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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2017 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/dynamic_sparse_normal_cholesky_solver.h"
#include <algorithm>
#include <cstring>
#include <ctime>
#include <memory>
#include <sstream>
#include "Eigen/SparseCore"
#include "ceres/compressed_row_sparse_matrix.h"
#include "ceres/cxsparse.h"
#include "ceres/internal/eigen.h"
#include "ceres/linear_solver.h"
#include "ceres/suitesparse.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "ceres/wall_time.h"
#ifdef CERES_USE_EIGEN_SPARSE
#include "Eigen/SparseCholesky"
#endif
namespace ceres {
namespace internal {
DynamicSparseNormalCholeskySolver::DynamicSparseNormalCholeskySolver(
const LinearSolver::Options& options)
: options_(options) {}
LinearSolver::Summary DynamicSparseNormalCholeskySolver::SolveImpl(
CompressedRowSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
const int num_cols = A->num_cols();
VectorRef(x, num_cols).setZero();
A->LeftMultiply(b, x);
if (per_solve_options.D != nullptr) {
// Temporarily append a diagonal block to the A matrix, but undo
// it before returning the matrix to the user.
std::unique_ptr<CompressedRowSparseMatrix> regularizer;
if (!A->col_blocks().empty()) {
regularizer.reset(CompressedRowSparseMatrix::CreateBlockDiagonalMatrix(
per_solve_options.D, A->col_blocks()));
} else {
regularizer.reset(
new CompressedRowSparseMatrix(per_solve_options.D, num_cols));
}
A->AppendRows(*regularizer);
}
LinearSolver::Summary summary;
switch (options_.sparse_linear_algebra_library_type) {
case SUITE_SPARSE:
summary = SolveImplUsingSuiteSparse(A, x);
break;
case CX_SPARSE:
summary = SolveImplUsingCXSparse(A, x);
break;
case EIGEN_SPARSE:
summary = SolveImplUsingEigen(A, x);
break;
default:
LOG(FATAL) << "Unsupported sparse linear algebra library for "
<< "dynamic sparsity: "
<< SparseLinearAlgebraLibraryTypeToString(
options_.sparse_linear_algebra_library_type);
}
if (per_solve_options.D != nullptr) {
A->DeleteRows(num_cols);
}
return summary;
}
LinearSolver::Summary DynamicSparseNormalCholeskySolver::SolveImplUsingEigen(
CompressedRowSparseMatrix* A, double* rhs_and_solution) {
#ifndef CERES_USE_EIGEN_SPARSE
LinearSolver::Summary summary;
summary.num_iterations = 0;
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
summary.message =
"SPARSE_NORMAL_CHOLESKY cannot be used with EIGEN_SPARSE "
"because Ceres was not built with support for "
"Eigen's SimplicialLDLT decomposition. "
"This requires enabling building with -DEIGENSPARSE=ON.";
return summary;
#else
EventLogger event_logger("DynamicSparseNormalCholeskySolver::Eigen::Solve");
Eigen::MappedSparseMatrix<double, Eigen::RowMajor> a(A->num_rows(),
A->num_cols(),
A->num_nonzeros(),
A->mutable_rows(),
A->mutable_cols(),
A->mutable_values());
Eigen::SparseMatrix<double> lhs = a.transpose() * a;
Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> solver;
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
solver.analyzePattern(lhs);
if (VLOG_IS_ON(2)) {
std::stringstream ss;
solver.dumpMemory(ss);
VLOG(2) << "Symbolic Analysis\n" << ss.str();
}
event_logger.AddEvent("Analyze");
if (solver.info() != Eigen::Success) {
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
summary.message = "Eigen failure. Unable to find symbolic factorization.";
return summary;
}
solver.factorize(lhs);
event_logger.AddEvent("Factorize");
if (solver.info() != Eigen::Success) {
summary.termination_type = LINEAR_SOLVER_FAILURE;
summary.message = "Eigen failure. Unable to find numeric factorization.";
return summary;
}
const Vector rhs = VectorRef(rhs_and_solution, lhs.cols());
VectorRef(rhs_and_solution, lhs.cols()) = solver.solve(rhs);
event_logger.AddEvent("Solve");
if (solver.info() != Eigen::Success) {
summary.termination_type = LINEAR_SOLVER_FAILURE;
summary.message = "Eigen failure. Unable to do triangular solve.";
return summary;
}
return summary;
#endif // CERES_USE_EIGEN_SPARSE
}
LinearSolver::Summary DynamicSparseNormalCholeskySolver::SolveImplUsingCXSparse(
CompressedRowSparseMatrix* A, double* rhs_and_solution) {
#ifdef CERES_NO_CXSPARSE
LinearSolver::Summary summary;
summary.num_iterations = 0;
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
summary.message =
"SPARSE_NORMAL_CHOLESKY cannot be used with CX_SPARSE "
"because Ceres was not built with support for CXSparse. "
"This requires enabling building with -DCXSPARSE=ON.";
return summary;
#else
EventLogger event_logger(
"DynamicSparseNormalCholeskySolver::CXSparse::Solve");
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
CXSparse cxsparse;
// Wrap the augmented Jacobian in a compressed sparse column matrix.
cs_di a_transpose = cxsparse.CreateSparseMatrixTransposeView(A);
// Compute the normal equations. J'J delta = J'f and solve them
// using a sparse Cholesky factorization. Notice that when compared
// to SuiteSparse we have to explicitly compute the transpose of Jt,
// and then the normal equations before they can be
// factorized. CHOLMOD/SuiteSparse on the other hand can just work
// off of Jt to compute the Cholesky factorization of the normal
// equations.
cs_di* a = cxsparse.TransposeMatrix(&a_transpose);
cs_di* lhs = cxsparse.MatrixMatrixMultiply(&a_transpose, a);
cxsparse.Free(a);
event_logger.AddEvent("NormalEquations");
if (!cxsparse.SolveCholesky(lhs, rhs_and_solution)) {
summary.termination_type = LINEAR_SOLVER_FAILURE;
summary.message = "CXSparse::SolveCholesky failed";
}
event_logger.AddEvent("Solve");
cxsparse.Free(lhs);
event_logger.AddEvent("TearDown");
return summary;
#endif
}
LinearSolver::Summary
DynamicSparseNormalCholeskySolver::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(
"DynamicSparseNormalCholeskySolver::SuiteSparse::Solve");
LinearSolver::Summary summary;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.num_iterations = 1;
summary.message = "Success.";
SuiteSparse ss;
const int num_cols = A->num_cols();
cholmod_sparse lhs = ss.CreateSparseMatrixTransposeView(A);
event_logger.AddEvent("Setup");
cholmod_factor* factor = ss.AnalyzeCholesky(&lhs, &summary.message);
event_logger.AddEvent("Analysis");
if (factor == nullptr) {
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
return summary;
}
summary.termination_type = ss.Cholesky(&lhs, factor, &summary.message);
if (summary.termination_type == LINEAR_SOLVER_SUCCESS) {
cholmod_dense cholmod_rhs =
ss.CreateDenseVectorView(rhs_and_solution, num_cols);
cholmod_dense* solution = ss.Solve(factor, &cholmod_rhs, &summary.message);
event_logger.AddEvent("Solve");
if (solution != nullptr) {
memcpy(
rhs_and_solution, solution->x, num_cols * sizeof(*rhs_and_solution));
ss.Free(solution);
} else {
summary.termination_type = LINEAR_SOLVER_FAILURE;
}
}
ss.Free(factor);
event_logger.AddEvent("Teardown");
return summary;
#endif
}
} // namespace internal
} // namespace ceres