internal/ceres/iterative_schur_complement_solver.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/iterative_schur_complement_solver.h"

#include <algorithm>
#include <cstring>
#include <vector>

#include "Eigen/Dense"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/conjugate_gradients_solver.h"
#include "ceres/detect_structure.h"
#include "ceres/implicit_schur_complement.h"
#include "ceres/internal/eigen.h"
#include "ceres/linear_solver.h"
#include "ceres/preconditioner.h"
#include "ceres/schur_jacobi_preconditioner.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "ceres/visibility_based_preconditioner.h"
#include "ceres/wall_time.h"
#include "glog/logging.h"

namespace ceres {
namespace internal {

IterativeSchurComplementSolver::IterativeSchurComplementSolver(
    const LinearSolver::Options& options)
    : options_(options) {
}

IterativeSchurComplementSolver::~IterativeSchurComplementSolver() {}

LinearSolver::Summary IterativeSchurComplementSolver::SolveImpl(
    BlockSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double* x) {
  EventLogger event_logger("IterativeSchurComplementSolver::Solve");

  CHECK_NOTNULL(A->block_structure());
  const int num_eliminate_blocks = options_.elimination_groups[0];
  // Initialize a ImplicitSchurComplement object.
  if (schur_complement_ == NULL) {
    DetectStructure(*(A->block_structure()),
                    num_eliminate_blocks,
                    &options_.row_block_size,
                    &options_.e_block_size,
                    &options_.f_block_size);
    schur_complement_.reset(new ImplicitSchurComplement(options_));
  }
  schur_complement_->Init(*A, per_solve_options.D, b);

  const int num_schur_complement_blocks =
      A->block_structure()->cols.size() - num_eliminate_blocks;
  if (num_schur_complement_blocks == 0) {
    VLOG(2) << "No parameter blocks left in the schur complement.";
    LinearSolver::Summary summary;
    summary.num_iterations = 0;
    summary.termination_type = LINEAR_SOLVER_SUCCESS;
    schur_complement_->BackSubstitute(NULL, x);
    return summary;
  }

  // Initialize the solution to the Schur complement system to zero.
  reduced_linear_system_solution_.resize(schur_complement_->num_rows());
  reduced_linear_system_solution_.setZero();

  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;

  CreatePreconditioner(A);
  if (preconditioner_.get() != NULL) {
    if (!preconditioner_->Update(*A, per_solve_options.D)) {
      LinearSolver::Summary summary;
      summary.num_iterations = 0;
      summary.termination_type = LINEAR_SOLVER_FAILURE;
      summary.message = "Preconditioner update failed.";
      return summary;
    }

    cg_per_solve_options.preconditioner = preconditioner_.get();
  }

  event_logger.AddEvent("Setup");
  LinearSolver::Summary summary =
      cg_solver.Solve(schur_complement_.get(),
                      schur_complement_->rhs().data(),
                      cg_per_solve_options,
                      reduced_linear_system_solution_.data());
  if (summary.termination_type != LINEAR_SOLVER_FAILURE &&
      summary.termination_type != LINEAR_SOLVER_FATAL_ERROR) {
    schur_complement_->BackSubstitute(reduced_linear_system_solution_.data(),
                                      x);
  }
  event_logger.AddEvent("Solve");
  return summary;
}

void IterativeSchurComplementSolver::CreatePreconditioner(
    BlockSparseMatrix* A) {
  if (options_.preconditioner_type == IDENTITY ||
      preconditioner_.get() != NULL) {
    return;
  }

  Preconditioner::Options preconditioner_options;
  preconditioner_options.type = options_.preconditioner_type;
  preconditioner_options.visibility_clustering_type =
      options_.visibility_clustering_type;
  preconditioner_options.sparse_linear_algebra_library_type =
      options_.sparse_linear_algebra_library_type;
  preconditioner_options.num_threads = options_.num_threads;
  preconditioner_options.row_block_size = options_.row_block_size;
  preconditioner_options.e_block_size = options_.e_block_size;
  preconditioner_options.f_block_size = options_.f_block_size;
  preconditioner_options.elimination_groups = options_.elimination_groups;
  CHECK(options_.context != NULL);
  preconditioner_options.context = options_.context;

  switch (options_.preconditioner_type) {
    case JACOBI:
      preconditioner_.reset(new SparseMatrixPreconditionerWrapper(
          schur_complement_->block_diagonal_FtF_inverse()));
      break;
    case SCHUR_JACOBI:
      preconditioner_.reset(new SchurJacobiPreconditioner(
          *A->block_structure(), preconditioner_options));
      break;
    case CLUSTER_JACOBI:
    case CLUSTER_TRIDIAGONAL:
      preconditioner_.reset(new VisibilityBasedPreconditioner(
          *A->block_structure(), preconditioner_options));
      break;
    default:
      LOG(FATAL) << "Unknown Preconditioner Type";
  }
};

}  // namespace internal
}  // namespace ceres