internal/ceres/iterative_schur_complement_solver.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/iterative_schur_complement_solver.h"

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

#include <glog/logging.h>
#include "Eigen/Dense"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/conjugate_gradients_solver.h"
#include "ceres/implicit_schur_complement.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/linear_solver.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "ceres/visibility_based_preconditioner.h"

namespace ceres {
namespace internal {

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

IterativeSchurComplementSolver::~IterativeSchurComplementSolver() {
}

LinearSolver::Summary IterativeSchurComplementSolver::SolveImpl(
    BlockSparseMatrixBase* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double* x) {
  CHECK_NOTNULL(A->block_structure());

  // Initialize a ImplicitSchurComplement object.
  if ((schur_complement_ == NULL) || (!options_.constant_sparsity)) {
    schur_complement_.reset(
        new ImplicitSchurComplement(options_.num_eliminate_blocks,
                                    options_.constant_sparsity,
                                    options_.preconditioner_type == JACOBI));
  }
  schur_complement_->Init(*A, per_solve_options.D, b);

  // Initialize the solution to the Schur complement system to zero.
  //
  // TODO(sameeragarwal): There maybe a better initialization than an
  // all zeros solution. Explore other cheap starting points.
  reduced_linear_system_solution_.resize(schur_complement_->num_rows());
  reduced_linear_system_solution_.setZero();

  // Instantiate a conjugate gradient solver that runs on the Schur complement
  // matrix with the block diagonal of the matrix F'F as the preconditioner.
  LinearSolver::Options cg_options;
  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;

  bool is_preconditioner_good = false;
  switch (options_.preconditioner_type) {
    case IDENTITY:
      is_preconditioner_good = true;
      break;
    case JACOBI:
      // We need to strip the constness of the block_diagonal_FtF_inverse
      // matrix here because the only other way to initialize the struct
      // cg_solve_options would be to add a constructor to it. We know
      // that the only method ever called on the preconditioner is the
      // RightMultiply which is a const method so we don't need to worry
      // about the object getting modified.
      cg_per_solve_options.preconditioner =
          const_cast<BlockSparseMatrix*>(
              schur_complement_->block_diagonal_FtF_inverse());
      is_preconditioner_good = true;
      break;
    case SCHUR_JACOBI:
    case CLUSTER_JACOBI:
    case CLUSTER_TRIDIAGONAL:
      if (visibility_based_preconditioner_.get() == NULL) {
        visibility_based_preconditioner_.reset(
            new VisibilityBasedPreconditioner(*A->block_structure(), options_));
      }
      is_preconditioner_good =
          visibility_based_preconditioner_->Compute(*A, per_solve_options.D);
      cg_per_solve_options.preconditioner =
          visibility_based_preconditioner_.get();
      break;
    default:
      LOG(FATAL) << "Unknown Preconditioner Type";
  }

  LinearSolver::Summary cg_summary;
  cg_summary.num_iterations = 0;
  cg_summary.termination_type = FAILURE;

  if (is_preconditioner_good) {
    cg_summary = cg_solver.Solve(schur_complement_.get(),
                                 schur_complement_->rhs().data(),
                                 cg_per_solve_options,
                                 reduced_linear_system_solution_.data());
    if (cg_summary.termination_type != FAILURE) {
      schur_complement_->BackSubstitute(
          reduced_linear_system_solution_.data(), x);
    }
  }

  VLOG(2) << "CG Iterations : " << cg_summary.num_iterations;
  return cg_summary;
}

}  // namespace internal
}  // namespace ceres