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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 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/sparse_normal_cholesky_solver.h"
#include <algorithm>
#include <cstring>
#include <ctime>
#include "ceres/compressed_row_sparse_matrix.h"
#include "ceres/cxsparse.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.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"
#include "Eigen/SparseCore"
#ifdef CERES_USE_EIGEN_SPARSE
#include "Eigen/SparseCholesky"
#endif
namespace ceres {
namespace internal {
namespace {
#ifdef CERES_USE_EIGEN_SPARSE
// A templated factorized and solve function, which allows us to use
// the same code independent of whether a AMD or a Natural ordering is
// used.
template <typename SimplicialCholeskySolver, typename SparseMatrixType>
LinearSolver::Summary SimplicialLDLTSolve(
const SparseMatrixType& lhs,
const bool do_symbolic_analysis,
SimplicialCholeskySolver* solver,
double* rhs_and_solution,
EventLogger* event_logger) {
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
if (do_symbolic_analysis) {
solver->analyzePattern(lhs);
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
#ifndef CERES_NO_CXSPARSE
LinearSolver::Summary ComputeNormalEquationsAndSolveUsingCXSparse(
CompressedRowSparseMatrix* A,
double * rhs_and_solution,
EventLogger* event_logger) {
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");
cs_dis* factor = cxsparse.AnalyzeCholesky(lhs);
event_logger->AddEvent("Analysis");
if (factor == NULL) {
summary.termination_type = LINEAR_SOLVER_FATAL_ERROR;
summary.message = "CXSparse::AnalyzeCholesky failed.";
} else if (!cxsparse.SolveCholesky(lhs, factor, rhs_and_solution)) {
summary.termination_type = LINEAR_SOLVER_FAILURE;
summary.message = "CXSparse::SolveCholesky failed.";
}
event_logger->AddEvent("Solve");
cxsparse.Free(lhs);
cxsparse.Free(factor);
event_logger->AddEvent("TearDown");
return summary;
}
#endif // CERES_NO_CXSPARSE
} // namespace
SparseNormalCholeskySolver::SparseNormalCholeskySolver(
const LinearSolver::Options& options)
: factor_(NULL),
cxsparse_factor_(NULL),
options_(options) {
}
void SparseNormalCholeskySolver::FreeFactorization() {
if (factor_ != NULL) {
ss_.Free(factor_);
factor_ = NULL;
}
if (cxsparse_factor_ != NULL) {
cxsparse_.Free(cxsparse_factor_);
cxsparse_factor_ = NULL;
}
}
SparseNormalCholeskySolver::~SparseNormalCholeskySolver() {
FreeFactorization();
}
LinearSolver::Summary SparseNormalCholeskySolver::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 != NULL) {
// Temporarily append a diagonal block to the A matrix, but undo
// it before returning the matrix to the user.
scoped_ptr<CompressedRowSparseMatrix> regularizer;
if (A->col_blocks().size() > 0) {
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) << "Unknown sparse linear algebra library : "
<< options_.sparse_linear_algebra_library_type;
}
if (per_solve_options.D != NULL) {
A->DeleteRows(num_cols);
}
return summary;
}
LinearSolver::Summary SparseNormalCholeskySolver::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("SparseNormalCholeskySolver::Eigen::Solve");
// 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 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.
if (options_.dynamic_sparsity) {
// In the case where the problem has dynamic sparsity, it is not
// worth using the ComputeOuterProduct routine, as the setup cost
// is not amortized over multiple calls to 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;
return SimplicialLDLTSolve(lhs,
true,
&solver,
rhs_and_solution,
&event_logger);
}
if (outer_product_.get() == NULL) {
outer_product_.reset(
CompressedRowSparseMatrix::CreateOuterProductMatrixAndProgram(
*A, &pattern_));
}
CompressedRowSparseMatrix::ComputeOuterProduct(
*A, pattern_, outer_product_.get());
// Map to an upper triangular column major matrix.
//
// outer_product_ is a compressed row sparse matrix and in lower
// triangular form, when mapped to a compressed column sparse
// matrix, it becomes an upper triangular matrix.
Eigen::MappedSparseMatrix<double, Eigen::ColMajor> lhs(
outer_product_->num_rows(),
outer_product_->num_rows(),
outer_product_->num_nonzeros(),
outer_product_->mutable_rows(),
outer_product_->mutable_cols(),
outer_product_->mutable_values());
bool do_symbolic_analysis = false;
// If using post ordering or an old version of Eigen, we cannot
// depend on a preordered jacobian, so we work with a SimplicialLDLT
// decomposition with AMD ordering.
if (options_.use_postordering ||
!EIGEN_VERSION_AT_LEAST(3, 2, 2)) {
if (amd_ldlt_.get() == NULL) {
amd_ldlt_.reset(new SimplicialLDLTWithAMDOrdering);
do_symbolic_analysis = true;
}
return SimplicialLDLTSolve(lhs,
do_symbolic_analysis,
amd_ldlt_.get(),
rhs_and_solution,
&event_logger);
}
#if EIGEN_VERSION_AT_LEAST(3,2,2)
// The common case
if (natural_ldlt_.get() == NULL) {
natural_ldlt_.reset(new SimplicialLDLTWithNaturalOrdering);
do_symbolic_analysis = true;
}
return SimplicialLDLTSolve(lhs,
do_symbolic_analysis,
natural_ldlt_.get(),
rhs_and_solution,
&event_logger);
#endif
#endif // EIGEN_USE_EIGEN_SPARSE
}
LinearSolver::Summary SparseNormalCholeskySolver::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("SparseNormalCholeskySolver::CXSparse::Solve");
if (options_.dynamic_sparsity) {
return ComputeNormalEquationsAndSolveUsingCXSparse(A,
rhs_and_solution,
&event_logger);
}
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
// 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 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.
if (outer_product_.get() == NULL) {
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