internal/ceres/dense_qr_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/dense_qr_solver.h"

#include <cstddef>

#include "Eigen/Dense"
#include "ceres/linear_solver.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/types.h"

namespace ceres {
namespace internal {

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

LinearSolver::Summary DenseQRSolver::SolveImpl(
    DenseSparseMatrix* A,
    const double* b,
    const LinearSolver::PerSolveOptions& per_solve_options,
    double* x) {
  const int num_rows = A->num_rows();
  const int num_cols = A->num_cols();
  VLOG(2) << "DenseQRSolver: "
          << num_rows << " x " << num_cols << " system.";

  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.
  Vector rhs(num_rows + ((per_solve_options.D !=NULL) ? num_cols : 0));
  rhs.setZero();
  rhs.head(num_rows) = ConstVectorRef(b, num_rows);

  // Solve the system.
  VectorRef(x, num_cols) = A->matrix().colPivHouseholderQr().solve(rhs);

  VLOG(3) << "A:\n" << A->matrix();
  VLOG(3) << "x:\n" << VectorRef(x, num_cols);
  VLOG(3) << "b:\n" << rhs;
  VLOG(3) << "error: " << (A->matrix() * VectorRef(x, num_cols) - rhs).norm();


  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 = TOLERANCE;
  return summary;
}

}   // namespace internal
}   // namespace ceres