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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:
//
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// 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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// Author: joydeepb@cs.utexas.edu (Joydeep Biswas)
#include <string>
#include "ceres/dense_qr.h"
#include "ceres/internal/eigen.h"
#include "gtest/gtest.h"
namespace ceres::internal {
#ifndef CERES_NO_CUDA
TEST(CUDADenseQR, InvalidOptionOnCreate) {
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
std::string error;
EXPECT_TRUE(context.InitCuda(&error)) << error;
auto dense_cuda_solver = CUDADenseQR::Create(options);
EXPECT_EQ(dense_cuda_solver, nullptr);
}
// Tests the CUDA QR solver with a simple 4x4 matrix.
TEST(CUDADenseQR, QR4x4Matrix) {
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;
std::string error;
EXPECT_TRUE(context.InitCuda(&error)) << error;
options.dense_linear_algebra_library_type = CUDA;
auto dense_cuda_solver = CUDADenseQR::Create(options);
ASSERT_NE(dense_cuda_solver, nullptr);
std::string error_string;
ASSERT_EQ(
dense_cuda_solver->Factorize(A.rows(), 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);
// Empirically observed accuracy of cuSolverDN's QR solver.
const double kEpsilon = std::numeric_limits<double>::epsilon() * 1500;
const Eigen::Vector4d x_expected(113.75 / 3.0, -31.0 / 3.0, 5.0 / 3.0, 1.0);
EXPECT_NEAR((x - x_expected).norm() / x_expected.norm(), 0.0, kEpsilon);
}
// Tests the CUDA QR solver with a simple 4x4 matrix.
TEST(CUDADenseQR, QR4x2Matrix) {
Eigen::Matrix<double, 4, 2> A;
// clang-format off
A << 4, 12,
12, 37,
-16, -43,
0, 0;
// clang-format on
const std::vector<double> b(4, 1.0);
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
std::string error;
EXPECT_TRUE(context.InitCuda(&error)) << error;
options.dense_linear_algebra_library_type = CUDA;
auto dense_cuda_solver = CUDADenseQR::Create(options);
ASSERT_NE(dense_cuda_solver, nullptr);
std::string error_string;
ASSERT_EQ(
dense_cuda_solver->Factorize(A.rows(), A.cols(), A.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
std::vector<double> x(2, 0);
ASSERT_EQ(dense_cuda_solver->Solve(b.data(), x.data(), &error_string),
LinearSolverTerminationType::SUCCESS);
// Empirically observed accuracy of cuSolverDN's QR solver.
const double kEpsilon = std::numeric_limits<double>::epsilon() * 10;
// Solution values computed with Octave.
const Eigen::Vector2d x_expected(-1.143410852713177, 0.4031007751937981);
EXPECT_NEAR((x[0] - x_expected[0]) / x_expected[0], 0.0, kEpsilon);
EXPECT_NEAR((x[1] - x_expected[1]) / x_expected[1], 0.0, kEpsilon);
}
TEST(CUDADenseQR, MustFactorizeBeforeSolve) {
const Eigen::Vector3d b = Eigen::Vector3d::Ones();
LinearSolver::Options options;
ContextImpl context;
options.context = &context;
std::string error;
EXPECT_TRUE(context.InitCuda(&error)) << error;
options.dense_linear_algebra_library_type = CUDA;
auto dense_cuda_solver = CUDADenseQR::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(CUDADenseQR, Randomized1600x100Tests) {
const int kNumRows = 1600;
const int kNumCols = 100;
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;
std::string error;
EXPECT_TRUE(context.InitCuda(&error)) << error;
options.dense_linear_algebra_library_type = ceres::CUDA;
std::unique_ptr<DenseQR> dense_qr = CUDADenseQR::Create(options);
const int kNumTrials = 20;
for (int i = 0; i < kNumTrials; ++i) {
LhsType lhs = LhsType::Random(kNumRows, 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(), kNumRows);
EXPECT_EQ(lhs.cols(), kNumCols);
EXPECT_EQ(rhs.rows(), kNumRows);
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_qr->FactorAndSolve(kNumRows,
kNumCols,
lhs.data(),
rhs.data(),
x_computed.data(),
&summary.message);
ASSERT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
ASSERT_NEAR((x_computed - x_expected).norm() / x_expected.norm(),
0.0,
std::numeric_limits<double>::epsilon() * 400);
}
}
#endif // CERES_NO_CUDA
} // namespace ceres::internal