// Ceres Solver - A fast non-linear least squares minimizer // Copyright 2010, 2011, 2012 Google Inc. All rights reserved. // http://code.google.com/p/ceres-solver/ // // 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 <numeric> #include "ceres/casts.h" #include "ceres/crs_matrix.h" #include "ceres/cxsparse.h" #include "ceres/internal/eigen.h" #include "ceres/internal/scoped_ptr.h" #include "ceres/linear_least_squares_problems.h" #include "ceres/random.h" #include "ceres/triplet_sparse_matrix.h" #include "glog/logging.h" #include "gtest/gtest.h" namespace ceres { namespace internal { 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->RightMultiply(x.data(), y_a.data()); b->RightMultiply(x.data(), y_b.data()); EXPECT_EQ((y_a - y_b).norm(), 0); } } class CompressedRowSparseMatrixTest : public ::testing::Test { protected : virtual void SetUp() { scoped_ptr<LinearLeastSquaresProblem> problem( CreateLinearLeastSquaresProblemFromId(1)); CHECK_NOTNULL(problem.get()); tsm.reset(down_cast<TripletSparseMatrix*>(problem->A.release())); crsm.reset(new CompressedRowSparseMatrix(*tsm)); num_rows = tsm->num_rows(); num_cols = tsm->num_cols(); vector<int>* row_blocks = crsm->mutable_row_blocks(); row_blocks->resize(num_rows); std::fill(row_blocks->begin(), row_blocks->end(), 1); vector<int>* col_blocks = crsm->mutable_col_blocks(); col_blocks->resize(num_cols); std::fill(col_blocks->begin(), col_blocks->end(), 1); } int num_rows; int num_cols; scoped_ptr<TripletSparseMatrix> tsm; scoped_ptr<CompressedRowSparseMatrix> crsm; }; TEST_F(CompressedRowSparseMatrixTest, RightMultiply) { CompareMatrices(tsm.get(), crsm.get()); } TEST_F(CompressedRowSparseMatrixTest, LeftMultiply) { for (int i = 0; i < num_rows; ++i) { Vector a = Vector::Zero(num_rows); a(i) = 1.0; Vector b1 = Vector::Zero(num_cols); Vector b2 = Vector::Zero(num_cols); tsm->LeftMultiply(a.data(), b1.data()); crsm->LeftMultiply(a.data(), b2.data()); EXPECT_EQ((b1 - b2).norm(), 0); } } TEST_F(CompressedRowSparseMatrixTest, ColumnNorm) { Vector b1 = Vector::Zero(num_cols); Vector b2 = Vector::Zero(num_cols); tsm->SquaredColumnNorm(b1.data()); crsm->SquaredColumnNorm(b2.data()); EXPECT_EQ((b1 - b2).norm(), 0); } 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); CompressedRowSparseMatrix crsm_appendage(tsm_appendage); crsm->AppendRows(crsm_appendage); CompareMatrices(tsm.get(), crsm.get()); } } TEST_F(CompressedRowSparseMatrixTest, AppendAndDeleteBlockDiagonalMatrix) { int num_diagonal_rows = crsm->num_cols(); scoped_array<double> diagonal(new double[num_diagonal_rows]); for (int i = 0; i < num_diagonal_rows; ++i) { diagonal[i] =i; } vector<int> row_and_column_blocks; row_and_column_blocks.push_back(1); row_and_column_blocks.push_back(2); row_and_column_blocks.push_back(2); const vector<int> pre_row_blocks = crsm->row_blocks(); const vector<int> pre_col_blocks = crsm->col_blocks(); scoped_ptr<CompressedRowSparseMatrix> appendage( CompressedRowSparseMatrix::CreateBlockDiagonalMatrix( diagonal.get(), row_and_column_blocks)); LOG(INFO) << appendage->row_blocks().size(); crsm->AppendRows(*appendage); const vector<int> post_row_blocks = crsm->row_blocks(); const vector<int> post_col_blocks = crsm->col_blocks(); vector<int> expected_row_blocks = pre_row_blocks; expected_row_blocks.insert(expected_row_blocks.end(), row_and_column_blocks.begin(), row_and_column_blocks.end()); vector<int> 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) { vector<int> blocks; blocks.push_back(1); blocks.push_back(2); blocks.push_back(2); Vector diagonal(5); for (int i = 0; i < 5; ++i) { diagonal(i) = i + 1; } scoped_ptr<CompressedRowSparseMatrix> 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->RightMultiply(x.data(), y.data()); for (int i = 0; i < diagonal.size(); ++i) { EXPECT_EQ(y[i], diagonal[i]); } y.setZero(); matrix->LeftMultiply(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); } class SolveLowerTriangularTest : public ::testing::Test { protected: void SetUp() { matrix_.reset(new CompressedRowSparseMatrix(4, 4, 7)); int* rows = matrix_->mutable_rows(); int* cols = matrix_->mutable_cols(); double* values = matrix_->mutable_values(); rows[0] = 0; cols[0] = 0; values[0] = 0.50754; rows[1] = 1; cols[1] = 1; values[1] = 0.80483; rows[2] = 2; cols[2] = 1; values[2] = 0.14120; cols[3] = 2; values[3] = 0.3; rows[3] = 4; cols[4] = 0; values[4] = 0.77696; cols[5] = 1; values[5] = 0.41860; cols[6] = 3; values[6] = 0.88979; rows[4] = 7; } scoped_ptr<CompressedRowSparseMatrix> matrix_; }; TEST_F(SolveLowerTriangularTest, SolveInPlace) { double rhs_and_solution[] = {1.0, 1.0, 2.0, 2.0}; double expected[] = {1.970288, 1.242498, 6.081864, -0.057255}; matrix_->SolveLowerTriangularInPlace(rhs_and_solution); for (int i = 0; i < 4; ++i) { EXPECT_NEAR(rhs_and_solution[i], expected[i], 1e-4) << i; } } TEST_F(SolveLowerTriangularTest, TransposeSolveInPlace) { double rhs_and_solution[] = {1.0, 1.0, 2.0, 2.0}; const double expected[] = { -1.4706, -1.0962, 6.6667, 2.2477}; matrix_->SolveLowerTriangularTransposeInPlace(rhs_and_solution); for (int i = 0; i < 4; ++i) { EXPECT_NEAR(rhs_and_solution[i], expected[i], 1e-4) << i; } } TEST(CompressedRowSparseMatrix, Transpose) { // 0 1 0 2 3 0 // 4 6 7 0 0 8 // 9 10 0 11 12 0 // 13 0 14 15 9 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()->push_back(3); matrix.mutable_row_blocks()->push_back(3); matrix.mutable_col_blocks()->push_back(4); matrix.mutable_col_blocks()->push_back(2); 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; copy(values, values + 17, cols); scoped_ptr<CompressedRowSparseMatrix> 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); } #ifndef CERES_NO_CXSPARSE struct RandomMatrixOptions { int num_row_blocks; int min_row_block_size; int max_row_block_size; int num_col_blocks; int min_col_block_size; int max_col_block_size; double block_density; }; CompressedRowSparseMatrix* CreateRandomCompressedRowSparseMatrix( const RandomMatrixOptions& options) { vector<int> row_blocks; for (int i = 0; i < options.num_row_blocks; ++i) { const int delta_block_size = Uniform(options.max_row_block_size - options.min_row_block_size); row_blocks.push_back(options.min_row_block_size + delta_block_size); } vector<int> col_blocks; for (int i = 0; i < options.num_col_blocks; ++i) { const int delta_block_size = Uniform(options.max_col_block_size - options.min_col_block_size); col_blocks.push_back(options.min_col_block_size + delta_block_size); } vector<int> rows; vector<int> cols; vector<double> values; while (values.size() == 0) { int row_block_begin = 0; for (int r = 0; r < options.num_row_blocks; ++r) { int col_block_begin = 0; for (int c = 0; c < options.num_col_blocks; ++c) { if (RandDouble() <= options.block_density) { for (int i = 0; i < row_blocks[r]; ++i) { for (int j = 0; j < col_blocks[c]; ++j) { rows.push_back(row_block_begin + i); cols.push_back(col_block_begin + j); values.push_back(RandNormal()); } } } col_block_begin += col_blocks[c]; } row_block_begin += row_blocks[r]; } } const int num_rows = std::accumulate(row_blocks.begin(), row_blocks.end(), 0); const int num_cols = std::accumulate(col_blocks.begin(), col_blocks.end(), 0); const int num_nonzeros = values.size(); TripletSparseMatrix tsm(num_rows, num_cols, num_nonzeros); std::copy(rows.begin(), rows.end(), tsm.mutable_rows()); std::copy(cols.begin(), cols.end(), tsm.mutable_cols()); std::copy(values.begin(), values.end(), tsm.mutable_values()); tsm.set_num_nonzeros(num_nonzeros); CompressedRowSparseMatrix* matrix = new CompressedRowSparseMatrix(tsm); (*matrix->mutable_row_blocks()) = row_blocks; (*matrix->mutable_col_blocks()) = col_blocks; return matrix; } void ToDenseMatrix(const cs_di* matrix, Matrix* dense_matrix) { dense_matrix->resize(matrix->m, matrix->n); dense_matrix->setZero(); for (int c = 0; c < matrix->n; ++c) { for (int idx = matrix->p[c]; idx < matrix->p[c + 1]; ++idx) { const int r = matrix->i[idx]; (*dense_matrix)(r, c) = matrix->x[idx]; } } } TEST(CompressedRowSparseMatrix, ComputeOuterProduct) { // "Randomly generated seed." SetRandomState(29823); int kMaxNumRowBlocks = 10; int kMaxNumColBlocks = 10; int kNumTrials = 10; CXSparse cxsparse; const double kTolerance = 1e-18; // Create a random matrix, compute its outer product using CXSParse // and ComputeOuterProduct. Convert both matrices to dense matrices // and compare their upper triangular parts. They should be within // kTolerance of each other. for (int num_row_blocks = 1; num_row_blocks < kMaxNumRowBlocks; ++num_row_blocks) { for (int num_col_blocks = 1; num_col_blocks < kMaxNumColBlocks; ++num_col_blocks) { for (int trial = 0; trial < kNumTrials; ++trial) { RandomMatrixOptions options; options.num_row_blocks = num_row_blocks; options.num_col_blocks = num_col_blocks; options.min_row_block_size = 1; options.max_row_block_size = 5; options.min_col_block_size = 1; options.max_col_block_size = 10; options.block_density = std::max(0.1, RandDouble()); VLOG(2) << "num row blocks: " << options.num_row_blocks; VLOG(2) << "num col blocks: " << options.num_col_blocks; VLOG(2) << "min row block size: " << options.min_row_block_size; VLOG(2) << "max row block size: " << options.max_row_block_size; VLOG(2) << "min col block size: " << options.min_col_block_size; VLOG(2) << "max col block size: " << options.max_col_block_size; VLOG(2) << "block density: " << options.block_density; scoped_ptr<CompressedRowSparseMatrix> matrix( CreateRandomCompressedRowSparseMatrix(options)); cs_di cs_matrix_transpose = cxsparse.CreateSparseMatrixTransposeView(matrix.get()); cs_di* cs_matrix = cxsparse.TransposeMatrix(&cs_matrix_transpose); cs_di* expected_outer_product = cxsparse.MatrixMatrixMultiply(&cs_matrix_transpose, cs_matrix); vector<int> program; scoped_ptr<CompressedRowSparseMatrix> outer_product( CompressedRowSparseMatrix::CreateOuterProductMatrixAndProgram( *matrix, &program)); CompressedRowSparseMatrix::ComputeOuterProduct(*matrix, program, outer_product.get()); cs_di actual_outer_product = cxsparse.CreateSparseMatrixTransposeView(outer_product.get()); ASSERT_EQ(actual_outer_product.m, actual_outer_product.n); ASSERT_EQ(expected_outer_product->m, expected_outer_product->n); ASSERT_EQ(actual_outer_product.m, expected_outer_product->m); Matrix actual_matrix; Matrix expected_matrix; ToDenseMatrix(expected_outer_product, &expected_matrix); expected_matrix.triangularView<Eigen::StrictlyLower>().setZero(); ToDenseMatrix(&actual_outer_product, &actual_matrix); const double diff_norm = (actual_matrix - expected_matrix).norm() / expected_matrix.norm(); ASSERT_NEAR(diff_norm, 0.0, kTolerance) << "expected: \n" << expected_matrix << "\nactual: \n" << actual_matrix; cxsparse.Free(cs_matrix); cxsparse.Free(expected_outer_product); } } } } #endif // CERES_NO_CXSPARSE } // namespace internal } // namespace ceres