// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
//
// This code initially comes from MINPACK whose original authors are:
// Copyright Jorge More - Argonne National Laboratory
// Copyright Burt Garbow - Argonne National Laboratory
// Copyright Ken Hillstrom - Argonne National Laboratory
//
// This Source Code Form is subject to the terms of the Minpack license
// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
#ifndef EIGEN_LMONESTEP_H
#define EIGEN_LMONESTEP_H
namespace Eigen {
template<typename FunctorType>
LevenbergMarquardtSpace::Status
LevenbergMarquardt<FunctorType>::minimizeOneStep(FVectorType &x)
{
using std::abs;
using std::sqrt;
RealScalar temp, temp1,temp2;
RealScalar ratio;
RealScalar pnorm, xnorm, fnorm1, actred, dirder, prered;
eigen_assert(x.size()==n); // check the caller is not cheating us
temp = 0.0; xnorm = 0.0;
/* calculate the jacobian matrix. */
Index df_ret = m_functor.df(x, m_fjac);
if (df_ret<0)
return LevenbergMarquardtSpace::UserAsked;
if (df_ret>0)
// numerical diff, we evaluated the function df_ret times
m_nfev += df_ret;
else m_njev++;
/* compute the qr factorization of the jacobian. */
for (int j = 0; j < x.size(); ++j)
m_wa2(j) = m_fjac.col(j).blueNorm();
QRSolver qrfac(m_fjac);
if(qrfac.info() != Success) {
m_info = NumericalIssue;
return LevenbergMarquardtSpace::ImproperInputParameters;
}
// Make a copy of the first factor with the associated permutation
m_rfactor = qrfac.matrixR();
m_permutation = (qrfac.colsPermutation());
/* on the first iteration and if external scaling is not used, scale according */
/* to the norms of the columns of the initial jacobian. */
if (m_iter == 1) {
if (!m_useExternalScaling)
for (Index j = 0; j < n; ++j)
m_diag[j] = (m_wa2[j]==0.)? 1. : m_wa2[j];
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound m_delta. */
xnorm = m_diag.cwiseProduct(x).stableNorm();
m_delta = m_factor * xnorm;
if (m_delta == 0.)
m_delta = m_factor;
}
/* form (q transpose)*m_fvec and store the first n components in */
/* m_qtf. */
m_wa4 = m_fvec;
m_wa4 = qrfac.matrixQ().adjoint() * m_fvec;
m_qtf = m_wa4.head(n);
/* compute the norm of the scaled gradient. */
m_gnorm = 0.;
if (m_fnorm != 0.)
for (Index j = 0; j < n; ++j)
if (m_wa2[m_permutation.indices()[j]] != 0.)
m_gnorm = (std::max)(m_gnorm, abs( m_rfactor.col(j).head(j+1).dot(m_qtf.head(j+1)/m_fnorm) / m_wa2[m_permutation.indices()[j]]));
/* test for convergence of the gradient norm. */
if (m_gnorm <= m_gtol) {
m_info = Success;
return LevenbergMarquardtSpace::CosinusTooSmall;
}
/* rescale if necessary. */
if (!m_useExternalScaling)
m_diag = m_diag.cwiseMax(m_wa2);
do {
/* determine the levenberg-marquardt parameter. */
internal::lmpar2(qrfac, m_diag, m_qtf, m_delta, m_par, m_wa1);
/* store the direction p and x + p. calculate the norm of p. */
m_wa1 = -m_wa1;
m_wa2 = x + m_wa1;
pnorm = m_diag.cwiseProduct(m_wa1).stableNorm();
/* on the first iteration, adjust the initial step bound. */
if (m_iter == 1)
m_delta = (std::min)(m_delta,pnorm);
/* evaluate the function at x + p and calculate its norm. */
if ( m_functor(m_wa2, m_wa4) < 0)
return LevenbergMarquardtSpace::UserAsked;
++m_nfev;
fnorm1 = m_wa4.stableNorm();
/* compute the scaled actual reduction. */
actred = -1.;
if (Scalar(.1) * fnorm1 < m_fnorm)
actred = 1. - numext::abs2(fnorm1 / m_fnorm);
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
m_wa3 = m_rfactor.template triangularView<Upper>() * (m_permutation.inverse() *m_wa1);
temp1 = numext::abs2(m_wa3.stableNorm() / m_fnorm);
temp2 = numext::abs2(sqrt(m_par) * pnorm / m_fnorm);
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered != 0.)
ratio = actred / prered;
/* update the step bound. */
if (ratio <= Scalar(.25)) {
if (actred >= 0.)
temp = RealScalar(.5);
if (actred < 0.)
temp = RealScalar(.5) * dirder / (dirder + RealScalar(.5) * actred);
if (RealScalar(.1) * fnorm1 >= m_fnorm || temp < RealScalar(.1))
temp = Scalar(.1);
/* Computing MIN */
m_delta = temp * (std::min)(m_delta, pnorm / RealScalar(.1));
m_par /= temp;
} else if (!(m_par != 0. && ratio < RealScalar(.75))) {
m_delta = pnorm / RealScalar(.5);
m_par = RealScalar(.5) * m_par;
}
/* test for successful iteration. */
if (ratio >= RealScalar(1e-4)) {
/* successful iteration. update x, m_fvec, and their norms. */
x = m_wa2;
m_wa2 = m_diag.cwiseProduct(x);
m_fvec = m_wa4;
xnorm = m_wa2.stableNorm();
m_fnorm = fnorm1;
++m_iter;
}
/* tests for convergence. */
if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1. && m_delta <= m_xtol * xnorm)
{
m_info = Success;
return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
}
if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1.)
{
m_info = Success;
return LevenbergMarquardtSpace::RelativeReductionTooSmall;
}
if (m_delta <= m_xtol * xnorm)
{
m_info = Success;
return LevenbergMarquardtSpace::RelativeErrorTooSmall;
}
/* tests for termination and stringent tolerances. */
if (m_nfev >= m_maxfev)
{
m_info = NoConvergence;
return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
}
if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
{
m_info = Success;
return LevenbergMarquardtSpace::FtolTooSmall;
}
if (m_delta <= NumTraits<Scalar>::epsilon() * xnorm)
{
m_info = Success;
return LevenbergMarquardtSpace::XtolTooSmall;
}
if (m_gnorm <= NumTraits<Scalar>::epsilon())
{
m_info = Success;
return LevenbergMarquardtSpace::GtolTooSmall;
}
} while (ratio < Scalar(1e-4));
return LevenbergMarquardtSpace::Running;
}
} // end namespace Eigen
#endif // EIGEN_LMONESTEP_H