CALL(*iterative_refiner, Refine(_, _, _, _, _)).Times(0);
RefinedDenseCholesky refined_dense_cholesky(std::move(dense_cholesky),
std::move(iterative_refiner));
double lhs;
std::string message;
double rhs;
double solution;
EXPECT_EQ(
refined_dense_cholesky.FactorAndSolve(1, &lhs, &rhs, &solution, &message),
LinearSolverTerminationType::FAILURE);
};
TEST(RefinedDenseCholesky, FactorAndSolveWithSuccess) {
auto dense_cholesky = std::make_unique<MockDenseCholesky>();
auto iterative_refiner = std::make_unique<MockDenseIterativeRefiner>();
EXPECT_CALL(*dense_cholesky, Factorize(_, _, _))
.Times(1)
.WillRepeatedly(Return(LinearSolverTerminationType::SUCCESS));
EXPECT_CALL(*dense_cholesky, Solve(_, _, _))
.Times(1)
.WillRepeatedly(Return(LinearSolverTerminationType::SUCCESS));
EXPECT_CALL(*iterative_refiner, Refine(_, _, _, _, _)).Times(1);
RefinedDenseCholesky refined_dense_cholesky(std::move(dense_cholesky),
std::move(iterative_refiner));
double lhs;
std::string message;
double rhs;
double solution;
EXPECT_EQ(
refined_dense_cholesky.FactorAndSolve(1, &lhs, &rhs, &solution, &message),
LinearSolverTerminationType::SUCCESS);
};
} // namespace ceres::internal