| // -*- coding: utf-8 | |
| // vim: set fileencoding=utf-8 | |
| // This file is part of Eigen, a lightweight C++ template library | |
| // for linear algebra. | |
| // | |
| // Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org> | |
| // | |
| // This Source Code Form is subject to the terms of the Mozilla | |
| // Public License v. 2.0. If a copy of the MPL was not distributed | |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. | |
| #ifndef EIGEN_LEVENBERGMARQUARDT__H | |
| #define EIGEN_LEVENBERGMARQUARDT__H | |
| namespace Eigen { | |
| namespace LevenbergMarquardtSpace { | |
| enum Status { | |
| NotStarted = -2, | |
| Running = -1, | |
| ImproperInputParameters = 0, | |
| RelativeReductionTooSmall = 1, | |
| RelativeErrorTooSmall = 2, | |
| RelativeErrorAndReductionTooSmall = 3, | |
| CosinusTooSmall = 4, | |
| TooManyFunctionEvaluation = 5, | |
| FtolTooSmall = 6, | |
| XtolTooSmall = 7, | |
| GtolTooSmall = 8, | |
| UserAsked = 9 | |
| }; | |
| } | |
| /** | |
| * \ingroup NonLinearOptimization_Module | |
| * \brief Performs non linear optimization over a non-linear function, | |
| * using a variant of the Levenberg Marquardt algorithm. | |
| * | |
| * Check wikipedia for more information. | |
| * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm | |
| */ | |
| template<typename FunctorType, typename Scalar=double> | |
| class LevenbergMarquardt | |
| { | |
| static Scalar sqrt_epsilon() | |
| { | |
| using std::sqrt; | |
| return sqrt(NumTraits<Scalar>::epsilon()); | |
| } | |
| public: | |
| LevenbergMarquardt(FunctorType &_functor) | |
| : functor(_functor) { nfev = njev = iter = 0; fnorm = gnorm = 0.; useExternalScaling=false; } | |
| typedef DenseIndex Index; | |
| struct Parameters { | |
| Parameters() | |
| : factor(Scalar(100.)) | |
| , maxfev(400) | |
| , ftol(sqrt_epsilon()) | |
| , xtol(sqrt_epsilon()) | |
| , gtol(Scalar(0.)) | |
| , epsfcn(Scalar(0.)) {} | |
| Scalar factor; | |
| Index maxfev; // maximum number of function evaluation | |
| Scalar ftol; | |
| Scalar xtol; | |
| Scalar gtol; | |
| Scalar epsfcn; | |
| }; | |
| typedef Matrix< Scalar, Dynamic, 1 > FVectorType; | |
| typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType; | |
| LevenbergMarquardtSpace::Status lmder1( | |
| FVectorType &x, | |
| const Scalar tol = sqrt_epsilon() | |
| ); | |
| LevenbergMarquardtSpace::Status minimize(FVectorType &x); | |
| LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x); | |
| LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x); | |
| static LevenbergMarquardtSpace::Status lmdif1( | |
| FunctorType &functor, | |
| FVectorType &x, | |
| Index *nfev, | |
| const Scalar tol = sqrt_epsilon() | |
| ); | |
| LevenbergMarquardtSpace::Status lmstr1( | |
| FVectorType &x, | |
| const Scalar tol = sqrt_epsilon() | |
| ); | |
| LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x); | |
| LevenbergMarquardtSpace::Status minimizeOptimumStorageInit(FVectorType &x); | |
| LevenbergMarquardtSpace::Status minimizeOptimumStorageOneStep(FVectorType &x); | |
| void resetParameters(void) { parameters = Parameters(); } | |
| Parameters parameters; | |
| FVectorType fvec, qtf, diag; | |
| JacobianType fjac; | |
| PermutationMatrix<Dynamic,Dynamic> permutation; | |
| Index nfev; | |
| Index njev; | |
| Index iter; | |
| Scalar fnorm, gnorm; | |
| bool useExternalScaling; | |
| Scalar lm_param(void) { return par; } | |
| private: | |
| FunctorType &functor; | |
| Index n; | |
| Index m; | |
| FVectorType wa1, wa2, wa3, wa4; | |
| Scalar par, sum; | |
| Scalar temp, temp1, temp2; | |
| Scalar delta; | |
| Scalar ratio; | |
| Scalar pnorm, xnorm, fnorm1, actred, dirder, prered; | |
| LevenbergMarquardt& operator=(const LevenbergMarquardt&); | |
| }; | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::lmder1( | |
| FVectorType &x, | |
| const Scalar tol | |
| ) | |
| { | |
| n = x.size(); | |
| m = functor.values(); | |
| /* check the input parameters for errors. */ | |
| if (n <= 0 || m < n || tol < 0.) | |
| return LevenbergMarquardtSpace::ImproperInputParameters; | |
| resetParameters(); | |
| parameters.ftol = tol; | |
| parameters.xtol = tol; | |
| parameters.maxfev = 100*(n+1); | |
| return minimize(x); | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x) | |
| { | |
| LevenbergMarquardtSpace::Status status = minimizeInit(x); | |
| if (status==LevenbergMarquardtSpace::ImproperInputParameters) | |
| return status; | |
| do { | |
| status = minimizeOneStep(x); | |
| } while (status==LevenbergMarquardtSpace::Running); | |
| return status; | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::minimizeInit(FVectorType &x) | |
| { | |
| n = x.size(); | |
| m = functor.values(); | |
| wa1.resize(n); wa2.resize(n); wa3.resize(n); | |
| wa4.resize(m); | |
| fvec.resize(m); | |
| fjac.resize(m, n); | |
| if (!useExternalScaling) | |
| diag.resize(n); | |
| eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'"); | |
| qtf.resize(n); | |
| /* Function Body */ | |
| nfev = 0; | |
| njev = 0; | |
| /* check the input parameters for errors. */ | |
| if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.) | |
| return LevenbergMarquardtSpace::ImproperInputParameters; | |
| if (useExternalScaling) | |
| for (Index j = 0; j < n; ++j) | |
| if (diag[j] <= 0.) | |
| return LevenbergMarquardtSpace::ImproperInputParameters; | |
| /* evaluate the function at the starting point */ | |
| /* and calculate its norm. */ | |
| nfev = 1; | |
| if ( functor(x, fvec) < 0) | |
| return LevenbergMarquardtSpace::UserAsked; | |
| fnorm = fvec.stableNorm(); | |
| /* initialize levenberg-marquardt parameter and iteration counter. */ | |
| par = 0.; | |
| iter = 1; | |
| return LevenbergMarquardtSpace::NotStarted; | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x) | |
| { | |
| using std::abs; | |
| using std::sqrt; | |
| eigen_assert(x.size()==n); // check the caller is not cheating us | |
| /* calculate the jacobian matrix. */ | |
| Index df_ret = functor.df(x, fjac); | |
| if (df_ret<0) | |
| return LevenbergMarquardtSpace::UserAsked; | |
| if (df_ret>0) | |
| // numerical diff, we evaluated the function df_ret times | |
| nfev += df_ret; | |
| else njev++; | |
| /* compute the qr factorization of the jacobian. */ | |
| wa2 = fjac.colwise().blueNorm(); | |
| ColPivHouseholderQR<JacobianType> qrfac(fjac); | |
| fjac = qrfac.matrixQR(); | |
| 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 (iter == 1) { | |
| if (!useExternalScaling) | |
| for (Index j = 0; j < n; ++j) | |
| diag[j] = (wa2[j]==0.)? 1. : wa2[j]; | |
| /* on the first iteration, calculate the norm of the scaled x */ | |
| /* and initialize the step bound delta. */ | |
| xnorm = diag.cwiseProduct(x).stableNorm(); | |
| delta = parameters.factor * xnorm; | |
| if (delta == 0.) | |
| delta = parameters.factor; | |
| } | |
| /* form (q transpose)*fvec and store the first n components in */ | |
| /* qtf. */ | |
| wa4 = fvec; | |
| wa4.applyOnTheLeft(qrfac.householderQ().adjoint()); | |
| qtf = wa4.head(n); | |
| /* compute the norm of the scaled gradient. */ | |
| gnorm = 0.; | |
| if (fnorm != 0.) | |
| for (Index j = 0; j < n; ++j) | |
| if (wa2[permutation.indices()[j]] != 0.) | |
| gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]])); | |
| /* test for convergence of the gradient norm. */ | |
| if (gnorm <= parameters.gtol) | |
| return LevenbergMarquardtSpace::CosinusTooSmall; | |
| /* rescale if necessary. */ | |
| if (!useExternalScaling) | |
| diag = diag.cwiseMax(wa2); | |
| do { | |
| /* determine the levenberg-marquardt parameter. */ | |
| internal::lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1); | |
| /* store the direction p and x + p. calculate the norm of p. */ | |
| wa1 = -wa1; | |
| wa2 = x + wa1; | |
| pnorm = diag.cwiseProduct(wa1).stableNorm(); | |
| /* on the first iteration, adjust the initial step bound. */ | |
| if (iter == 1) | |
| delta = (std::min)(delta,pnorm); | |
| /* evaluate the function at x + p and calculate its norm. */ | |
| if ( functor(wa2, wa4) < 0) | |
| return LevenbergMarquardtSpace::UserAsked; | |
| ++nfev; | |
| fnorm1 = wa4.stableNorm(); | |
| /* compute the scaled actual reduction. */ | |
| actred = -1.; | |
| if (Scalar(.1) * fnorm1 < fnorm) | |
| actred = 1. - numext::abs2(fnorm1 / fnorm); | |
| /* compute the scaled predicted reduction and */ | |
| /* the scaled directional derivative. */ | |
| wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1); | |
| temp1 = numext::abs2(wa3.stableNorm() / fnorm); | |
| temp2 = numext::abs2(sqrt(par) * pnorm / 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 = Scalar(.5); | |
| if (actred < 0.) | |
| temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred); | |
| if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1)) | |
| temp = Scalar(.1); | |
| /* Computing MIN */ | |
| delta = temp * (std::min)(delta, pnorm / Scalar(.1)); | |
| par /= temp; | |
| } else if (!(par != 0. && ratio < Scalar(.75))) { | |
| delta = pnorm / Scalar(.5); | |
| par = Scalar(.5) * par; | |
| } | |
| /* test for successful iteration. */ | |
| if (ratio >= Scalar(1e-4)) { | |
| /* successful iteration. update x, fvec, and their norms. */ | |
| x = wa2; | |
| wa2 = diag.cwiseProduct(x); | |
| fvec = wa4; | |
| xnorm = wa2.stableNorm(); | |
| fnorm = fnorm1; | |
| ++iter; | |
| } | |
| /* tests for convergence. */ | |
| if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm) | |
| return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall; | |
| if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.) | |
| return LevenbergMarquardtSpace::RelativeReductionTooSmall; | |
| if (delta <= parameters.xtol * xnorm) | |
| return LevenbergMarquardtSpace::RelativeErrorTooSmall; | |
| /* tests for termination and stringent tolerances. */ | |
| if (nfev >= parameters.maxfev) | |
| return LevenbergMarquardtSpace::TooManyFunctionEvaluation; | |
| if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.) | |
| return LevenbergMarquardtSpace::FtolTooSmall; | |
| if (delta <= NumTraits<Scalar>::epsilon() * xnorm) | |
| return LevenbergMarquardtSpace::XtolTooSmall; | |
| if (gnorm <= NumTraits<Scalar>::epsilon()) | |
| return LevenbergMarquardtSpace::GtolTooSmall; | |
| } while (ratio < Scalar(1e-4)); | |
| return LevenbergMarquardtSpace::Running; | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::lmstr1( | |
| FVectorType &x, | |
| const Scalar tol | |
| ) | |
| { | |
| n = x.size(); | |
| m = functor.values(); | |
| /* check the input parameters for errors. */ | |
| if (n <= 0 || m < n || tol < 0.) | |
| return LevenbergMarquardtSpace::ImproperInputParameters; | |
| resetParameters(); | |
| parameters.ftol = tol; | |
| parameters.xtol = tol; | |
| parameters.maxfev = 100*(n+1); | |
| return minimizeOptimumStorage(x); | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(FVectorType &x) | |
| { | |
| n = x.size(); | |
| m = functor.values(); | |
| wa1.resize(n); wa2.resize(n); wa3.resize(n); | |
| wa4.resize(m); | |
| fvec.resize(m); | |
| // Only R is stored in fjac. Q is only used to compute 'qtf', which is | |
| // Q.transpose()*rhs. qtf will be updated using givens rotation, | |
| // instead of storing them in Q. | |
| // The purpose it to only use a nxn matrix, instead of mxn here, so | |
| // that we can handle cases where m>>n : | |
| fjac.resize(n, n); | |
| if (!useExternalScaling) | |
| diag.resize(n); | |
| eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'"); | |
| qtf.resize(n); | |
| /* Function Body */ | |
| nfev = 0; | |
| njev = 0; | |
| /* check the input parameters for errors. */ | |
| if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.) | |
| return LevenbergMarquardtSpace::ImproperInputParameters; | |
| if (useExternalScaling) | |
| for (Index j = 0; j < n; ++j) | |
| if (diag[j] <= 0.) | |
| return LevenbergMarquardtSpace::ImproperInputParameters; | |
| /* evaluate the function at the starting point */ | |
| /* and calculate its norm. */ | |
| nfev = 1; | |
| if ( functor(x, fvec) < 0) | |
| return LevenbergMarquardtSpace::UserAsked; | |
| fnorm = fvec.stableNorm(); | |
| /* initialize levenberg-marquardt parameter and iteration counter. */ | |
| par = 0.; | |
| iter = 1; | |
| return LevenbergMarquardtSpace::NotStarted; | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType &x) | |
| { | |
| using std::abs; | |
| using std::sqrt; | |
| eigen_assert(x.size()==n); // check the caller is not cheating us | |
| Index i, j; | |
| bool sing; | |
| /* compute the qr factorization of the jacobian matrix */ | |
| /* calculated one row at a time, while simultaneously */ | |
| /* forming (q transpose)*fvec and storing the first */ | |
| /* n components in qtf. */ | |
| qtf.fill(0.); | |
| fjac.fill(0.); | |
| Index rownb = 2; | |
| for (i = 0; i < m; ++i) { | |
| if (functor.df(x, wa3, rownb) < 0) return LevenbergMarquardtSpace::UserAsked; | |
| internal::rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]); | |
| ++rownb; | |
| } | |
| ++njev; | |
| /* if the jacobian is rank deficient, call qrfac to */ | |
| /* reorder its columns and update the components of qtf. */ | |
| sing = false; | |
| for (j = 0; j < n; ++j) { | |
| if (fjac(j,j) == 0.) | |
| sing = true; | |
| wa2[j] = fjac.col(j).head(j).stableNorm(); | |
| } | |
| permutation.setIdentity(n); | |
| if (sing) { | |
| wa2 = fjac.colwise().blueNorm(); | |
| // TODO We have no unit test covering this code path, do not modify | |
| // until it is carefully tested | |
| ColPivHouseholderQR<JacobianType> qrfac(fjac); | |
| fjac = qrfac.matrixQR(); | |
| wa1 = fjac.diagonal(); | |
| fjac.diagonal() = qrfac.hCoeffs(); | |
| permutation = qrfac.colsPermutation(); | |
| // TODO : avoid this: | |
| for(Index ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors | |
| for (j = 0; j < n; ++j) { | |
| if (fjac(j,j) != 0.) { | |
| sum = 0.; | |
| for (i = j; i < n; ++i) | |
| sum += fjac(i,j) * qtf[i]; | |
| temp = -sum / fjac(j,j); | |
| for (i = j; i < n; ++i) | |
| qtf[i] += fjac(i,j) * temp; | |
| } | |
| fjac(j,j) = wa1[j]; | |
| } | |
| } | |
| /* on the first iteration and if external scaling is not used, scale according */ | |
| /* to the norms of the columns of the initial jacobian. */ | |
| if (iter == 1) { | |
| if (!useExternalScaling) | |
| for (j = 0; j < n; ++j) | |
| diag[j] = (wa2[j]==0.)? 1. : wa2[j]; | |
| /* on the first iteration, calculate the norm of the scaled x */ | |
| /* and initialize the step bound delta. */ | |
| xnorm = diag.cwiseProduct(x).stableNorm(); | |
| delta = parameters.factor * xnorm; | |
| if (delta == 0.) | |
| delta = parameters.factor; | |
| } | |
| /* compute the norm of the scaled gradient. */ | |
| gnorm = 0.; | |
| if (fnorm != 0.) | |
| for (j = 0; j < n; ++j) | |
| if (wa2[permutation.indices()[j]] != 0.) | |
| gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]])); | |
| /* test for convergence of the gradient norm. */ | |
| if (gnorm <= parameters.gtol) | |
| return LevenbergMarquardtSpace::CosinusTooSmall; | |
| /* rescale if necessary. */ | |
| if (!useExternalScaling) | |
| diag = diag.cwiseMax(wa2); | |
| do { | |
| /* determine the levenberg-marquardt parameter. */ | |
| internal::lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1); | |
| /* store the direction p and x + p. calculate the norm of p. */ | |
| wa1 = -wa1; | |
| wa2 = x + wa1; | |
| pnorm = diag.cwiseProduct(wa1).stableNorm(); | |
| /* on the first iteration, adjust the initial step bound. */ | |
| if (iter == 1) | |
| delta = (std::min)(delta,pnorm); | |
| /* evaluate the function at x + p and calculate its norm. */ | |
| if ( functor(wa2, wa4) < 0) | |
| return LevenbergMarquardtSpace::UserAsked; | |
| ++nfev; | |
| fnorm1 = wa4.stableNorm(); | |
| /* compute the scaled actual reduction. */ | |
| actred = -1.; | |
| if (Scalar(.1) * fnorm1 < fnorm) | |
| actred = 1. - numext::abs2(fnorm1 / fnorm); | |
| /* compute the scaled predicted reduction and */ | |
| /* the scaled directional derivative. */ | |
| wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1); | |
| temp1 = numext::abs2(wa3.stableNorm() / fnorm); | |
| temp2 = numext::abs2(sqrt(par) * pnorm / 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 = Scalar(.5); | |
| if (actred < 0.) | |
| temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred); | |
| if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1)) | |
| temp = Scalar(.1); | |
| /* Computing MIN */ | |
| delta = temp * (std::min)(delta, pnorm / Scalar(.1)); | |
| par /= temp; | |
| } else if (!(par != 0. && ratio < Scalar(.75))) { | |
| delta = pnorm / Scalar(.5); | |
| par = Scalar(.5) * par; | |
| } | |
| /* test for successful iteration. */ | |
| if (ratio >= Scalar(1e-4)) { | |
| /* successful iteration. update x, fvec, and their norms. */ | |
| x = wa2; | |
| wa2 = diag.cwiseProduct(x); | |
| fvec = wa4; | |
| xnorm = wa2.stableNorm(); | |
| fnorm = fnorm1; | |
| ++iter; | |
| } | |
| /* tests for convergence. */ | |
| if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm) | |
| return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall; | |
| if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.) | |
| return LevenbergMarquardtSpace::RelativeReductionTooSmall; | |
| if (delta <= parameters.xtol * xnorm) | |
| return LevenbergMarquardtSpace::RelativeErrorTooSmall; | |
| /* tests for termination and stringent tolerances. */ | |
| if (nfev >= parameters.maxfev) | |
| return LevenbergMarquardtSpace::TooManyFunctionEvaluation; | |
| if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.) | |
| return LevenbergMarquardtSpace::FtolTooSmall; | |
| if (delta <= NumTraits<Scalar>::epsilon() * xnorm) | |
| return LevenbergMarquardtSpace::XtolTooSmall; | |
| if (gnorm <= NumTraits<Scalar>::epsilon()) | |
| return LevenbergMarquardtSpace::GtolTooSmall; | |
| } while (ratio < Scalar(1e-4)); | |
| return LevenbergMarquardtSpace::Running; | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(FVectorType &x) | |
| { | |
| LevenbergMarquardtSpace::Status status = minimizeOptimumStorageInit(x); | |
| if (status==LevenbergMarquardtSpace::ImproperInputParameters) | |
| return status; | |
| do { | |
| status = minimizeOptimumStorageOneStep(x); | |
| } while (status==LevenbergMarquardtSpace::Running); | |
| return status; | |
| } | |
| template<typename FunctorType, typename Scalar> | |
| LevenbergMarquardtSpace::Status | |
| LevenbergMarquardt<FunctorType,Scalar>::lmdif1( | |
| FunctorType &functor, | |
| FVectorType &x, | |
| Index *nfev, | |
| const Scalar tol | |
| ) | |
| { | |
| Index n = x.size(); | |
| Index m = functor.values(); | |
| /* check the input parameters for errors. */ | |
| if (n <= 0 || m < n || tol < 0.) | |
| return LevenbergMarquardtSpace::ImproperInputParameters; | |
| NumericalDiff<FunctorType> numDiff(functor); | |
| // embedded LevenbergMarquardt | |
| LevenbergMarquardt<NumericalDiff<FunctorType>, Scalar > lm(numDiff); | |
| lm.parameters.ftol = tol; | |
| lm.parameters.xtol = tol; | |
| lm.parameters.maxfev = 200*(n+1); | |
| LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x)); | |
| if (nfev) | |
| * nfev = lm.nfev; | |
| return info; | |
| } | |
| } // end namespace Eigen | |
| #endif // EIGEN_LEVENBERGMARQUARDT__H | |
| //vim: ai ts=4 sts=4 et sw=4 |