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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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// 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
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// 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 <utility>
#include "Eigen/SparseCore"
#include "absl/log/log.h"
#include "ceres/compressed_row_sparse_matrix.h"
#include "ceres/internal/config.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"
#include "cuda_sparse_cholesky.h"
#ifdef CERES_USE_EIGEN_SPARSE
#include "Eigen/SparseCholesky"
#endif
namespace ceres::internal {
DynamicSparseNormalCholeskySolver::DynamicSparseNormalCholeskySolver(
LinearSolver::Options options)
: options_(std::move(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->LeftMultiplyAndAccumulate(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 = CompressedRowSparseMatrix::CreateBlockDiagonalMatrix(
per_solve_options.D, A->col_blocks());
} else {
regularizer = std::make_unique<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 EIGEN_SPARSE:
summary = SolveImplUsingEigen(A, x);
break;
case CUDA_SPARSE:
summary = SolveImplUsingCuda(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 = LinearSolverTerminationType::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::Map<Eigen::SparseMatrix<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 = LinearSolverTerminationType::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 = LinearSolverTerminationType::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 = LinearSolverTerminationType::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 = LinearSolverTerminationType::FAILURE;
summary.message = "Eigen failure. Unable to do triangular solve.";
return summary;
}
return summary;
#endif // CERES_USE_EIGEN_SPARSE
}
LinearSolver::Summary
DynamicSparseNormalCholeskySolver::SolveImplUsingSuiteSparse(
CompressedRowSparseMatrix* A, double* rhs_and_solution) {
#ifdef CERES_NO_SUITESPARSE
(void)A;
(void)rhs_and_solution;
LinearSolver::Summary summary;
summary.num_iterations = 0;
summary.termination_type = LinearSolverTerminationType::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 = LinearSolverTerminationType::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, options_.ordering_type, &summary.message);
event_logger.AddEvent("Analysis");
if (factor == nullptr) {
summary.termination_type = LinearSolverTerminationType::FATAL_ERROR;
return summary;
}
summary.termination_type = ss.Cholesky(&lhs, factor, &summary.message);
if (summary.termination_type == LinearSolverTerminationType::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 = LinearSolverTerminationType::FAILURE;
}
}
ss.Free(factor);
event_logger.AddEvent("Teardown");
return summary;
#endif
}
LinearSolver::Summary DynamicSparseNormalCholeskySolver::SolveImplUsingCuda(
CompressedRowSparseMatrix* A, double* rhs_and_solution) {
#ifdef CERES_NO_CUDSS
(void)A;
(void)rhs_and_solution;
LinearSolver::Summary summary;
summary.num_iterations = 0;
summary.termination_type = LinearSolverTerminationType::FATAL_ERROR;
summary.message =
"SPARSE_NORMAL_CHOLESKY cannot be used with CUDA_SPARSE "
"because Ceres was not built with support for cuDSS. "
"This requires enabling building with -DUSE_CUDA=ON and ensuring that "
"cuDSS is found.";
return summary;
#else
EventLogger event_logger("DynamicSparseNormalCholeskySolver::cuDSS::Solve");
// TODO: Consider computing A^T*A on device via cuSPARSE
// https://github.com/ceres-solver/ceres-solver/issues/1066
Eigen::Map<Eigen::SparseMatrix<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, Eigen::RowMajor> ata =
(a.transpose() * a).triangularView<Eigen::Lower>();
CompressedRowSparseMatrix lhs(ata.rows(), ata.cols(), ata.nonZeros());
std::copy_n(ata.outerIndexPtr(), lhs.num_rows() + 1, lhs.mutable_rows());
std::copy_n(ata.innerIndexPtr(), lhs.num_nonzeros(), lhs.mutable_cols());
std::copy_n(ata.valuePtr(), lhs.num_nonzeros(), lhs.mutable_values());
lhs.set_storage_type(
CompressedRowSparseMatrix::StorageType::LOWER_TRIANGULAR);
event_logger.AddEvent("Compute A^T * A");
auto sparse_cholesky = CudaSparseCholesky<double>::Create(
options_.context, options_.ordering_type);
LinearSolver::Summary summary;
summary.num_iterations = 1;
summary.termination_type = sparse_cholesky->Factorize(&lhs, &summary.message);
if (summary.termination_type != LinearSolverTerminationType::SUCCESS) {
return summary;
}
event_logger.AddEvent("Analyze");
const Vector rhs = ConstVectorRef(rhs_and_solution, A->num_cols());
summary.termination_type =
sparse_cholesky->Solve(rhs.data(), rhs_and_solution, &summary.message);
event_logger.AddEvent("Solve");
return summary;
#endif
}
} // namespace ceres::internal