// Ceres Solver - A fast non-linear least squares minimizer // Copyright 2023 Google Inc. All rights reserved. // http://ceres-solver.org/ // // Redistribution and use in source and binary forms, with or without // 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 // and/or other materials provided with the distribution. // * Neither the name of Google Inc. nor the names of its contributors may be // used to endorse or promote products derived from this software without // specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE // POSSIBILITY OF SUCH DAMAGE. // // Author: sameeragarwal@google.com (Sameer Agarwal) #include "ceres/compressed_row_sparse_matrix.h" #include #include #include #include #include #include #include "Eigen/SparseCore" #include "ceres/casts.h" #include "ceres/context_impl.h" #include "ceres/crs_matrix.h" #include "ceres/internal/eigen.h" #include "ceres/linear_least_squares_problems.h" #include "ceres/triplet_sparse_matrix.h" #include "glog/logging.h" #include "gtest/gtest.h" namespace ceres::internal { static void CompareMatrices(const SparseMatrix* a, const SparseMatrix* b) { EXPECT_EQ(a->num_rows(), b->num_rows()); EXPECT_EQ(a->num_cols(), b->num_cols()); int num_rows = a->num_rows(); int num_cols = a->num_cols(); for (int i = 0; i < num_cols; ++i) { Vector x = Vector::Zero(num_cols); x(i) = 1.0; Vector y_a = Vector::Zero(num_rows); Vector y_b = Vector::Zero(num_rows); a->RightMultiplyAndAccumulate(x.data(), y_a.data()); b->RightMultiplyAndAccumulate(x.data(), y_b.data()); EXPECT_EQ((y_a - y_b).norm(), 0); } } class CompressedRowSparseMatrixTest : public ::testing::Test { protected: void SetUp() final { auto problem = CreateLinearLeastSquaresProblemFromId(1); CHECK(problem != nullptr); tsm.reset(down_cast(problem->A.release())); crsm = CompressedRowSparseMatrix::FromTripletSparseMatrix(*tsm); num_rows = tsm->num_rows(); num_cols = tsm->num_cols(); std::vector* row_blocks = crsm->mutable_row_blocks(); row_blocks->resize(num_rows); for (int i = 0; i < row_blocks->size(); ++i) { (*row_blocks)[i] = Block(1, i); } std::vector* col_blocks = crsm->mutable_col_blocks(); col_blocks->resize(num_cols); for (int i = 0; i < col_blocks->size(); ++i) { (*col_blocks)[i] = Block(1, i); } } int num_rows; int num_cols; std::unique_ptr tsm; std::unique_ptr crsm; }; TEST_F(CompressedRowSparseMatrixTest, Scale) { Vector scale(num_cols); for (int i = 0; i < num_cols; ++i) { scale(i) = i + 1; } tsm->ScaleColumns(scale.data()); crsm->ScaleColumns(scale.data()); CompareMatrices(tsm.get(), crsm.get()); } TEST_F(CompressedRowSparseMatrixTest, DeleteRows) { // Clear the row and column blocks as these are purely scalar tests. crsm->mutable_row_blocks()->clear(); crsm->mutable_col_blocks()->clear(); for (int i = 0; i < num_rows; ++i) { tsm->Resize(num_rows - i, num_cols); crsm->DeleteRows(crsm->num_rows() - tsm->num_rows()); CompareMatrices(tsm.get(), crsm.get()); } } TEST_F(CompressedRowSparseMatrixTest, AppendRows) { // Clear the row and column blocks as these are purely scalar tests. crsm->mutable_row_blocks()->clear(); crsm->mutable_col_blocks()->clear(); for (int i = 0; i < num_rows; ++i) { TripletSparseMatrix tsm_appendage(*tsm); tsm_appendage.Resize(i, num_cols); tsm->AppendRows(tsm_appendage); auto crsm_appendage = CompressedRowSparseMatrix::FromTripletSparseMatrix(tsm_appendage); crsm->AppendRows(*crsm_appendage); CompareMatrices(tsm.get(), crsm.get()); } } TEST_F(CompressedRowSparseMatrixTest, AppendAndDeleteBlockDiagonalMatrix) { int num_diagonal_rows = crsm->num_cols(); auto diagonal = std::make_unique(num_diagonal_rows); for (int i = 0; i < num_diagonal_rows; ++i) { diagonal[i] = i; } std::vector row_and_column_blocks; row_and_column_blocks.emplace_back(1, 0); row_and_column_blocks.emplace_back(2, 1); row_and_column_blocks.emplace_back(2, 3); const std::vector pre_row_blocks = crsm->row_blocks(); const std::vector pre_col_blocks = crsm->col_blocks(); auto appendage = CompressedRowSparseMatrix::CreateBlockDiagonalMatrix( diagonal.get(), row_and_column_blocks); crsm->AppendRows(*appendage); const std::vector post_row_blocks = crsm->row_blocks(); const std::vector post_col_blocks = crsm->col_blocks(); std::vector expected_row_blocks = pre_row_blocks; expected_row_blocks.insert(expected_row_blocks.end(), row_and_column_blocks.begin(), row_and_column_blocks.end()); std::vector expected_col_blocks = pre_col_blocks; EXPECT_EQ(expected_row_blocks, crsm->row_blocks()); EXPECT_EQ(expected_col_blocks, crsm->col_blocks()); crsm->DeleteRows(num_diagonal_rows); EXPECT_EQ(crsm->row_blocks(), pre_row_blocks); EXPECT_EQ(crsm->col_blocks(), pre_col_blocks); } TEST_F(CompressedRowSparseMatrixTest, ToDenseMatrix) { Matrix tsm_dense; Matrix crsm_dense; tsm->ToDenseMatrix(&tsm_dense); crsm->ToDenseMatrix(&crsm_dense); EXPECT_EQ((tsm_dense - crsm_dense).norm(), 0.0); } TEST_F(CompressedRowSparseMatrixTest, ToCRSMatrix) { CRSMatrix crs_matrix; crsm->ToCRSMatrix(&crs_matrix); EXPECT_EQ(crsm->num_rows(), crs_matrix.num_rows); EXPECT_EQ(crsm->num_cols(), crs_matrix.num_cols); EXPECT_EQ(crsm->num_rows() + 1, crs_matrix.rows.size()); EXPECT_EQ(crsm->num_nonzeros(), crs_matrix.cols.size()); EXPECT_EQ(crsm->num_nonzeros(), crs_matrix.values.size()); for (int i = 0; i < crsm->num_rows() + 1; ++i) { EXPECT_EQ(crsm->rows()[i], crs_matrix.rows[i]); } for (int i = 0; i < crsm->num_nonzeros(); ++i) { EXPECT_EQ(crsm->cols()[i], crs_matrix.cols[i]); EXPECT_EQ(crsm->values()[i], crs_matrix.values[i]); } } TEST(CompressedRowSparseMatrix, CreateBlockDiagonalMatrix) { std::vector blocks; blocks.emplace_back(1, 0); blocks.emplace_back(2, 1); blocks.emplace_back(2, 3); Vector diagonal(5); for (int i = 0; i < 5; ++i) { diagonal(i) = i + 1; } auto matrix = CompressedRowSparseMatrix::CreateBlockDiagonalMatrix( diagonal.data(), blocks); EXPECT_EQ(matrix->num_rows(), 5); EXPECT_EQ(matrix->num_cols(), 5); EXPECT_EQ(matrix->num_nonzeros(), 9); EXPECT_EQ(blocks, matrix->row_blocks()); EXPECT_EQ(blocks, matrix->col_blocks()); Vector x(5); Vector y(5); x.setOnes(); y.setZero(); matrix->RightMultiplyAndAccumulate(x.data(), y.data()); for (int i = 0; i < diagonal.size(); ++i) { EXPECT_EQ(y[i], diagonal[i]); } y.setZero(); matrix->LeftMultiplyAndAccumulate(x.data(), y.data()); for (int i = 0; i < diagonal.size(); ++i) { EXPECT_EQ(y[i], diagonal[i]); } Matrix dense; matrix->ToDenseMatrix(&dense); EXPECT_EQ((dense.diagonal() - diagonal).norm(), 0.0); } TEST(CompressedRowSparseMatrix, Transpose) { // 0 1 0 2 3 0 // 4 5 6 0 0 7 // 8 9 0 10 11 0 // 12 0 13 14 15 0 // 0 16 17 0 0 0 // Block structure: // A A A A B B // A A A A B B // A A A A B B // C C C C D D // C C C C D D // C C C C D D CompressedRowSparseMatrix matrix(5, 6, 30); int* rows = matrix.mutable_rows(); int* cols = matrix.mutable_cols(); double* values = matrix.mutable_values(); matrix.mutable_row_blocks()->emplace_back(3, 0); matrix.mutable_row_blocks()->emplace_back(3, 3); matrix.mutable_col_blocks()->emplace_back(4, 0); matrix.mutable_col_blocks()->emplace_back(2, 4); rows[0] = 0; cols[0] = 1; cols[1] = 3; cols[2] = 4; rows[1] = 3; cols[3] = 0; cols[4] = 1; cols[5] = 2; cols[6] = 5; rows[2] = 7; cols[7] = 0; cols[8] = 1; cols[9] = 3; cols[10] = 4; rows[3] = 11; cols[11] = 0; cols[12] = 2; cols[13] = 3; cols[14] = 4; rows[4] = 15; cols[15] = 1; cols[16] = 2; rows[5] = 17; std::iota(values, values + 17, 1); auto transpose = matrix.Transpose(); ASSERT_EQ(transpose->row_blocks().size(), matrix.col_blocks().size()); for (int i = 0; i < transpose->row_blocks().size(); ++i) { EXPECT_EQ(transpose->row_blocks()[i], matrix.col_blocks()[i]); } ASSERT_EQ(transpose->col_blocks().size(), matrix.row_blocks().size()); for (int i = 0; i < transpose->col_blocks().size(); ++i) { EXPECT_EQ(transpose->col_blocks()[i], matrix.row_blocks()[i]); } Matrix dense_matrix; matrix.ToDenseMatrix(&dense_matrix); Matrix dense_transpose; transpose->ToDenseMatrix(&dense_transpose); EXPECT_NEAR((dense_matrix - dense_transpose.transpose()).norm(), 0.0, 1e-14); } TEST(CompressedRowSparseMatrix, FromTripletSparseMatrix) { std::mt19937 prng; TripletSparseMatrix::RandomMatrixOptions options; options.num_rows = 5; options.num_cols = 7; options.density = 0.5; const int kNumTrials = 10; for (int i = 0; i < kNumTrials; ++i) { auto tsm = TripletSparseMatrix::CreateRandomMatrix(options, prng); auto crsm = CompressedRowSparseMatrix::FromTripletSparseMatrix(*tsm); Matrix expected; tsm->ToDenseMatrix(&expected); Matrix actual; crsm->ToDenseMatrix(&actual); EXPECT_NEAR((expected - actual).norm() / actual.norm(), 0.0, std::numeric_limits::epsilon()) << "\nexpected: \n" << expected << "\nactual: \n" << actual; } } TEST(CompressedRowSparseMatrix, FromTripletSparseMatrixTransposed) { std::mt19937 prng; TripletSparseMatrix::RandomMatrixOptions options; options.num_rows = 5; options.num_cols = 7; options.density = 0.5; const int kNumTrials = 10; for (int i = 0; i < kNumTrials; ++i) { auto tsm = TripletSparseMatrix::CreateRandomMatrix(options, prng); auto crsm = CompressedRowSparseMatrix::FromTripletSparseMatrixTransposed(*tsm); Matrix tmp; tsm->ToDenseMatrix(&tmp); Matrix expected = tmp.transpose(); Matrix actual; crsm->ToDenseMatrix(&actual); EXPECT_NEAR((expected - actual).norm() / actual.norm(), 0.0, std::numeric_limits::epsilon()) << "\nexpected: \n" << expected << "\nactual: \n" << actual; } } using Param = ::testing::tuple; static std::string ParamInfoToString(testing::TestParamInfo info) { if (::testing::get<0>(info.param) == CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR) { return "UPPER"; } if (::testing::get<0>(info.param) == CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR) { return "LOWER"; } return "UNSYMMETRIC"; } class RightMultiplyAndAccumulateTest : public ::testing::TestWithParam { }; TEST_P(RightMultiplyAndAccumulateTest, _) { const int kMinNumBlocks = 1; const int kMaxNumBlocks = 10; const int kMinBlockSize = 1; const int kMaxBlockSize = 5; const int kNumTrials = 10; std::mt19937 prng; std::uniform_real_distribution uniform(0.5, 1.0); for (int num_blocks = kMinNumBlocks; num_blocks < kMaxNumBlocks; ++num_blocks) { for (int trial = 0; trial < kNumTrials; ++trial) { Param param = GetParam(); CompressedRowSparseMatrix::RandomMatrixOptions options; options.num_col_blocks = num_blocks; options.min_col_block_size = kMinBlockSize; options.max_col_block_size = kMaxBlockSize; options.num_row_blocks = 2 * num_blocks; options.min_row_block_size = kMinBlockSize; options.max_row_block_size = kMaxBlockSize; options.block_density = uniform(prng); options.storage_type = ::testing::get<0>(param); auto matrix = CompressedRowSparseMatrix::CreateRandomMatrix(options, prng); const int num_rows = matrix->num_rows(); const int num_cols = matrix->num_cols(); Vector x(num_cols); x.setRandom(); Vector actual_y(num_rows); actual_y.setZero(); matrix->RightMultiplyAndAccumulate(x.data(), actual_y.data()); Matrix dense; matrix->ToDenseMatrix(&dense); Vector expected_y; if (::testing::get<0>(param) == CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR) { expected_y = dense.selfadjointView() * x; } else if (::testing::get<0>(param) == CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR) { expected_y = dense.selfadjointView() * x; } else { expected_y = dense * x; } ASSERT_NEAR((expected_y - actual_y).norm() / actual_y.norm(), 0.0, std::numeric_limits::epsilon() * 10) << "\n" << dense << "x:\n" << x.transpose() << "\n" << "expected: \n" << expected_y.transpose() << "\n" << "actual: \n" << actual_y.transpose(); } } } INSTANTIATE_TEST_SUITE_P( CompressedRowSparseMatrix, RightMultiplyAndAccumulateTest, ::testing::Values(CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR, CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR, CompressedRowSparseMatrix::StorageType::UNSYMMETRIC), ParamInfoToString); class LeftMultiplyAndAccumulateTest : public ::testing::TestWithParam {}; TEST_P(LeftMultiplyAndAccumulateTest, _) { const int kMinNumBlocks = 1; const int kMaxNumBlocks = 10; const int kMinBlockSize = 1; const int kMaxBlockSize = 5; const int kNumTrials = 10; std::mt19937 prng; std::uniform_real_distribution uniform(0.5, 1.0); for (int num_blocks = kMinNumBlocks; num_blocks < kMaxNumBlocks; ++num_blocks) { for (int trial = 0; trial < kNumTrials; ++trial) { Param param = GetParam(); CompressedRowSparseMatrix::RandomMatrixOptions options; options.num_col_blocks = num_blocks; options.min_col_block_size = kMinBlockSize; options.max_col_block_size = kMaxBlockSize; options.num_row_blocks = 2 * num_blocks; options.min_row_block_size = kMinBlockSize; options.max_row_block_size = kMaxBlockSize; options.block_density = uniform(prng); options.storage_type = ::testing::get<0>(param); auto matrix = CompressedRowSparseMatrix::CreateRandomMatrix(options, prng); const int num_rows = matrix->num_rows(); const int num_cols = matrix->num_cols(); Vector x(num_rows); x.setRandom(); Vector actual_y(num_cols); actual_y.setZero(); matrix->LeftMultiplyAndAccumulate(x.data(), actual_y.data()); Matrix dense; matrix->ToDenseMatrix(&dense); Vector expected_y; if (::testing::get<0>(param) == CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR) { expected_y = dense.selfadjointView() * x; } else if (::testing::get<0>(param) == CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR) { expected_y = dense.selfadjointView() * x; } else { expected_y = dense.transpose() * x; } ASSERT_NEAR((expected_y - actual_y).norm() / actual_y.norm(), 0.0, std::numeric_limits::epsilon() * 10) << "\n" << dense << "x\n" << x.transpose() << "\n" << "expected: \n" << expected_y.transpose() << "\n" << "actual: \n" << actual_y.transpose(); } } } INSTANTIATE_TEST_SUITE_P( CompressedRowSparseMatrix, LeftMultiplyAndAccumulateTest, ::testing::Values(CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR, CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR, CompressedRowSparseMatrix::StorageType::UNSYMMETRIC), ParamInfoToString); class SquaredColumnNormTest : public ::testing::TestWithParam {}; TEST_P(SquaredColumnNormTest, _) { const int kMinNumBlocks = 1; const int kMaxNumBlocks = 10; const int kMinBlockSize = 1; const int kMaxBlockSize = 5; const int kNumTrials = 10; std::mt19937 prng; std::uniform_real_distribution uniform(0.5, 1.0); for (int num_blocks = kMinNumBlocks; num_blocks < kMaxNumBlocks; ++num_blocks) { for (int trial = 0; trial < kNumTrials; ++trial) { Param param = GetParam(); CompressedRowSparseMatrix::RandomMatrixOptions options; options.num_col_blocks = num_blocks; options.min_col_block_size = kMinBlockSize; options.max_col_block_size = kMaxBlockSize; options.num_row_blocks = 2 * num_blocks; options.min_row_block_size = kMinBlockSize; options.max_row_block_size = kMaxBlockSize; options.block_density = uniform(prng); options.storage_type = ::testing::get<0>(param); auto matrix = CompressedRowSparseMatrix::CreateRandomMatrix(options, prng); const int num_cols = matrix->num_cols(); Vector actual(num_cols); actual.setZero(); matrix->SquaredColumnNorm(actual.data()); Matrix dense; matrix->ToDenseMatrix(&dense); Vector expected; if (::testing::get<0>(param) == CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR) { const Matrix full = dense.selfadjointView(); expected = full.colwise().squaredNorm(); } else if (::testing::get<0>(param) == CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR) { const Matrix full = dense.selfadjointView(); expected = full.colwise().squaredNorm(); } else { expected = dense.colwise().squaredNorm(); } ASSERT_NEAR((expected - actual).norm() / actual.norm(), 0.0, std::numeric_limits::epsilon() * 10) << "\n" << dense << "expected: \n" << expected.transpose() << "\n" << "actual: \n" << actual.transpose(); } } } INSTANTIATE_TEST_SUITE_P( CompressedRowSparseMatrix, SquaredColumnNormTest, ::testing::Values(CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR, CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR, CompressedRowSparseMatrix::StorageType::UNSYMMETRIC), ParamInfoToString); const int kMaxNumThreads = 8; class CompressedRowSparseMatrixParallelTest : public ::testing::TestWithParam { void SetUp() final { context_.EnsureMinimumThreads(kMaxNumThreads); } protected: ContextImpl context_; }; TEST_P(CompressedRowSparseMatrixParallelTest, RightMultiplyAndAccumulateUnsymmetric) { const int kMinNumBlocks = 1; const int kMaxNumBlocks = 10; const int kMinBlockSize = 1; const int kMaxBlockSize = 5; const int kNumTrials = 10; const int kNumThreads = GetParam(); std::mt19937 prng; std::uniform_real_distribution uniform(0.5, 1.0); for (int num_blocks = kMinNumBlocks; num_blocks < kMaxNumBlocks; ++num_blocks) { for (int trial = 0; trial < kNumTrials; ++trial) { CompressedRowSparseMatrix::RandomMatrixOptions options; options.num_col_blocks = num_blocks; options.min_col_block_size = kMinBlockSize; options.max_col_block_size = kMaxBlockSize; options.num_row_blocks = 2 * num_blocks; options.min_row_block_size = kMinBlockSize; options.max_row_block_size = kMaxBlockSize; options.block_density = uniform(prng); options.storage_type = CompressedRowSparseMatrix::StorageType::UNSYMMETRIC; auto matrix = CompressedRowSparseMatrix::CreateRandomMatrix(options, prng); const int num_rows = matrix->num_rows(); const int num_cols = matrix->num_cols(); Vector x(num_cols); x.setRandom(); Vector actual_y(num_rows); actual_y.setZero(); matrix->RightMultiplyAndAccumulate( x.data(), actual_y.data(), &context_, kNumThreads); Matrix dense; matrix->ToDenseMatrix(&dense); Vector expected_y = dense * x; ASSERT_NEAR((expected_y - actual_y).norm() / actual_y.norm(), 0.0, std::numeric_limits::epsilon() * 10) << "\n" << dense << "x:\n" << x.transpose() << "\n" << "expected: \n" << expected_y.transpose() << "\n" << "actual: \n" << actual_y.transpose(); } } } INSTANTIATE_TEST_SUITE_P(ParallelProducts, CompressedRowSparseMatrixParallelTest, ::testing::Values(1, 2, 4, 8), ::testing::PrintToStringParamName()); // TODO(sameeragarwal) Add tests for the random matrix creation methods. } // namespace ceres::internal