internal/ceres/dense_qr_solver.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/dense_qr_solver.h"

#include <cstddef>
#include "Eigen/Dense"
#include "ceres/dense_sparse_matrix.h"
#include "ceres/internal/eigen.h"
#include "ceres/lapack.h"
#include "ceres/linear_solver.h"
#include "ceres/types.h"
#include "ceres/wall_time.h"

namespace ceres {
namespace internal {

DenseQRSolver::DenseQRSolver(const LinearSolver::Options& options)
    : options_(options) {
  work_.resize(1);
}

LinearSolver::Summary DenseQRSolver::SolveImpl(
    DenseSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double* x) {
  if (options_.dense_linear_algebra_library_type == EIGEN) {
    return SolveUsingEigen(A, b, per_solve_options, x);
  } else {
    return SolveUsingLAPACK(A, b, per_solve_options, x);
  }
}

LinearSolver::Summary DenseQRSolver::SolveUsingLAPACK(
    DenseSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double* x) {
  EventLogger event_logger("DenseQRSolver::Solve");

  const int num_rows = A->num_rows();
  const int num_cols = A->num_cols();

  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.
    A->AppendDiagonal(per_solve_options.D);
  }

  // TODO(sameeragarwal): Since we are copying anyways, the diagonal
  // can be appended to the matrix instead of doing it on A.
  lhs_ =  A->matrix();

  if (per_solve_options.D != NULL) {
    // Undo the modifications to the matrix A.
    A->RemoveDiagonal();
  }

  // rhs = [b;0] to account for the additional rows in the lhs.
  if (rhs_.rows() != lhs_.rows()) {
    rhs_.resize(lhs_.rows());
  }
  rhs_.setZero();
  rhs_.head(num_rows) = ConstVectorRef(b, num_rows);

  if (work_.rows() == 1) {
    const int work_size =
        LAPACK::EstimateWorkSizeForQR(lhs_.rows(), lhs_.cols());
    VLOG(3) << "Working memory for Dense QR factorization: "
            << work_size * sizeof(double);
    work_.resize(work_size);
  }

  LinearSolver::Summary summary;
  summary.num_iterations = 1;
  summary.termination_type = LAPACK::SolveInPlaceUsingQR(lhs_.rows(),
                                                         lhs_.cols(),
                                                         lhs_.data(),
                                                         work_.rows(),
                                                         work_.data(),
                                                         rhs_.data(),
                                                         &summary.message);
  event_logger.AddEvent("Solve");
  if (summary.termination_type == LINEAR_SOLVER_SUCCESS) {
    VectorRef(x, num_cols) = rhs_.head(num_cols);
  }

  event_logger.AddEvent("TearDown");
  return summary;
}

LinearSolver::Summary DenseQRSolver::SolveUsingEigen(
    DenseSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double* x) {
  EventLogger event_logger("DenseQRSolver::Solve");

  const int num_rows = A->num_rows();
  const int num_cols = A->num_cols();

  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.
    A->AppendDiagonal(per_solve_options.D);
  }

  // rhs = [b;0] to account for the additional rows in the lhs.
  const int augmented_num_rows =
      num_rows + ((per_solve_options.D != NULL) ? num_cols : 0);
  if (rhs_.rows() != augmented_num_rows) {
    rhs_.resize(augmented_num_rows);
    rhs_.setZero();
  }
  rhs_.head(num_rows) = ConstVectorRef(b, num_rows);
  event_logger.AddEvent("Setup");

  // Solve the system.
  VectorRef(x, num_cols) = A->matrix().householderQr().solve(rhs_);
  event_logger.AddEvent("Solve");

  if (per_solve_options.D != NULL) {
    // Undo the modifications to the matrix A.
    A->RemoveDiagonal();
  }

  // We always succeed, since the QR solver returns the best solution
  // it can. It is the job of the caller to determine if the solution
  // is good enough or not.
  LinearSolver::Summary summary;
  summary.num_iterations = 1;
  summary.termination_type = LINEAR_SOLVER_SUCCESS;
  summary.message = "Success.";

  event_logger.AddEvent("TearDown");
  return summary;
}

}   // namespace internal
}   // namespace ceres