ceres-solver/internal/ceres/corrector.h

// 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)
//
// Class definition for the object that is responsible for applying a
// second order correction to the Gauss-Newton based on the ideas in
// BANS by Triggs et al.

#ifndef CERES_INTERNAL_CORRECTOR_H_
#define CERES_INTERNAL_CORRECTOR_H_

namespace ceres {
namespace internal {

// Corrector is responsible for applying the second order correction
// to the residual and jacobian of a least squares problem based on a
// radial robust loss.
//
// The key idea here is to look at the expressions for the robustified
// gauss newton approximation and then take its squareroot to get the
// corresponding corrections to the residual and jacobian.  For the
// full expressions see Eq. 10 and 11 in BANS by Triggs et al.
class Corrector {
 public:
  // The constructor takes the squared norm, the value, the first and
  // second derivatives of the LossFunction. It precalculates some of
  // the constants that are needed to apply the correction. The
  // correction constant alpha is constrained to be smaller than 1, if
  // it becomes larger than 1, then it will reverse the sign of the
  // residual and the correction. If alpha is equal to 1 will result
  // in a divide by zero error. Thus we constrain alpha to be upper
  // bounded by 1 - epsilon_.
  //
  // rho[1] needs to be positive. The constructor will crash if this
  // condition is not met.
  //
  // In practical use CorrectJacobian should always be called before
  // CorrectResidual, because the jacobian correction depends on the
  // value of the uncorrected residual values.
  explicit Corrector(double sq_norm, const double rho[3]);

  // residuals *= sqrt(rho[1]) / (1 - alpha)
  void CorrectResiduals(int num_rows, double* residuals);

  // jacobian = sqrt(rho[1]) * jacobian -
  // sqrt(rho[1]) * alpha / sq_norm * residuals residuals' * jacobian.
  //
  // The method assumes that the jacobian has row-major storage. It is
  // the caller's responsibility to ensure that the pointer to
  // jacobian is not null.
  void CorrectJacobian(int num_rows,
                       int num_cols,
                       double* residuals,
                       double* jacobian);

 private:
  double sqrt_rho1_;
  double residual_scaling_;
  double alpha_sq_norm_;
};
}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_CORRECTOR_H_