| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2022 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 |
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| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
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| // 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/schur_complement_solver.h" |
| |
| #include <algorithm> |
| #include <ctime> |
| #include <memory> |
| #include <set> |
| #include <utility> |
| #include <vector> |
| |
| #include "Eigen/Dense" |
| #include "Eigen/SparseCore" |
| #include "ceres/block_random_access_dense_matrix.h" |
| #include "ceres/block_random_access_matrix.h" |
| #include "ceres/block_random_access_sparse_matrix.h" |
| #include "ceres/block_sparse_matrix.h" |
| #include "ceres/block_structure.h" |
| #include "ceres/conjugate_gradients_solver.h" |
| #include "ceres/detect_structure.h" |
| #include "ceres/internal/eigen.h" |
| #include "ceres/linear_solver.h" |
| #include "ceres/sparse_cholesky.h" |
| #include "ceres/triplet_sparse_matrix.h" |
| #include "ceres/types.h" |
| #include "ceres/wall_time.h" |
| |
| namespace ceres::internal { |
| namespace { |
| |
| class BlockRandomAccessSparseMatrixAdapter final |
| : public ConjugateGradientsLinearOperator<Vector> { |
| public: |
| explicit BlockRandomAccessSparseMatrixAdapter( |
| const BlockRandomAccessSparseMatrix& m) |
| : m_(m) {} |
| |
| void RightMultiplyAndAccumulate(const Vector& x, Vector& y) final { |
| m_.SymmetricRightMultiplyAndAccumulate(x.data(), y.data()); |
| } |
| |
| private: |
| const BlockRandomAccessSparseMatrix& m_; |
| }; |
| |
| class BlockRandomAccessDiagonalMatrixAdapter final |
| : public ConjugateGradientsLinearOperator<Vector> { |
| public: |
| explicit BlockRandomAccessDiagonalMatrixAdapter( |
| const BlockRandomAccessDiagonalMatrix& m) |
| : m_(m) {} |
| |
| // y = y + Ax; |
| void RightMultiplyAndAccumulate(const Vector& x, Vector& y) final { |
| m_.RightMultiplyAndAccumulate(x.data(), y.data()); |
| } |
| |
| private: |
| const BlockRandomAccessDiagonalMatrix& m_; |
| }; |
| |
| } // namespace |
| |
| SchurComplementSolver::SchurComplementSolver( |
| const LinearSolver::Options& options) |
| : options_(options) { |
| CHECK_GT(options.elimination_groups.size(), 1); |
| CHECK_GT(options.elimination_groups[0], 0); |
| CHECK(options.context != nullptr); |
| } |
| |
| LinearSolver::Summary SchurComplementSolver::SolveImpl( |
| BlockSparseMatrix* A, |
| const double* b, |
| const LinearSolver::PerSolveOptions& per_solve_options, |
| double* x) { |
| EventLogger event_logger("SchurComplementSolver::Solve"); |
| |
| const CompressedRowBlockStructure* bs = A->block_structure(); |
| if (eliminator_ == nullptr) { |
| const int num_eliminate_blocks = options_.elimination_groups[0]; |
| const int num_f_blocks = bs->cols.size() - num_eliminate_blocks; |
| |
| InitStorage(bs); |
| DetectStructure(*bs, |
| num_eliminate_blocks, |
| &options_.row_block_size, |
| &options_.e_block_size, |
| &options_.f_block_size); |
| |
| // For the special case of the static structure <2,3,6> with |
| // exactly one f block use the SchurEliminatorForOneFBlock. |
| // |
| // TODO(sameeragarwal): A more scalable template specialization |
| // mechanism that does not cause binary bloat. |
| if (options_.row_block_size == 2 && options_.e_block_size == 3 && |
| options_.f_block_size == 6 && num_f_blocks == 1) { |
| eliminator_ = std::make_unique<SchurEliminatorForOneFBlock<2, 3, 6>>(); |
| } else { |
| eliminator_ = SchurEliminatorBase::Create(options_); |
| } |
| |
| CHECK(eliminator_); |
| const bool kFullRankETE = true; |
| eliminator_->Init(num_eliminate_blocks, kFullRankETE, bs); |
| } |
| |
| std::fill(x, x + A->num_cols(), 0.0); |
| event_logger.AddEvent("Setup"); |
| |
| eliminator_->Eliminate(BlockSparseMatrixData(*A), |
| b, |
| per_solve_options.D, |
| lhs_.get(), |
| rhs_.data()); |
| event_logger.AddEvent("Eliminate"); |
| |
| double* reduced_solution = x + A->num_cols() - lhs_->num_cols(); |
| const LinearSolver::Summary summary = |
| SolveReducedLinearSystem(per_solve_options, reduced_solution); |
| event_logger.AddEvent("ReducedSolve"); |
| |
| if (summary.termination_type == LinearSolverTerminationType::SUCCESS) { |
| eliminator_->BackSubstitute( |
| BlockSparseMatrixData(*A), b, per_solve_options.D, reduced_solution, x); |
| event_logger.AddEvent("BackSubstitute"); |
| } |
| |
| return summary; |
| } |
| DenseSchurComplementSolver::DenseSchurComplementSolver( |
| const LinearSolver::Options& options) |
| : SchurComplementSolver(options), |
| cholesky_(DenseCholesky::Create(options)) {} |
| |
| DenseSchurComplementSolver::~DenseSchurComplementSolver() = default; |
| |
| // Initialize a BlockRandomAccessDenseMatrix to store the Schur |
| // complement. |
| void DenseSchurComplementSolver::InitStorage( |
| const CompressedRowBlockStructure* bs) { |
| const int num_eliminate_blocks = options().elimination_groups[0]; |
| const int num_col_blocks = bs->cols.size(); |
| auto blocks = Tail(bs->cols, num_col_blocks - num_eliminate_blocks); |
| set_lhs(std::make_unique<BlockRandomAccessDenseMatrix>( |
| blocks, options().context, options().num_threads)); |
| ResizeRhs(lhs()->num_rows()); |
| } |
| |
| // Solve the system Sx = r, assuming that the matrix S is stored in a |
| // BlockRandomAccessDenseMatrix. The linear system is solved using |
| // Eigen's Cholesky factorization. |
| LinearSolver::Summary DenseSchurComplementSolver::SolveReducedLinearSystem( |
| const LinearSolver::PerSolveOptions& /*per_solve_options*/, |
| double* solution) { |
| LinearSolver::Summary summary; |
| summary.num_iterations = 0; |
| summary.termination_type = LinearSolverTerminationType::SUCCESS; |
| summary.message = "Success."; |
| |
| auto* m = down_cast<BlockRandomAccessDenseMatrix*>(mutable_lhs()); |
| const int num_rows = m->num_rows(); |
| |
| // The case where there are no f blocks, and the system is block |
| // diagonal. |
| if (num_rows == 0) { |
| return summary; |
| } |
| |
| summary.num_iterations = 1; |
| summary.termination_type = cholesky_->FactorAndSolve( |
| num_rows, m->mutable_values(), rhs().data(), solution, &summary.message); |
| return summary; |
| } |
| |
| SparseSchurComplementSolver::SparseSchurComplementSolver( |
| const LinearSolver::Options& options) |
| : SchurComplementSolver(options) { |
| if (options.type != ITERATIVE_SCHUR) { |
| sparse_cholesky_ = SparseCholesky::Create(options); |
| } |
| } |
| |
| SparseSchurComplementSolver::~SparseSchurComplementSolver() { |
| for (int i = 0; i < 4; ++i) { |
| if (scratch_[i]) { |
| delete scratch_[i]; |
| scratch_[i] = nullptr; |
| } |
| } |
| } |
| |
| // Determine the non-zero blocks in the Schur Complement matrix, and |
| // initialize a BlockRandomAccessSparseMatrix object. |
| void SparseSchurComplementSolver::InitStorage( |
| const CompressedRowBlockStructure* bs) { |
| const int num_eliminate_blocks = options().elimination_groups[0]; |
| const int num_col_blocks = bs->cols.size(); |
| const int num_row_blocks = bs->rows.size(); |
| |
| blocks_ = Tail(bs->cols, num_col_blocks - num_eliminate_blocks); |
| |
| std::set<std::pair<int, int>> block_pairs; |
| for (int i = 0; i < blocks_.size(); ++i) { |
| block_pairs.emplace(i, i); |
| } |
| |
| int r = 0; |
| while (r < num_row_blocks) { |
| int e_block_id = bs->rows[r].cells.front().block_id; |
| if (e_block_id >= num_eliminate_blocks) { |
| break; |
| } |
| std::vector<int> f_blocks; |
| |
| // Add to the chunk until the first block in the row is |
| // different than the one in the first row for the chunk. |
| for (; r < num_row_blocks; ++r) { |
| const CompressedRow& row = bs->rows[r]; |
| if (row.cells.front().block_id != e_block_id) { |
| break; |
| } |
| |
| // Iterate over the blocks in the row, ignoring the first |
| // block since it is the one to be eliminated. |
| for (int c = 1; c < row.cells.size(); ++c) { |
| const Cell& cell = row.cells[c]; |
| f_blocks.push_back(cell.block_id - num_eliminate_blocks); |
| } |
| } |
| |
| sort(f_blocks.begin(), f_blocks.end()); |
| f_blocks.erase(unique(f_blocks.begin(), f_blocks.end()), f_blocks.end()); |
| for (int i = 0; i < f_blocks.size(); ++i) { |
| for (int j = i + 1; j < f_blocks.size(); ++j) { |
| block_pairs.emplace(f_blocks[i], f_blocks[j]); |
| } |
| } |
| } |
| |
| // Remaining rows do not contribute to the chunks and directly go |
| // into the schur complement via an outer product. |
| for (; r < num_row_blocks; ++r) { |
| const CompressedRow& row = bs->rows[r]; |
| CHECK_GE(row.cells.front().block_id, num_eliminate_blocks); |
| for (int i = 0; i < row.cells.size(); ++i) { |
| int r_block1_id = row.cells[i].block_id - num_eliminate_blocks; |
| for (const auto& cell : row.cells) { |
| int r_block2_id = cell.block_id - num_eliminate_blocks; |
| if (r_block1_id <= r_block2_id) { |
| block_pairs.emplace(r_block1_id, r_block2_id); |
| } |
| } |
| } |
| } |
| |
| set_lhs(std::make_unique<BlockRandomAccessSparseMatrix>( |
| blocks_, block_pairs, options().context, options().num_threads)); |
| ResizeRhs(lhs()->num_rows()); |
| } |
| |
| LinearSolver::Summary SparseSchurComplementSolver::SolveReducedLinearSystem( |
| const LinearSolver::PerSolveOptions& per_solve_options, double* solution) { |
| if (options().type == ITERATIVE_SCHUR) { |
| return SolveReducedLinearSystemUsingConjugateGradients(per_solve_options, |
| solution); |
| } |
| |
| LinearSolver::Summary summary; |
| summary.num_iterations = 0; |
| summary.termination_type = LinearSolverTerminationType::SUCCESS; |
| summary.message = "Success."; |
| |
| const BlockSparseMatrix* bsm = |
| down_cast<const BlockRandomAccessSparseMatrix*>(lhs())->matrix(); |
| if (bsm->num_rows() == 0) { |
| return summary; |
| } |
| |
| const CompressedRowSparseMatrix::StorageType storage_type = |
| sparse_cholesky_->StorageType(); |
| if (storage_type == |
| CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR) { |
| if (!crs_lhs_) { |
| crs_lhs_ = bsm->ToCompressedRowSparseMatrix(); |
| crs_lhs_->set_storage_type( |
| CompressedRowSparseMatrix::StorageType::UPPER_TRIANGULAR); |
| } else { |
| bsm->UpdateCompressedRowSparseMatrix(crs_lhs_.get()); |
| } |
| } else { |
| if (!crs_lhs_) { |
| crs_lhs_ = bsm->ToCompressedRowSparseMatrixTranspose(); |
| crs_lhs_->set_storage_type( |
| CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR); |
| } else { |
| bsm->UpdateCompressedRowSparseMatrixTranspose(crs_lhs_.get()); |
| } |
| } |
| |
| summary.num_iterations = 1; |
| summary.termination_type = sparse_cholesky_->FactorAndSolve( |
| crs_lhs_.get(), rhs().data(), solution, &summary.message); |
| return summary; |
| } |
| |
| LinearSolver::Summary |
| SparseSchurComplementSolver::SolveReducedLinearSystemUsingConjugateGradients( |
| const LinearSolver::PerSolveOptions& per_solve_options, double* solution) { |
| CHECK(options().use_explicit_schur_complement); |
| const int num_rows = lhs()->num_rows(); |
| // The case where there are no f blocks, and the system is block |
| // diagonal. |
| if (num_rows == 0) { |
| LinearSolver::Summary summary; |
| summary.num_iterations = 0; |
| summary.termination_type = LinearSolverTerminationType::SUCCESS; |
| summary.message = "Success."; |
| return summary; |
| } |
| |
| // Only SCHUR_JACOBI is supported over here right now. |
| CHECK_EQ(options().preconditioner_type, SCHUR_JACOBI); |
| |
| if (preconditioner_ == nullptr) { |
| preconditioner_ = std::make_unique<BlockRandomAccessDiagonalMatrix>( |
| blocks_, options().context, options().num_threads); |
| } |
| |
| auto* sc = down_cast<BlockRandomAccessSparseMatrix*>(mutable_lhs()); |
| |
| // Extract block diagonal from the Schur complement to construct the |
| // schur_jacobi preconditioner. |
| for (int i = 0; i < blocks_.size(); ++i) { |
| const int block_size = blocks_[i].size; |
| |
| int sc_r, sc_c, sc_row_stride, sc_col_stride; |
| CellInfo* sc_cell_info = |
| sc->GetCell(i, i, &sc_r, &sc_c, &sc_row_stride, &sc_col_stride); |
| CHECK(sc_cell_info != nullptr); |
| MatrixRef sc_m(sc_cell_info->values, sc_row_stride, sc_col_stride); |
| |
| int pre_r, pre_c, pre_row_stride, pre_col_stride; |
| CellInfo* pre_cell_info = preconditioner_->GetCell( |
| i, i, &pre_r, &pre_c, &pre_row_stride, &pre_col_stride); |
| CHECK(pre_cell_info != nullptr); |
| MatrixRef pre_m(pre_cell_info->values, pre_row_stride, pre_col_stride); |
| |
| pre_m.block(pre_r, pre_c, block_size, block_size) = |
| sc_m.block(sc_r, sc_c, block_size, block_size); |
| } |
| preconditioner_->Invert(); |
| |
| VectorRef(solution, num_rows).setZero(); |
| |
| auto lhs = std::make_unique<BlockRandomAccessSparseMatrixAdapter>(*sc); |
| auto preconditioner = |
| std::make_unique<BlockRandomAccessDiagonalMatrixAdapter>( |
| *preconditioner_); |
| |
| ConjugateGradientsSolverOptions cg_options; |
| cg_options.min_num_iterations = options().min_num_iterations; |
| cg_options.max_num_iterations = options().max_num_iterations; |
| cg_options.residual_reset_period = options().residual_reset_period; |
| cg_options.q_tolerance = per_solve_options.q_tolerance; |
| cg_options.r_tolerance = per_solve_options.r_tolerance; |
| |
| cg_solution_ = Vector::Zero(sc->num_rows()); |
| for (int i = 0; i < 4; ++i) { |
| if (scratch_[i] == nullptr) { |
| scratch_[i] = new Vector(sc->num_rows()); |
| } |
| } |
| auto summary = ConjugateGradientsSolver<Vector>( |
| cg_options, *lhs, rhs(), *preconditioner, scratch_, cg_solution_); |
| VectorRef(solution, sc->num_rows()) = cg_solution_; |
| return summary; |
| } |
| |
| } // namespace ceres::internal |