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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:
//
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// this list of conditions and the following disclaimer in the documentation
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// Author: joydeepb@cs.utexas.edu (Joydeep Biswas)
#include <string>
#include "ceres/dense_cholesky.h"
#include "ceres/internal/config.h"
#include "ceres/internal/eigen.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
#ifndef CERES_NO_CUDA
TEST(CUDADenseCholesky, InvalidOptionOnCreate) {
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
auto dense_cuda_solver = CUDADenseCholesky::Create(options);
EXPECT_EQ(dense_cuda_solver, nullptr);
}
// Tests the CUDA Cholesky solver with a simple 4x4 matrix.
TEST(CUDADenseCholesky, Cholesky4x4Matrix) {
Eigen::Matrix4d A;
// clang-format off
A << 4, 12, -16, 0,
12, 37, -43, 0,
-16, -43, 98, 0,
0, 0, 0, 1;
// clang-format on
const Eigen::Vector4d b = Eigen::Vector4d::Ones();
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = CUDA;
auto dense_cuda_solver = CUDADenseCholesky::Create(options);
ASSERT_NE(dense_cuda_solver, nullptr);
std::string error_string;
ASSERT_EQ(dense_cuda_solver->Factorize(A.cols(), A.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
Eigen::Vector4d x = Eigen::Vector4d::Zero();
ASSERT_EQ(dense_cuda_solver->Solve(b.data(), x.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
EXPECT_NEAR(x(0), 113.75 / 3.0, std::numeric_limits<double>::epsilon() * 10);
EXPECT_NEAR(x(1), -31.0 / 3.0, std::numeric_limits<double>::epsilon() * 10);
EXPECT_NEAR(x(2), 5.0 / 3.0, std::numeric_limits<double>::epsilon() * 10);
EXPECT_NEAR(x(3), 1.0000, std::numeric_limits<double>::epsilon() * 10);
}
TEST(CUDADenseCholesky, SingularMatrix) {
Eigen::Matrix3d A;
// clang-format off
A << 1, 0, 0,
0, 1, 0,
0, 0, 0;
// clang-format on
const Eigen::Vector3d b = Eigen::Vector3d::Ones();
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = CUDA;
auto dense_cuda_solver = CUDADenseCholesky::Create(options);
ASSERT_NE(dense_cuda_solver, nullptr);
std::string error_string;
ASSERT_EQ(dense_cuda_solver->Factorize(A.cols(), A.data(), &error_string),
LinearSolverTerminationType::FAILURE);
}
TEST(CUDADenseCholesky, NegativeMatrix) {
Eigen::Matrix3d A;
// clang-format off
A << 1, 0, 0,
0, 1, 0,
0, 0, -1;
// clang-format on
const Eigen::Vector3d b = Eigen::Vector3d::Ones();
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = CUDA;
auto dense_cuda_solver = CUDADenseCholesky::Create(options);
ASSERT_NE(dense_cuda_solver, nullptr);
std::string error_string;
ASSERT_EQ(dense_cuda_solver->Factorize(A.cols(), A.data(), &error_string),
LinearSolverTerminationType::FAILURE);
}
TEST(CUDADenseCholesky, MustFactorizeBeforeSolve) {
const Eigen::Vector3d b = Eigen::Vector3d::Ones();
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = CUDA;
auto dense_cuda_solver = CUDADenseCholesky::Create(options);
ASSERT_NE(dense_cuda_solver, nullptr);
std::string error_string;
ASSERT_EQ(dense_cuda_solver->Solve(b.data(), nullptr, &error_string),
LinearSolverTerminationType::FATAL_ERROR);
}
TEST(CUDADenseCholesky, Randomized1600x1600Tests) {
const int kNumCols = 1600;
using LhsType = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>;
using RhsType = Eigen::Matrix<double, Eigen::Dynamic, 1>;
using SolutionType = Eigen::Matrix<double, Eigen::Dynamic, 1>;
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = ceres::CUDA;
std::unique_ptr<DenseCholesky> dense_cholesky =
CUDADenseCholesky::Create(options);
const int kNumTrials = 20;
for (int i = 0; i < kNumTrials; ++i) {
LhsType lhs = LhsType::Random(kNumCols, kNumCols);
lhs = lhs.transpose() * lhs;
lhs += 1e-3 * LhsType::Identity(kNumCols, kNumCols);
SolutionType x_expected = SolutionType::Random(kNumCols);
RhsType rhs = lhs * x_expected;
SolutionType x_computed = SolutionType::Zero(kNumCols);
// Sanity check the random matrix sizes.
EXPECT_EQ(lhs.rows(), kNumCols);
EXPECT_EQ(lhs.cols(), kNumCols);
EXPECT_EQ(rhs.rows(), kNumCols);
EXPECT_EQ(rhs.cols(), 1);
EXPECT_EQ(x_expected.rows(), kNumCols);
EXPECT_EQ(x_expected.cols(), 1);
EXPECT_EQ(x_computed.rows(), kNumCols);
EXPECT_EQ(x_computed.cols(), 1);
LinearSolver::Summary summary;
summary.termination_type = dense_cholesky->FactorAndSolve(
kNumCols, lhs.data(), rhs.data(), x_computed.data(), &summary.message);
ASSERT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
static const double kEpsilon = std::numeric_limits<double>::epsilon() * 2e5;
ASSERT_NEAR(
(x_computed - x_expected).norm() / x_expected.norm(), 0.0, kEpsilon);
}
}
TEST(CUDADenseCholeskyMixedPrecision, InvalidOptionsOnCreate) {
{
// Did not ask for CUDA, and did not ask for mixed precision.
LinearSolver::Options options;
auto solver = CUDADenseCholeskyMixedPrecision::Create(options);
ASSERT_EQ(solver, nullptr);
}
{
// Asked for CUDA, but did not ask for mixed precision.
LinearSolver::Options options;
options.dense_linear_algebra_library_type = ceres::CUDA;
auto solver = CUDADenseCholeskyMixedPrecision::Create(options);
ASSERT_EQ(solver, nullptr);
}
}
// Tests the CUDA Cholesky solver with a simple 4x4 matrix.
TEST(CUDADenseCholeskyMixedPrecision, Cholesky4x4Matrix1Step) {
Eigen::Matrix4d A;
// clang-format off
// A common test Cholesky decomposition test matrix, see :
// https://en.wikipedia.org/w/index.php?title=Cholesky_decomposition&oldid=1080607368#Example
A << 4, 12, -16, 0,
12, 37, -43, 0,
-16, -43, 98, 0,
0, 0, 0, 1;
// clang-format on
const Eigen::Vector4d b = Eigen::Vector4d::Ones();
LinearSolver::Options options;
options.max_num_refinement_iterations = 0;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = CUDA;
options.use_mixed_precision_solves = true;
auto solver = CUDADenseCholeskyMixedPrecision::Create(options);
ASSERT_NE(solver, nullptr);
std::string error_string;
ASSERT_EQ(solver->Factorize(A.cols(), A.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
Eigen::Vector4d x = Eigen::Vector4d::Zero();
ASSERT_EQ(solver->Solve(b.data(), x.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
// A single step of the mixed precision solver will be equivalent to solving
// in low precision (FP32). Hence the tolerance is defined w.r.t. FP32 epsilon
// instead of FP64 epsilon.
static const double kEpsilon = std::numeric_limits<float>::epsilon() * 15.0f;
EXPECT_NEAR(x(0), 113.75 / 3.0, kEpsilon);
EXPECT_NEAR(x(1), -31.0 / 3.0, kEpsilon);
EXPECT_NEAR(x(2), 5.0 / 3.0, kEpsilon);
EXPECT_NEAR(x(3), 1.0000, kEpsilon);
}
// Tests the CUDA Cholesky solver with a simple 4x4 matrix.
TEST(CUDADenseCholeskyMixedPrecision, Cholesky4x4Matrix4Steps) {
Eigen::Matrix4d A;
// clang-format off
A << 4, 12, -16, 0,
12, 37, -43, 0,
-16, -43, 98, 0,
0, 0, 0, 1;
// clang-format on
const Eigen::Vector4d b = Eigen::Vector4d::Ones();
LinearSolver::Options options;
options.max_num_refinement_iterations = 3;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = CUDA;
options.use_mixed_precision_solves = true;
auto solver = CUDADenseCholeskyMixedPrecision::Create(options);
ASSERT_NE(solver, nullptr);
std::string error_string;
ASSERT_EQ(solver->Factorize(A.cols(), A.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
Eigen::Vector4d x = Eigen::Vector4d::Zero();
ASSERT_EQ(solver->Solve(b.data(), x.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
// The error does not reduce beyond four iterations, and stagnates at this
// level of precision.
static const double kEpsilon = std::numeric_limits<double>::epsilon() * 3e2;
EXPECT_NEAR(x(0), 113.75 / 3.0, kEpsilon);
EXPECT_NEAR(x(1), -31.0 / 3.0, kEpsilon);
EXPECT_NEAR(x(2), 5.0 / 3.0, kEpsilon);
EXPECT_NEAR(x(3), 1.0000, kEpsilon);
}
TEST(CUDADenseCholeskyMixedPrecision, Randomized1600x1600Tests) {
const int kNumCols = 1600;
using LhsType = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>;
using RhsType = Eigen::Matrix<double, Eigen::Dynamic, 1>;
using SolutionType = Eigen::Matrix<double, Eigen::Dynamic, 1>;
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
options.dense_linear_algebra_library_type = ceres::CUDA;
options.use_mixed_precision_solves = true;
options.max_num_refinement_iterations = 20;
std::unique_ptr<CUDADenseCholeskyMixedPrecision> dense_cholesky =
CUDADenseCholeskyMixedPrecision::Create(options);
const int kNumTrials = 20;
for (int i = 0; i < kNumTrials; ++i) {
LhsType lhs = LhsType::Random(kNumCols, kNumCols);
lhs = lhs.transpose() * lhs;
lhs += 1e-3 * LhsType::Identity(kNumCols, kNumCols);
SolutionType x_expected = SolutionType::Random(kNumCols);
RhsType rhs = lhs * x_expected;
SolutionType x_computed = SolutionType::Zero(kNumCols);
// Sanity check the random matrix sizes.
EXPECT_EQ(lhs.rows(), kNumCols);
EXPECT_EQ(lhs.cols(), kNumCols);
EXPECT_EQ(rhs.rows(), kNumCols);
EXPECT_EQ(rhs.cols(), 1);
EXPECT_EQ(x_expected.rows(), kNumCols);
EXPECT_EQ(x_expected.cols(), 1);
EXPECT_EQ(x_computed.rows(), kNumCols);
EXPECT_EQ(x_computed.cols(), 1);
LinearSolver::Summary summary;
summary.termination_type = dense_cholesky->FactorAndSolve(
kNumCols, lhs.data(), rhs.data(), x_computed.data(), &summary.message);
ASSERT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
static const double kEpsilon = std::numeric_limits<double>::epsilon() * 1e6;
ASSERT_NEAR(
(x_computed - x_expected).norm() / x_expected.norm(), 0.0, kEpsilon);
}
}
#endif // CERES_NO_CUDA
} // namespace internal
} // namespace ceres