203 lines
6.5 KiB
C
203 lines
6.5 KiB
C
|
// 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
|