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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: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/partitioned_matrix_view.h"
#include <memory>
#include <random>
#include <sstream>
#include <string>
#include <vector>
#include "ceres/block_structure.h"
#include "ceres/casts.h"
#include "ceres/internal/eigen.h"
#include "ceres/linear_least_squares_problems.h"
#include "ceres/sparse_matrix.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres {
namespace internal {
const double kEpsilon = 1e-14;
// Param = <problem_id, num_threads>
using Param = ::testing::tuple<int, int>;
static std::string ParamInfoToString(testing::TestParamInfo<Param> info) {
Param param = info.param;
std::stringstream ss;
ss << ::testing::get<0>(param) << "_" << ::testing::get<1>(param);
return ss.str();
}
class PartitionedMatrixViewTest : public ::testing::TestWithParam<Param> {
protected:
void SetUp() final {
const int problem_id = ::testing::get<0>(GetParam());
const int num_threads = ::testing::get<1>(GetParam());
auto problem = CreateLinearLeastSquaresProblemFromId(problem_id);
CHECK(problem != nullptr);
A_ = std::move(problem->A);
auto block_sparse = down_cast<BlockSparseMatrix*>(A_.get());
options_.num_threads = num_threads;
options_.context = &context_;
options_.elimination_groups.push_back(problem->num_eliminate_blocks);
pmv_ = PartitionedMatrixViewBase::Create(options_, *block_sparse);
LinearSolver::Options options_single_threaded = options_;
options_single_threaded.num_threads = 1;
pmv_single_threaded_ =
PartitionedMatrixViewBase::Create(options_, *block_sparse);
EXPECT_EQ(pmv_->num_col_blocks_e(), problem->num_eliminate_blocks);
EXPECT_EQ(pmv_->num_col_blocks_f(),
block_sparse->block_structure()->cols.size() -
problem->num_eliminate_blocks);
EXPECT_EQ(pmv_->num_cols(), A_->num_cols());
EXPECT_EQ(pmv_->num_rows(), A_->num_rows());
}
double RandDouble() { return distribution_(prng_); }
LinearSolver::Options options_;
ContextImpl context_;
std::unique_ptr<LinearLeastSquaresProblem> problem_;
std::unique_ptr<SparseMatrix> A_;
std::unique_ptr<PartitionedMatrixViewBase> pmv_;
std::unique_ptr<PartitionedMatrixViewBase> pmv_single_threaded_;
std::mt19937 prng_;
std::uniform_real_distribution<double> distribution_ =
std::uniform_real_distribution<double>(0.0, 1.0);
};
TEST_P(PartitionedMatrixViewTest, RightMultiplyAndAccumulateE) {
Vector x1(pmv_->num_cols_e());
Vector x2(pmv_->num_cols());
x2.setZero();
for (int i = 0; i < pmv_->num_cols_e(); ++i) {
x1(i) = x2(i) = RandDouble();
}
Vector expected = Vector::Zero(pmv_->num_rows());
A_->RightMultiplyAndAccumulate(x2.data(), expected.data());
Vector actual = Vector::Zero(pmv_->num_rows());
pmv_->RightMultiplyAndAccumulateE(x1.data(), actual.data());
for (int i = 0; i < pmv_->num_rows(); ++i) {
EXPECT_NEAR(actual(i), expected(i), kEpsilon);
}
}
TEST_P(PartitionedMatrixViewTest, RightMultiplyAndAccumulateF) {
Vector x1(pmv_->num_cols_f());
Vector x2(pmv_->num_cols());
x2.setZero();
for (int i = 0; i < pmv_->num_cols_f(); ++i) {
x1(i) = x2(i + pmv_->num_cols_e()) = RandDouble();
}
Vector actual = Vector::Zero(pmv_->num_rows());
pmv_->RightMultiplyAndAccumulateF(x1.data(), actual.data());
Vector expected = Vector::Zero(pmv_->num_rows());
A_->RightMultiplyAndAccumulate(x2.data(), expected.data());
for (int i = 0; i < pmv_->num_rows(); ++i) {
EXPECT_NEAR(actual(i), expected(i), kEpsilon);
}
}
TEST_P(PartitionedMatrixViewTest, LeftMultiplyAndAccumulate) {
Vector x = Vector::Zero(pmv_->num_rows());
for (int i = 0; i < pmv_->num_rows(); ++i) {
x(i) = RandDouble();
}
Vector x_pre = x;
Vector expected = Vector::Zero(pmv_->num_cols());
Vector e_actual = Vector::Zero(pmv_->num_cols_e());
Vector f_actual = Vector::Zero(pmv_->num_cols_f());
A_->LeftMultiplyAndAccumulate(x.data(), expected.data());
pmv_->LeftMultiplyAndAccumulateE(x.data(), e_actual.data());
pmv_->LeftMultiplyAndAccumulateF(x.data(), f_actual.data());
for (int i = 0; i < pmv_->num_cols(); ++i) {
EXPECT_NEAR(expected(i),
(i < pmv_->num_cols_e()) ? e_actual(i)
: f_actual(i - pmv_->num_cols_e()),
kEpsilon);
}
}
TEST_P(PartitionedMatrixViewTest, BlockDiagonalFtF) {
std::unique_ptr<BlockSparseMatrix> block_diagonal_ff(
pmv_->CreateBlockDiagonalFtF());
const auto bs_diagonal = block_diagonal_ff->block_structure();
const int num_rows = pmv_->num_rows();
const int num_cols_f = pmv_->num_cols_f();
const int num_cols_e = pmv_->num_cols_e();
const int num_col_blocks_f = pmv_->num_col_blocks_f();
const int num_col_blocks_e = pmv_->num_col_blocks_e();
CHECK_EQ(block_diagonal_ff->num_rows(), num_cols_f);
CHECK_EQ(block_diagonal_ff->num_cols(), num_cols_f);
EXPECT_EQ(bs_diagonal->cols.size(), num_col_blocks_f);
EXPECT_EQ(bs_diagonal->rows.size(), num_col_blocks_f);
Matrix EF;
A_->ToDenseMatrix(&EF);
const auto F = EF.topRightCorner(num_rows, num_cols_f);
Matrix expected_FtF = F.transpose() * F;
Matrix actual_FtF;
block_diagonal_ff->ToDenseMatrix(&actual_FtF);
// FtF might be not block-diagonal
auto bs = down_cast<BlockSparseMatrix*>(A_.get())->block_structure();
for (int i = 0; i < num_col_blocks_f; ++i) {
const auto col_block_f = bs->cols[num_col_blocks_e + i];
const int block_size = col_block_f.size;
const int block_pos = col_block_f.position - num_cols_e;
const auto cell_expected =
expected_FtF.block(block_pos, block_pos, block_size, block_size);
auto cell_actual =
actual_FtF.block(block_pos, block_pos, block_size, block_size);
cell_actual -= cell_expected;
EXPECT_NEAR(cell_actual.norm(), 0., kEpsilon);
}
// There should be nothing remaining outside block-diagonal
EXPECT_NEAR(actual_FtF.norm(), 0., kEpsilon);
}
TEST_P(PartitionedMatrixViewTest, BlockDiagonalEtE) {
std::unique_ptr<BlockSparseMatrix> block_diagonal_ee(
pmv_->CreateBlockDiagonalEtE());
const CompressedRowBlockStructure* bs = block_diagonal_ee->block_structure();
const int num_rows = pmv_->num_rows();
const int num_cols_e = pmv_->num_cols_e();
const int num_col_blocks_e = pmv_->num_col_blocks_e();
CHECK_EQ(block_diagonal_ee->num_rows(), num_cols_e);
CHECK_EQ(block_diagonal_ee->num_cols(), num_cols_e);
EXPECT_EQ(bs->cols.size(), num_col_blocks_e);
EXPECT_EQ(bs->rows.size(), num_col_blocks_e);
Matrix EF;
A_->ToDenseMatrix(&EF);
const auto E = EF.topLeftCorner(num_rows, num_cols_e);
Matrix expected_EtE = E.transpose() * E;
Matrix actual_EtE;
block_diagonal_ee->ToDenseMatrix(&actual_EtE);
EXPECT_NEAR((expected_EtE - actual_EtE).norm(), 0., kEpsilon);
}
TEST_P(PartitionedMatrixViewTest, UpdateBlockDiagonalEtE) {
std::unique_ptr<BlockSparseMatrix> block_diagonal_ete(
pmv_->CreateBlockDiagonalEtE());
const int num_cols = pmv_->num_cols_e();
Matrix multi_threaded(num_cols, num_cols);
pmv_->UpdateBlockDiagonalEtE(block_diagonal_ete.get());
block_diagonal_ete->ToDenseMatrix(&multi_threaded);
Matrix single_threaded(num_cols, num_cols);
pmv_single_threaded_->UpdateBlockDiagonalEtE(block_diagonal_ete.get());
block_diagonal_ete->ToDenseMatrix(&single_threaded);
EXPECT_NEAR((multi_threaded - single_threaded).norm(), 0., kEpsilon);
}
TEST_P(PartitionedMatrixViewTest, UpdateBlockDiagonalFtF) {
std::unique_ptr<BlockSparseMatrix> block_diagonal_ftf(
pmv_->CreateBlockDiagonalFtF());
const int num_cols = pmv_->num_cols_f();
Matrix multi_threaded(num_cols, num_cols);
pmv_->UpdateBlockDiagonalFtF(block_diagonal_ftf.get());
block_diagonal_ftf->ToDenseMatrix(&multi_threaded);
Matrix single_threaded(num_cols, num_cols);
pmv_single_threaded_->UpdateBlockDiagonalFtF(block_diagonal_ftf.get());
block_diagonal_ftf->ToDenseMatrix(&single_threaded);
EXPECT_NEAR((multi_threaded - single_threaded).norm(), 0., kEpsilon);
}
INSTANTIATE_TEST_SUITE_P(
ParallelProducts,
PartitionedMatrixViewTest,
::testing::Combine(::testing::Values(2, 4, 6),
::testing::Values(1, 2, 3, 4, 5, 6, 7, 8)),
ParamInfoToString);
} // namespace internal
} // namespace ceres