487 lines
16 KiB
C++
487 lines
16 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/sparse_normal_cholesky_solver.h"
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#include <algorithm>
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#include <cstring>
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#include <ctime>
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#include "ceres/compressed_row_sparse_matrix.h"
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#include "ceres/cxsparse.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/linear_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/SparseCore"
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#ifdef CERES_USE_EIGEN_SPARSE
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#include "Eigen/SparseCholesky"
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#endif
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namespace ceres {
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namespace internal {
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namespace {
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#ifdef CERES_USE_EIGEN_SPARSE
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// A templated factorized and solve function, which allows us to use
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// the same code independent of whether a AMD or a Natural ordering is
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// used.
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template <typename SimplicialCholeskySolver, typename SparseMatrixType>
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LinearSolver::Summary SimplicialLDLTSolve(
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const SparseMatrixType& lhs,
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const bool do_symbolic_analysis,
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SimplicialCholeskySolver* solver,
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double* rhs_and_solution,
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EventLogger* event_logger) {
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LinearSolver::Summary summary;
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summary.num_iterations = 1;
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summary.termination_type = LINEAR_SOLVER_SUCCESS;
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summary.message = "Success.";
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if (do_symbolic_analysis) {
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solver->analyzePattern(lhs);
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event_logger->AddEvent("Analyze");
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if (solver->info() != Eigen::Success) {
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summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
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summary.message =
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"Eigen failure. Unable to find symbolic factorization.";
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return summary;
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}
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}
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solver->factorize(lhs);
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event_logger->AddEvent("Factorize");
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if (solver->info() != Eigen::Success) {
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summary.termination_type = LINEAR_SOLVER_FAILURE;
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summary.message = "Eigen failure. Unable to find numeric factorization.";
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return summary;
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}
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const Vector rhs = VectorRef(rhs_and_solution, lhs.cols());
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VectorRef(rhs_and_solution, lhs.cols()) = solver->solve(rhs);
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event_logger->AddEvent("Solve");
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if (solver->info() != Eigen::Success) {
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summary.termination_type = LINEAR_SOLVER_FAILURE;
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summary.message = "Eigen failure. Unable to do triangular solve.";
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return summary;
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}
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return summary;
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}
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#endif // CERES_USE_EIGEN_SPARSE
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#ifndef CERES_NO_CXSPARSE
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LinearSolver::Summary ComputeNormalEquationsAndSolveUsingCXSparse(
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CompressedRowSparseMatrix* A,
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double * rhs_and_solution,
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EventLogger* event_logger) {
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LinearSolver::Summary summary;
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summary.num_iterations = 1;
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summary.termination_type = LINEAR_SOLVER_SUCCESS;
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summary.message = "Success.";
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CXSparse cxsparse;
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// Wrap the augmented Jacobian in a compressed sparse column matrix.
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cs_di a_transpose = cxsparse.CreateSparseMatrixTransposeView(A);
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// Compute the normal equations. J'J delta = J'f and solve them
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// using a sparse Cholesky factorization. Notice that when compared
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// to SuiteSparse we have to explicitly compute the transpose of Jt,
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// and then the normal equations before they can be
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// factorized. CHOLMOD/SuiteSparse on the other hand can just work
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// off of Jt to compute the Cholesky factorization of the normal
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// equations.
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cs_di* a = cxsparse.TransposeMatrix(&a_transpose);
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cs_di* lhs = cxsparse.MatrixMatrixMultiply(&a_transpose, a);
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cxsparse.Free(a);
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event_logger->AddEvent("NormalEquations");
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cs_dis* factor = cxsparse.AnalyzeCholesky(lhs);
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event_logger->AddEvent("Analysis");
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if (factor == NULL) {
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summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
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summary.message = "CXSparse::AnalyzeCholesky failed.";
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} else if (!cxsparse.SolveCholesky(lhs, factor, rhs_and_solution)) {
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summary.termination_type = LINEAR_SOLVER_FAILURE;
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summary.message = "CXSparse::SolveCholesky failed.";
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}
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event_logger->AddEvent("Solve");
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cxsparse.Free(lhs);
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cxsparse.Free(factor);
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event_logger->AddEvent("TearDown");
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return summary;
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}
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#endif // CERES_NO_CXSPARSE
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} // namespace
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SparseNormalCholeskySolver::SparseNormalCholeskySolver(
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const LinearSolver::Options& options)
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: factor_(NULL),
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cxsparse_factor_(NULL),
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options_(options) {
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}
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void SparseNormalCholeskySolver::FreeFactorization() {
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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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SparseNormalCholeskySolver::~SparseNormalCholeskySolver() {
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FreeFactorization();
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}
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LinearSolver::Summary SparseNormalCholeskySolver::SolveImpl(
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CompressedRowSparseMatrix* 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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const int num_cols = A->num_cols();
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VectorRef(x, num_cols).setZero();
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A->LeftMultiply(b, x);
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if (per_solve_options.D != NULL) {
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// Temporarily append a diagonal block to the A matrix, but undo
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// it before returning the matrix to the user.
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scoped_ptr<CompressedRowSparseMatrix> regularizer;
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if (A->col_blocks().size() > 0) {
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regularizer.reset(CompressedRowSparseMatrix::CreateBlockDiagonalMatrix(
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per_solve_options.D, A->col_blocks()));
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} else {
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regularizer.reset(new CompressedRowSparseMatrix(
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per_solve_options.D, num_cols));
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}
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A->AppendRows(*regularizer);
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}
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LinearSolver::Summary summary;
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switch (options_.sparse_linear_algebra_library_type) {
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case SUITE_SPARSE:
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summary = SolveImplUsingSuiteSparse(A, x);
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break;
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case CX_SPARSE:
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summary = SolveImplUsingCXSparse(A, x);
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break;
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case EIGEN_SPARSE:
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summary = SolveImplUsingEigen(A, x);
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break;
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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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if (per_solve_options.D != NULL) {
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A->DeleteRows(num_cols);
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}
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return summary;
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}
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LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingEigen(
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CompressedRowSparseMatrix* A,
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double * rhs_and_solution) {
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#ifndef CERES_USE_EIGEN_SPARSE
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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 =
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"SPARSE_NORMAL_CHOLESKY cannot be used with EIGEN_SPARSE "
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"because Ceres was not built with support for "
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"Eigen's SimplicialLDLT decomposition. "
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"This requires enabling building with -DEIGENSPARSE=ON.";
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return summary;
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#else
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EventLogger event_logger("SparseNormalCholeskySolver::Eigen::Solve");
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// Compute the normal equations. J'J delta = J'f and solve them
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// using a sparse Cholesky factorization. Notice that when compared
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// to SuiteSparse we have to explicitly compute the normal equations
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// before they can be factorized. CHOLMOD/SuiteSparse on the other
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// hand can just work off of Jt to compute the Cholesky
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// factorization of the normal equations.
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if (options_.dynamic_sparsity) {
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// In the case where the problem has dynamic sparsity, it is not
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// worth using the ComputeOuterProduct routine, as the setup cost
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// is not amortized over multiple calls to Solve.
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Eigen::MappedSparseMatrix<double, Eigen::RowMajor> a(
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A->num_rows(),
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A->num_cols(),
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A->num_nonzeros(),
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A->mutable_rows(),
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A->mutable_cols(),
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A->mutable_values());
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Eigen::SparseMatrix<double> lhs = a.transpose() * a;
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Eigen::SimplicialLDLT<Eigen::SparseMatrix<double> > solver;
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return SimplicialLDLTSolve(lhs,
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true,
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&solver,
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rhs_and_solution,
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&event_logger);
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}
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if (outer_product_.get() == NULL) {
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outer_product_.reset(
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CompressedRowSparseMatrix::CreateOuterProductMatrixAndProgram(
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*A, &pattern_));
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}
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CompressedRowSparseMatrix::ComputeOuterProduct(
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*A, pattern_, outer_product_.get());
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// Map to an upper triangular column major matrix.
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//
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// outer_product_ is a compressed row sparse matrix and in lower
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// triangular form, when mapped to a compressed column sparse
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// matrix, it becomes an upper triangular matrix.
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Eigen::MappedSparseMatrix<double, Eigen::ColMajor> lhs(
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outer_product_->num_rows(),
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outer_product_->num_rows(),
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outer_product_->num_nonzeros(),
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outer_product_->mutable_rows(),
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outer_product_->mutable_cols(),
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outer_product_->mutable_values());
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bool do_symbolic_analysis = false;
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// If using post ordering or an old version of Eigen, we cannot
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// depend on a preordered jacobian, so we work with a SimplicialLDLT
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// decomposition with AMD ordering.
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if (options_.use_postordering ||
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!EIGEN_VERSION_AT_LEAST(3, 2, 2)) {
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if (amd_ldlt_.get() == NULL) {
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amd_ldlt_.reset(new SimplicialLDLTWithAMDOrdering);
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do_symbolic_analysis = true;
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}
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return SimplicialLDLTSolve(lhs,
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do_symbolic_analysis,
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amd_ldlt_.get(),
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rhs_and_solution,
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&event_logger);
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}
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#if EIGEN_VERSION_AT_LEAST(3,2,2)
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// The common case
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if (natural_ldlt_.get() == NULL) {
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natural_ldlt_.reset(new SimplicialLDLTWithNaturalOrdering);
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do_symbolic_analysis = true;
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}
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return SimplicialLDLTSolve(lhs,
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do_symbolic_analysis,
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natural_ldlt_.get(),
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rhs_and_solution,
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&event_logger);
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#endif
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#endif // EIGEN_USE_EIGEN_SPARSE
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}
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LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingCXSparse(
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CompressedRowSparseMatrix* A,
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double * rhs_and_solution) {
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#ifdef CERES_NO_CXSPARSE
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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 =
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"SPARSE_NORMAL_CHOLESKY cannot be used with CX_SPARSE "
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"because Ceres was not built with support for CXSparse. "
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"This requires enabling building with -DCXSPARSE=ON.";
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return summary;
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#else
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EventLogger event_logger("SparseNormalCholeskySolver::CXSparse::Solve");
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if (options_.dynamic_sparsity) {
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return ComputeNormalEquationsAndSolveUsingCXSparse(A,
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rhs_and_solution,
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&event_logger);
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}
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LinearSolver::Summary summary;
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summary.num_iterations = 1;
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summary.termination_type = LINEAR_SOLVER_SUCCESS;
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summary.message = "Success.";
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// Compute the normal equations. J'J delta = J'f and solve them
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// using a sparse Cholesky factorization. Notice that when compared
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// to SuiteSparse we have to explicitly compute the normal equations
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// before they can be factorized. CHOLMOD/SuiteSparse on the other
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// hand can just work off of Jt to compute the Cholesky
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// factorization of the normal equations.
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if (outer_product_.get() == NULL) {
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|
|
outer_product_.reset(
|
||
|
|
CompressedRowSparseMatrix::CreateOuterProductMatrixAndProgram(
|
||
|
|
*A, &pattern_));
|
||
|
|
}
|
||
|
|
|
||
|
|
CompressedRowSparseMatrix::ComputeOuterProduct(
|
||
|
|
*A, pattern_, outer_product_.get());
|
||
|
|
cs_di lhs =
|
||
|
|
cxsparse_.CreateSparseMatrixTransposeView(outer_product_.get());
|
||
|
|
|
||
|
|
event_logger.AddEvent("Setup");
|
||
|
|
|
||
|
|
// Compute symbolic factorization if not available.
|
||
|
|
if (cxsparse_factor_ == NULL) {
|
||
|
|
if (options_.use_postordering) {
|
||
|
|
cxsparse_factor_ = cxsparse_.BlockAnalyzeCholesky(&lhs,
|
||
|
|
A->col_blocks(),
|
||
|
|
A->col_blocks());
|
||
|
|
} else {
|
||
|
|
cxsparse_factor_ = cxsparse_.AnalyzeCholeskyWithNaturalOrdering(&lhs);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
event_logger.AddEvent("Analysis");
|
||
|
|
|
||
|
|
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_,
|
||
|
|
rhs_and_solution)) {
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FAILURE;
|
||
|
|
summary.message = "CXSparse::SolveCholesky failed.";
|
||
|
|
}
|
||
|
|
event_logger.AddEvent("Solve");
|
||
|
|
|
||
|
|
return summary;
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingSuiteSparse(
|
||
|
|
CompressedRowSparseMatrix* A,
|
||
|
|
double * rhs_and_solution) {
|
||
|
|
#ifdef CERES_NO_SUITESPARSE
|
||
|
|
|
||
|
|
LinearSolver::Summary summary;
|
||
|
|
summary.num_iterations = 0;
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
|
||
|
|
summary.message =
|
||
|
|
"SPARSE_NORMAL_CHOLESKY cannot be used with SUITE_SPARSE "
|
||
|
|
"because Ceres was not built with support for SuiteSparse. "
|
||
|
|
"This requires enabling building with -DSUITESPARSE=ON.";
|
||
|
|
return summary;
|
||
|
|
|
||
|
|
#else
|
||
|
|
|
||
|
|
EventLogger event_logger("SparseNormalCholeskySolver::SuiteSparse::Solve");
|
||
|
|
LinearSolver::Summary summary;
|
||
|
|
summary.termination_type = LINEAR_SOLVER_SUCCESS;
|
||
|
|
summary.num_iterations = 1;
|
||
|
|
summary.message = "Success.";
|
||
|
|
|
||
|
|
const int num_cols = A->num_cols();
|
||
|
|
cholmod_sparse lhs = ss_.CreateSparseMatrixTransposeView(A);
|
||
|
|
event_logger.AddEvent("Setup");
|
||
|
|
|
||
|
|
if (options_.dynamic_sparsity) {
|
||
|
|
FreeFactorization();
|
||
|
|
}
|
||
|
|
|
||
|
|
if (factor_ == NULL) {
|
||
|
|
if (options_.use_postordering) {
|
||
|
|
factor_ = ss_.BlockAnalyzeCholesky(&lhs,
|
||
|
|
A->col_blocks(),
|
||
|
|
A->row_blocks(),
|
||
|
|
&summary.message);
|
||
|
|
} else {
|
||
|
|
if (options_.dynamic_sparsity) {
|
||
|
|
factor_ = ss_.AnalyzeCholesky(&lhs, &summary.message);
|
||
|
|
} else {
|
||
|
|
factor_ = ss_.AnalyzeCholeskyWithNaturalOrdering(&lhs,
|
||
|
|
&summary.message);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
event_logger.AddEvent("Analysis");
|
||
|
|
|
||
|
|
if (factor_ == NULL) {
|
||
|
|
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(&lhs, factor_, &summary.message);
|
||
|
|
if (summary.termination_type != LINEAR_SOLVER_SUCCESS) {
|
||
|
|
return summary;
|
||
|
|
}
|
||
|
|
|
||
|
|
cholmod_dense* rhs = ss_.CreateDenseVector(rhs_and_solution,
|
||
|
|
num_cols,
|
||
|
|
num_cols);
|
||
|
|
cholmod_dense* solution = ss_.Solve(factor_, rhs, &summary.message);
|
||
|
|
event_logger.AddEvent("Solve");
|
||
|
|
|
||
|
|
ss_.Free(rhs);
|
||
|
|
if (solution != NULL) {
|
||
|
|
memcpy(rhs_and_solution, solution->x, num_cols * sizeof(*rhs_and_solution));
|
||
|
|
ss_.Free(solution);
|
||
|
|
} else {
|
||
|
|
// No need to set message as it has already been set by the
|
||
|
|
// numeric factorization routine above.
|
||
|
|
summary.termination_type = LINEAR_SOLVER_FAILURE;
|
||
|
|
}
|
||
|
|
|
||
|
|
event_logger.AddEvent("Teardown");
|
||
|
|
return summary;
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace internal
|
||
|
|
} // namespace ceres
|