671 lines
23 KiB
C++
671 lines
23 KiB
C++
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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#include "ceres/internal/port.h"
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#include <algorithm>
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#include <ctime>
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#include <set>
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#include <vector>
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#include "ceres/block_random_access_dense_matrix.h"
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#include "ceres/block_random_access_matrix.h"
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#include "ceres/block_random_access_sparse_matrix.h"
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#include "ceres/block_sparse_matrix.h"
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#include "ceres/block_structure.h"
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#include "ceres/conjugate_gradients_solver.h"
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#include "ceres/cxsparse.h"
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#include "ceres/detect_structure.h"
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#include "ceres/internal/eigen.h"
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#include "ceres/internal/scoped_ptr.h"
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#include "ceres/lapack.h"
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#include "ceres/linear_solver.h"
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#include "ceres/schur_complement_solver.h"
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#include "ceres/suitesparse.h"
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#include "ceres/triplet_sparse_matrix.h"
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#include "ceres/types.h"
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#include "ceres/wall_time.h"
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#include "Eigen/Dense"
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#include "Eigen/SparseCore"
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namespace ceres {
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namespace internal {
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using std::make_pair;
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using std::pair;
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using std::set;
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using std::vector;
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namespace {
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class BlockRandomAccessSparseMatrixAdapter : public LinearOperator {
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public:
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explicit BlockRandomAccessSparseMatrixAdapter(
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const BlockRandomAccessSparseMatrix& m)
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: m_(m) {
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}
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virtual ~BlockRandomAccessSparseMatrixAdapter() {}
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// y = y + Ax;
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virtual void RightMultiply(const double* x, double* y) const {
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m_.SymmetricRightMultiply(x, y);
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}
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// y = y + A'x;
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virtual void LeftMultiply(const double* x, double* y) const {
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m_.SymmetricRightMultiply(x, y);
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}
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virtual int num_rows() const { return m_.num_rows(); }
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virtual int num_cols() const { return m_.num_rows(); }
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private:
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const BlockRandomAccessSparseMatrix& m_;
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};
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class BlockRandomAccessDiagonalMatrixAdapter : public LinearOperator {
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public:
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explicit BlockRandomAccessDiagonalMatrixAdapter(
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const BlockRandomAccessDiagonalMatrix& m)
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: m_(m) {
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}
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virtual ~BlockRandomAccessDiagonalMatrixAdapter() {}
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// y = y + Ax;
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virtual void RightMultiply(const double* x, double* y) const {
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m_.RightMultiply(x, y);
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}
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// y = y + A'x;
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virtual void LeftMultiply(const double* x, double* y) const {
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m_.RightMultiply(x, y);
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}
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virtual int num_rows() const { return m_.num_rows(); }
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virtual int num_cols() const { return m_.num_rows(); }
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private:
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const BlockRandomAccessDiagonalMatrix& m_;
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};
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} // namespace
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LinearSolver::Summary SchurComplementSolver::SolveImpl(
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BlockSparseMatrix* A,
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const double* b,
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const LinearSolver::PerSolveOptions& per_solve_options,
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double* x) {
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EventLogger event_logger("SchurComplementSolver::Solve");
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if (eliminator_.get() == NULL) {
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InitStorage(A->block_structure());
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DetectStructure(*A->block_structure(),
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options_.elimination_groups[0],
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&options_.row_block_size,
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&options_.e_block_size,
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&options_.f_block_size);
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eliminator_.reset(CHECK_NOTNULL(SchurEliminatorBase::Create(options_)));
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eliminator_->Init(options_.elimination_groups[0], A->block_structure());
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};
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std::fill(x, x + A->num_cols(), 0.0);
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event_logger.AddEvent("Setup");
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eliminator_->Eliminate(A, b, per_solve_options.D, lhs_.get(), rhs_.get());
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event_logger.AddEvent("Eliminate");
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double* reduced_solution = x + A->num_cols() - lhs_->num_cols();
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const LinearSolver::Summary summary =
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SolveReducedLinearSystem(per_solve_options, reduced_solution);
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event_logger.AddEvent("ReducedSolve");
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if (summary.termination_type == LINEAR_SOLVER_SUCCESS) {
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eliminator_->BackSubstitute(A, b, per_solve_options.D, reduced_solution, x);
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event_logger.AddEvent("BackSubstitute");
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}
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return summary;
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}
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// Initialize a BlockRandomAccessDenseMatrix to store the Schur
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// complement.
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void DenseSchurComplementSolver::InitStorage(
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const CompressedRowBlockStructure* bs) {
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const int num_eliminate_blocks = options().elimination_groups[0];
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const int num_col_blocks = bs->cols.size();
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vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
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for (int i = num_eliminate_blocks, j = 0;
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i < num_col_blocks;
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++i, ++j) {
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blocks[j] = bs->cols[i].size;
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}
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set_lhs(new BlockRandomAccessDenseMatrix(blocks));
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set_rhs(new double[lhs()->num_rows()]);
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}
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// Solve the system Sx = r, assuming that the matrix S is stored in a
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// BlockRandomAccessDenseMatrix. The linear system is solved using
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// Eigen's Cholesky factorization.
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LinearSolver::Summary
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DenseSchurComplementSolver::SolveReducedLinearSystem(
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const LinearSolver::PerSolveOptions& per_solve_options,
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double* solution) {
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LinearSolver::Summary summary;
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summary.num_iterations = 0;
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summary.termination_type = LINEAR_SOLVER_SUCCESS;
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summary.message = "Success.";
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const BlockRandomAccessDenseMatrix* m =
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down_cast<const BlockRandomAccessDenseMatrix*>(lhs());
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const int num_rows = m->num_rows();
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// The case where there are no f blocks, and the system is block
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// diagonal.
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if (num_rows == 0) {
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return summary;
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}
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summary.num_iterations = 1;
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if (options().dense_linear_algebra_library_type == EIGEN) {
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Eigen::LLT<Matrix, Eigen::Upper> llt =
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ConstMatrixRef(m->values(), num_rows, num_rows)
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.selfadjointView<Eigen::Upper>()
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.llt();
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if (llt.info() != Eigen::Success) {
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summary.termination_type = LINEAR_SOLVER_FAILURE;
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summary.message =
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"Eigen failure. Unable to perform dense Cholesky factorization.";
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return summary;
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}
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VectorRef(solution, num_rows) = llt.solve(ConstVectorRef(rhs(), num_rows));
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} else {
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VectorRef(solution, num_rows) = ConstVectorRef(rhs(), num_rows);
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summary.termination_type =
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LAPACK::SolveInPlaceUsingCholesky(num_rows,
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m->values(),
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solution,
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&summary.message);
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}
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return summary;
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}
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SparseSchurComplementSolver::SparseSchurComplementSolver(
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const LinearSolver::Options& options)
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: SchurComplementSolver(options),
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factor_(NULL),
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cxsparse_factor_(NULL) {
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}
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SparseSchurComplementSolver::~SparseSchurComplementSolver() {
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if (factor_ != NULL) {
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ss_.Free(factor_);
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factor_ = NULL;
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}
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if (cxsparse_factor_ != NULL) {
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cxsparse_.Free(cxsparse_factor_);
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cxsparse_factor_ = NULL;
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}
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}
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// Determine the non-zero blocks in the Schur Complement matrix, and
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// initialize a BlockRandomAccessSparseMatrix object.
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void SparseSchurComplementSolver::InitStorage(
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const CompressedRowBlockStructure* bs) {
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const int num_eliminate_blocks = options().elimination_groups[0];
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const int num_col_blocks = bs->cols.size();
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const int num_row_blocks = bs->rows.size();
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blocks_.resize(num_col_blocks - num_eliminate_blocks, 0);
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for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
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blocks_[i - num_eliminate_blocks] = bs->cols[i].size;
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}
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set<pair<int, int> > block_pairs;
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for (int i = 0; i < blocks_.size(); ++i) {
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block_pairs.insert(make_pair(i, i));
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}
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int r = 0;
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while (r < num_row_blocks) {
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int e_block_id = bs->rows[r].cells.front().block_id;
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if (e_block_id >= num_eliminate_blocks) {
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break;
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}
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vector<int> f_blocks;
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// Add to the chunk until the first block in the row is
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// different than the one in the first row for the chunk.
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for (; r < num_row_blocks; ++r) {
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const CompressedRow& row = bs->rows[r];
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if (row.cells.front().block_id != e_block_id) {
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break;
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}
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// Iterate over the blocks in the row, ignoring the first
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// block since it is the one to be eliminated.
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for (int c = 1; c < row.cells.size(); ++c) {
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const Cell& cell = row.cells[c];
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f_blocks.push_back(cell.block_id - num_eliminate_blocks);
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}
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}
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sort(f_blocks.begin(), f_blocks.end());
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f_blocks.erase(unique(f_blocks.begin(), f_blocks.end()), f_blocks.end());
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for (int i = 0; i < f_blocks.size(); ++i) {
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for (int j = i + 1; j < f_blocks.size(); ++j) {
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block_pairs.insert(make_pair(f_blocks[i], f_blocks[j]));
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}
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}
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}
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// Remaing rows do not contribute to the chunks and directly go
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// into the schur complement via an outer product.
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for (; r < num_row_blocks; ++r) {
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const CompressedRow& row = bs->rows[r];
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CHECK_GE(row.cells.front().block_id, num_eliminate_blocks);
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for (int i = 0; i < row.cells.size(); ++i) {
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int r_block1_id = row.cells[i].block_id - num_eliminate_blocks;
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for (int j = 0; j < row.cells.size(); ++j) {
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int r_block2_id = row.cells[j].block_id - num_eliminate_blocks;
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if (r_block1_id <= r_block2_id) {
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block_pairs.insert(make_pair(r_block1_id, r_block2_id));
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}
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}
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}
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}
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set_lhs(new BlockRandomAccessSparseMatrix(blocks_, block_pairs));
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set_rhs(new double[lhs()->num_rows()]);
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}
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LinearSolver::Summary
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SparseSchurComplementSolver::SolveReducedLinearSystem(
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const LinearSolver::PerSolveOptions& per_solve_options,
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double* solution) {
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if (options().type == ITERATIVE_SCHUR) {
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CHECK(options().use_explicit_schur_complement);
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return SolveReducedLinearSystemUsingConjugateGradients(per_solve_options,
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solution);
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}
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switch (options().sparse_linear_algebra_library_type) {
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case SUITE_SPARSE:
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return SolveReducedLinearSystemUsingSuiteSparse(per_solve_options,
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solution);
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case CX_SPARSE:
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return SolveReducedLinearSystemUsingCXSparse(per_solve_options,
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solution);
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case EIGEN_SPARSE:
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return SolveReducedLinearSystemUsingEigen(per_solve_options,
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solution);
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default:
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LOG(FATAL) << "Unknown sparse linear algebra library : "
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<< options().sparse_linear_algebra_library_type;
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}
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return LinearSolver::Summary();
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}
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// Solve the system Sx = r, assuming that the matrix S is stored in a
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// BlockRandomAccessSparseMatrix. The linear system is solved using
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// CHOLMOD's sparse cholesky factorization routines.
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LinearSolver::Summary
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SparseSchurComplementSolver::SolveReducedLinearSystemUsingSuiteSparse(
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const LinearSolver::PerSolveOptions& per_solve_options,
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double* solution) {
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#ifdef CERES_NO_SUITESPARSE
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LinearSolver::Summary summary;
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summary.num_iterations = 0;
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summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
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summary.message = "Ceres was not built with SuiteSparse support. "
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"Therefore, SPARSE_SCHUR cannot be used with SUITE_SPARSE";
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return summary;
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#else
|
||
|
|
|
||
|
|
LinearSolver::Summary summary;
|
||
|
|
summary.num_iterations = 0;
|
||
|
|
summary.termination_type = LINEAR_SOLVER_SUCCESS;
|
||
|
|
summary.message = "Success.";
|
||
|
|
|
||
|
|
TripletSparseMatrix* tsm =
|
||
|
|
const_cast<TripletSparseMatrix*>(
|
||
|
|
down_cast<const BlockRandomAccessSparseMatrix*>(lhs())->matrix());
|
||
|
|
const int num_rows = tsm->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;
|
||
|
|
cholmod_sparse* cholmod_lhs = NULL;
|
||
|
|
if (options().use_postordering) {
|
||
|
|
// If we are going to do a full symbolic analysis of the schur
|
||
|
|
// complement matrix from scratch and not rely on the
|
||
|
|
// pre-ordering, then the fastest path in cholmod_factorize is the
|
||
|
|
// one corresponding to upper triangular matrices.
|
||
|
|
|
||
|
|
// Create a upper triangular symmetric matrix.
|
||
|
|
cholmod_lhs = ss_.CreateSparseMatrix(tsm);
|
||
|
|
cholmod_lhs->stype = 1;
|
||
|
|
|
||
|
|
if (factor_ == NULL) {
|
||
|
|
factor_ = ss_.BlockAnalyzeCholesky(cholmod_lhs,
|
||
|
|
blocks_,
|
||
|
|
blocks_,
|
||
|
|
&summary.message);
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
// If we are going to use the natural ordering (i.e. rely on the
|
||
|
|
// pre-ordering computed by solver_impl.cc), then the fastest
|
||
|
|
// path in cholmod_factorize is the one corresponding to lower
|
||
|
|
// triangular matrices.
|
||
|
|
|
||
|
|
// Create a upper triangular symmetric matrix.
|
||
|
|
cholmod_lhs = ss_.CreateSparseMatrixTranspose(tsm);
|
||
|
|
cholmod_lhs->stype = -1;
|
||
|
|
|
||
|
|
if (factor_ == NULL) {
|
||
|
|
factor_ = ss_.AnalyzeCholeskyWithNaturalOrdering(cholmod_lhs,
|
||
|
|
&summary.message);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if (factor_ == NULL) {
|
||
|
|
ss_.Free(cholmod_lhs);
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
|
||
|
|
// No need to set message as it has already been set by the
|
||
|
|
// symbolic analysis routines above.
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
summary.termination_type =
|
||
|
|
ss_.Cholesky(cholmod_lhs, factor_, &summary.message);
|
||
|
|
|
||
|
|
ss_.Free(cholmod_lhs);
|
||
|
|
|
||
|
|
if (summary.termination_type != LINEAR_SOLVER_SUCCESS) {
|
||
|
|
// No need to set message as it has already been set by the
|
||
|
|
// numeric factorization routine above.
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
cholmod_dense* cholmod_rhs =
|
||
|
|
ss_.CreateDenseVector(const_cast<double*>(rhs()), num_rows, num_rows);
|
||
|
|
cholmod_dense* cholmod_solution = ss_.Solve(factor_,
|
||
|
|
cholmod_rhs,
|
||
|
|
&summary.message);
|
||
|
|
ss_.Free(cholmod_rhs);
|
||
|
|
|
||
|
|
if (cholmod_solution == NULL) {
|
||
|
|
summary.message =
|
||
|
|
"SuiteSparse failure. Unable to perform triangular solve.";
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FAILURE;
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
VectorRef(solution, num_rows)
|
||
|
|
= VectorRef(static_cast<double*>(cholmod_solution->x), num_rows);
|
||
|
|
ss_.Free(cholmod_solution);
|
||
|
|
return summary;
|
||
|
|
#endif // CERES_NO_SUITESPARSE
|
||
|
|
}
|
||
|
|
|
||
|
|
// Solve the system Sx = r, assuming that the matrix S is stored in a
|
||
|
|
// BlockRandomAccessSparseMatrix. The linear system is solved using
|
||
|
|
// CXSparse's sparse cholesky factorization routines.
|
||
|
|
LinearSolver::Summary
|
||
|
|
SparseSchurComplementSolver::SolveReducedLinearSystemUsingCXSparse(
|
||
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
||
|
|
double* solution) {
|
||
|
|
#ifdef CERES_NO_CXSPARSE
|
||
|
|
|
||
|
|
LinearSolver::Summary summary;
|
||
|
|
summary.num_iterations = 0;
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
|
||
|
|
summary.message = "Ceres was not built with CXSparse support. "
|
||
|
|
"Therefore, SPARSE_SCHUR cannot be used with CX_SPARSE";
|
||
|
|
return summary;
|
||
|
|
|
||
|
|
#else
|
||
|
|
|
||
|
|
LinearSolver::Summary summary;
|
||
|
|
summary.num_iterations = 0;
|
||
|
|
summary.termination_type = LINEAR_SOLVER_SUCCESS;
|
||
|
|
summary.message = "Success.";
|
||
|
|
|
||
|
|
// Extract the TripletSparseMatrix that is used for actually storing S.
|
||
|
|
TripletSparseMatrix* tsm =
|
||
|
|
const_cast<TripletSparseMatrix*>(
|
||
|
|
down_cast<const BlockRandomAccessSparseMatrix*>(lhs())->matrix());
|
||
|
|
const int num_rows = tsm->num_rows();
|
||
|
|
|
||
|
|
// The case where there are no f blocks, and the system is block
|
||
|
|
// diagonal.
|
||
|
|
if (num_rows == 0) {
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
cs_di* lhs = CHECK_NOTNULL(cxsparse_.CreateSparseMatrix(tsm));
|
||
|
|
VectorRef(solution, num_rows) = ConstVectorRef(rhs(), num_rows);
|
||
|
|
|
||
|
|
// Compute symbolic factorization if not available.
|
||
|
|
if (cxsparse_factor_ == NULL) {
|
||
|
|
cxsparse_factor_ = cxsparse_.BlockAnalyzeCholesky(lhs, blocks_, blocks_);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (cxsparse_factor_ == NULL) {
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
|
||
|
|
summary.message =
|
||
|
|
"CXSparse failure. Unable to find symbolic factorization.";
|
||
|
|
} else if (!cxsparse_.SolveCholesky(lhs, cxsparse_factor_, solution)) {
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FAILURE;
|
||
|
|
summary.message = "CXSparse::SolveCholesky failed.";
|
||
|
|
}
|
||
|
|
|
||
|
|
cxsparse_.Free(lhs);
|
||
|
|
return summary;
|
||
|
|
#endif // CERES_NO_CXPARSE
|
||
|
|
}
|
||
|
|
|
||
|
|
// Solve the system Sx = r, assuming that the matrix S is stored in a
|
||
|
|
// BlockRandomAccessSparseMatrix. The linear system is solved using
|
||
|
|
// Eigen's sparse cholesky factorization routines.
|
||
|
|
LinearSolver::Summary
|
||
|
|
SparseSchurComplementSolver::SolveReducedLinearSystemUsingEigen(
|
||
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
||
|
|
double* solution) {
|
||
|
|
#ifndef CERES_USE_EIGEN_SPARSE
|
||
|
|
|
||
|
|
LinearSolver::Summary summary;
|
||
|
|
summary.num_iterations = 0;
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
|
||
|
|
summary.message =
|
||
|
|
"SPARSE_SCHUR cannot be used with EIGEN_SPARSE. "
|
||
|
|
"Ceres was not built with support for "
|
||
|
|
"Eigen's SimplicialLDLT decomposition. "
|
||
|
|
"This requires enabling building with -DEIGENSPARSE=ON.";
|
||
|
|
return summary;
|
||
|
|
|
||
|
|
#else
|
||
|
|
EventLogger event_logger("SchurComplementSolver::EigenSolve");
|
||
|
|
LinearSolver::Summary summary;
|
||
|
|
summary.num_iterations = 0;
|
||
|
|
summary.termination_type = LINEAR_SOLVER_SUCCESS;
|
||
|
|
summary.message = "Success.";
|
||
|
|
|
||
|
|
// Extract the TripletSparseMatrix that is used for actually storing S.
|
||
|
|
TripletSparseMatrix* tsm =
|
||
|
|
const_cast<TripletSparseMatrix*>(
|
||
|
|
down_cast<const BlockRandomAccessSparseMatrix*>(lhs())->matrix());
|
||
|
|
const int num_rows = tsm->num_rows();
|
||
|
|
|
||
|
|
// The case where there are no f blocks, and the system is block
|
||
|
|
// diagonal.
|
||
|
|
if (num_rows == 0) {
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
// This is an upper triangular matrix.
|
||
|
|
CompressedRowSparseMatrix crsm(*tsm);
|
||
|
|
// Map this to a column major, lower triangular matrix.
|
||
|
|
Eigen::MappedSparseMatrix<double, Eigen::ColMajor> eigen_lhs(
|
||
|
|
crsm.num_rows(),
|
||
|
|
crsm.num_rows(),
|
||
|
|
crsm.num_nonzeros(),
|
||
|
|
crsm.mutable_rows(),
|
||
|
|
crsm.mutable_cols(),
|
||
|
|
crsm.mutable_values());
|
||
|
|
event_logger.AddEvent("ToCompressedRowSparseMatrix");
|
||
|
|
|
||
|
|
// Compute symbolic factorization if one does not exist.
|
||
|
|
if (simplicial_ldlt_.get() == NULL) {
|
||
|
|
simplicial_ldlt_.reset(new SimplicialLDLT);
|
||
|
|
// This ordering is quite bad. The scalar ordering produced by the
|
||
|
|
// AMD algorithm is quite bad and can be an order of magnitude
|
||
|
|
// worse than the one computed using the block version of the
|
||
|
|
// algorithm.
|
||
|
|
simplicial_ldlt_->analyzePattern(eigen_lhs);
|
||
|
|
event_logger.AddEvent("Analysis");
|
||
|
|
if (simplicial_ldlt_->info() != Eigen::Success) {
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
|
||
|
|
summary.message =
|
||
|
|
"Eigen failure. Unable to find symbolic factorization.";
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
simplicial_ldlt_->factorize(eigen_lhs);
|
||
|
|
event_logger.AddEvent("Factorize");
|
||
|
|
if (simplicial_ldlt_->info() != Eigen::Success) {
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FAILURE;
|
||
|
|
summary.message = "Eigen failure. Unable to find numeric factoriztion.";
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
VectorRef(solution, num_rows) =
|
||
|
|
simplicial_ldlt_->solve(ConstVectorRef(rhs(), num_rows));
|
||
|
|
event_logger.AddEvent("Solve");
|
||
|
|
if (simplicial_ldlt_->info() != Eigen::Success) {
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FAILURE;
|
||
|
|
summary.message = "Eigen failure. Unable to do triangular solve.";
|
||
|
|
}
|
||
|
|
|
||
|
|
return summary;
|
||
|
|
#endif // CERES_USE_EIGEN_SPARSE
|
||
|
|
}
|
||
|
|
|
||
|
|
LinearSolver::Summary
|
||
|
|
SparseSchurComplementSolver::SolveReducedLinearSystemUsingConjugateGradients(
|
||
|
|
const LinearSolver::PerSolveOptions& per_solve_options,
|
||
|
|
double* solution) {
|
||
|
|
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 = LINEAR_SOLVER_SUCCESS;
|
||
|
|
summary.message = "Success.";
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Only SCHUR_JACOBI is supported over here right now.
|
||
|
|
CHECK_EQ(options().preconditioner_type, SCHUR_JACOBI);
|
||
|
|
|
||
|
|
if (preconditioner_.get() == NULL) {
|
||
|
|
preconditioner_.reset(new BlockRandomAccessDiagonalMatrix(blocks_));
|
||
|
|
}
|
||
|
|
|
||
|
|
BlockRandomAccessSparseMatrix* sc =
|
||
|
|
down_cast<BlockRandomAccessSparseMatrix*>(
|
||
|
|
const_cast<BlockRandomAccessMatrix*>(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];
|
||
|
|
|
||
|
|
int sc_r, sc_c, sc_row_stride, sc_col_stride;
|
||
|
|
CellInfo* sc_cell_info =
|
||
|
|
CHECK_NOTNULL(sc->GetCell(i, i,
|
||
|
|
&sc_r, &sc_c,
|
||
|
|
&sc_row_stride, &sc_col_stride));
|
||
|
|
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 = CHECK_NOTNULL(
|
||
|
|
preconditioner_->GetCell(i, i,
|
||
|
|
&pre_r, &pre_c,
|
||
|
|
&pre_row_stride, &pre_col_stride));
|
||
|
|
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();
|
||
|
|
|
||
|
|
scoped_ptr<LinearOperator> lhs_adapter(
|
||
|
|
new BlockRandomAccessSparseMatrixAdapter(*sc));
|
||
|
|
scoped_ptr<LinearOperator> preconditioner_adapter(
|
||
|
|
new BlockRandomAccessDiagonalMatrixAdapter(*preconditioner_));
|
||
|
|
|
||
|
|
|
||
|
|
LinearSolver::Options cg_options;
|
||
|
|
cg_options.min_num_iterations = options().min_num_iterations;
|
||
|
|
cg_options.max_num_iterations = options().max_num_iterations;
|
||
|
|
ConjugateGradientsSolver cg_solver(cg_options);
|
||
|
|
|
||
|
|
LinearSolver::PerSolveOptions cg_per_solve_options;
|
||
|
|
cg_per_solve_options.r_tolerance = per_solve_options.r_tolerance;
|
||
|
|
cg_per_solve_options.q_tolerance = per_solve_options.q_tolerance;
|
||
|
|
cg_per_solve_options.preconditioner = preconditioner_adapter.get();
|
||
|
|
|
||
|
|
return cg_solver.Solve(lhs_adapter.get(),
|
||
|
|
rhs(),
|
||
|
|
cg_per_solve_options,
|
||
|
|
solution);
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace internal
|
||
|
|
} // namespace ceres
|