[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
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| 5 | // Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
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| 6 | //
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| 7 | // The algorithm of this class initially comes from MINPACK whose original authors are:
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| 8 | // Copyright Jorge More - Argonne National Laboratory
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| 9 | // Copyright Burt Garbow - Argonne National Laboratory
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| 10 | // Copyright Ken Hillstrom - Argonne National Laboratory
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| 11 | //
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| 12 | // This Source Code Form is subject to the terms of the Minpack license
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| 13 | // (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
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| 14 | //
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| 15 | // This Source Code Form is subject to the terms of the Mozilla
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| 16 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 17 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 18 |
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| 19 | #ifndef EIGEN_LEVENBERGMARQUARDT_H
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| 20 | #define EIGEN_LEVENBERGMARQUARDT_H
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| 21 |
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| 22 |
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| 23 | namespace Eigen {
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| 24 | namespace LevenbergMarquardtSpace {
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| 25 | enum Status {
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| 26 | NotStarted = -2,
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| 27 | Running = -1,
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| 28 | ImproperInputParameters = 0,
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| 29 | RelativeReductionTooSmall = 1,
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| 30 | RelativeErrorTooSmall = 2,
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| 31 | RelativeErrorAndReductionTooSmall = 3,
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| 32 | CosinusTooSmall = 4,
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| 33 | TooManyFunctionEvaluation = 5,
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| 34 | FtolTooSmall = 6,
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| 35 | XtolTooSmall = 7,
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| 36 | GtolTooSmall = 8,
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| 37 | UserAsked = 9
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| 38 | };
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| 39 | }
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| 40 |
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| 41 | template <typename _Scalar, int NX=Dynamic, int NY=Dynamic>
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| 42 | struct DenseFunctor
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| 43 | {
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| 44 | typedef _Scalar Scalar;
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| 45 | enum {
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| 46 | InputsAtCompileTime = NX,
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| 47 | ValuesAtCompileTime = NY
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| 48 | };
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| 49 | typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
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| 50 | typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
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| 51 | typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
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| 52 | typedef ColPivHouseholderQR<JacobianType> QRSolver;
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| 53 | const int m_inputs, m_values;
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| 54 |
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| 55 | DenseFunctor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
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| 56 | DenseFunctor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
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| 57 |
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| 58 | int inputs() const { return m_inputs; }
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| 59 | int values() const { return m_values; }
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| 60 |
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| 61 | //int operator()(const InputType &x, ValueType& fvec) { }
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| 62 | // should be defined in derived classes
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| 63 |
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| 64 | //int df(const InputType &x, JacobianType& fjac) { }
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| 65 | // should be defined in derived classes
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| 66 | };
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| 67 |
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| 68 | template <typename _Scalar, typename _Index>
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| 69 | struct SparseFunctor
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| 70 | {
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| 71 | typedef _Scalar Scalar;
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| 72 | typedef _Index Index;
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| 73 | typedef Matrix<Scalar,Dynamic,1> InputType;
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| 74 | typedef Matrix<Scalar,Dynamic,1> ValueType;
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| 75 | typedef SparseMatrix<Scalar, ColMajor, Index> JacobianType;
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| 76 | typedef SparseQR<JacobianType, COLAMDOrdering<int> > QRSolver;
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| 77 | enum {
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| 78 | InputsAtCompileTime = Dynamic,
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| 79 | ValuesAtCompileTime = Dynamic
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| 80 | };
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| 81 |
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| 82 | SparseFunctor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
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| 83 |
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| 84 | int inputs() const { return m_inputs; }
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| 85 | int values() const { return m_values; }
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| 86 |
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| 87 | const int m_inputs, m_values;
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| 88 | //int operator()(const InputType &x, ValueType& fvec) { }
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| 89 | // to be defined in the functor
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| 90 |
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| 91 | //int df(const InputType &x, JacobianType& fjac) { }
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| 92 | // to be defined in the functor if no automatic differentiation
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| 93 |
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| 94 | };
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| 95 | namespace internal {
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| 96 | template <typename QRSolver, typename VectorType>
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| 97 | void lmpar2(const QRSolver &qr, const VectorType &diag, const VectorType &qtb,
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| 98 | typename VectorType::Scalar m_delta, typename VectorType::Scalar &par,
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| 99 | VectorType &x);
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| 100 | }
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| 101 | /**
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| 102 | * \ingroup NonLinearOptimization_Module
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| 103 | * \brief Performs non linear optimization over a non-linear function,
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| 104 | * using a variant of the Levenberg Marquardt algorithm.
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| 105 | *
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| 106 | * Check wikipedia for more information.
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| 107 | * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm
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| 108 | */
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| 109 | template<typename _FunctorType>
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| 110 | class LevenbergMarquardt : internal::no_assignment_operator
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| 111 | {
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| 112 | public:
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| 113 | typedef _FunctorType FunctorType;
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| 114 | typedef typename FunctorType::QRSolver QRSolver;
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| 115 | typedef typename FunctorType::JacobianType JacobianType;
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| 116 | typedef typename JacobianType::Scalar Scalar;
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| 117 | typedef typename JacobianType::RealScalar RealScalar;
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| 118 | typedef typename JacobianType::Index Index;
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| 119 | typedef typename QRSolver::Index PermIndex;
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| 120 | typedef Matrix<Scalar,Dynamic,1> FVectorType;
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| 121 | typedef PermutationMatrix<Dynamic,Dynamic> PermutationType;
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| 122 | public:
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| 123 | LevenbergMarquardt(FunctorType& functor)
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| 124 | : m_functor(functor),m_nfev(0),m_njev(0),m_fnorm(0.0),m_gnorm(0),
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| 125 | m_isInitialized(false),m_info(InvalidInput)
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| 126 | {
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| 127 | resetParameters();
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| 128 | m_useExternalScaling=false;
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| 129 | }
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| 130 |
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| 131 | LevenbergMarquardtSpace::Status minimize(FVectorType &x);
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| 132 | LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x);
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| 133 | LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x);
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| 134 | LevenbergMarquardtSpace::Status lmder1(
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| 135 | FVectorType &x,
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| 136 | const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
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| 137 | );
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| 138 | static LevenbergMarquardtSpace::Status lmdif1(
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| 139 | FunctorType &functor,
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| 140 | FVectorType &x,
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| 141 | Index *nfev,
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| 142 | const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
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| 143 | );
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| 144 |
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| 145 | /** Sets the default parameters */
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| 146 | void resetParameters()
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| 147 | {
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| 148 | m_factor = 100.;
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| 149 | m_maxfev = 400;
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| 150 | m_ftol = std::sqrt(NumTraits<RealScalar>::epsilon());
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| 151 | m_xtol = std::sqrt(NumTraits<RealScalar>::epsilon());
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| 152 | m_gtol = 0. ;
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| 153 | m_epsfcn = 0. ;
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| 154 | }
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| 155 |
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| 156 | /** Sets the tolerance for the norm of the solution vector*/
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| 157 | void setXtol(RealScalar xtol) { m_xtol = xtol; }
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| 158 |
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| 159 | /** Sets the tolerance for the norm of the vector function*/
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| 160 | void setFtol(RealScalar ftol) { m_ftol = ftol; }
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| 161 |
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| 162 | /** Sets the tolerance for the norm of the gradient of the error vector*/
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| 163 | void setGtol(RealScalar gtol) { m_gtol = gtol; }
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| 164 |
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| 165 | /** Sets the step bound for the diagonal shift */
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| 166 | void setFactor(RealScalar factor) { m_factor = factor; }
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| 167 |
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| 168 | /** Sets the error precision */
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| 169 | void setEpsilon (RealScalar epsfcn) { m_epsfcn = epsfcn; }
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| 170 |
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| 171 | /** Sets the maximum number of function evaluation */
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| 172 | void setMaxfev(Index maxfev) {m_maxfev = maxfev; }
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| 173 |
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| 174 | /** Use an external Scaling. If set to true, pass a nonzero diagonal to diag() */
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| 175 | void setExternalScaling(bool value) {m_useExternalScaling = value; }
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| 176 |
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| 177 | /** \returns a reference to the diagonal of the jacobian */
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| 178 | FVectorType& diag() {return m_diag; }
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| 179 |
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| 180 | /** \returns the number of iterations performed */
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| 181 | Index iterations() { return m_iter; }
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| 182 |
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| 183 | /** \returns the number of functions evaluation */
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| 184 | Index nfev() { return m_nfev; }
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| 185 |
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| 186 | /** \returns the number of jacobian evaluation */
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| 187 | Index njev() { return m_njev; }
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| 188 |
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| 189 | /** \returns the norm of current vector function */
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| 190 | RealScalar fnorm() {return m_fnorm; }
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| 191 |
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| 192 | /** \returns the norm of the gradient of the error */
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| 193 | RealScalar gnorm() {return m_gnorm; }
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| 194 |
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| 195 | /** \returns the LevenbergMarquardt parameter */
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| 196 | RealScalar lm_param(void) { return m_par; }
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| 197 |
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| 198 | /** \returns a reference to the current vector function
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| 199 | */
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| 200 | FVectorType& fvec() {return m_fvec; }
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| 201 |
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| 202 | /** \returns a reference to the matrix where the current Jacobian matrix is stored
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| 203 | */
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| 204 | JacobianType& jacobian() {return m_fjac; }
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| 205 |
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| 206 | /** \returns a reference to the triangular matrix R from the QR of the jacobian matrix.
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| 207 | * \sa jacobian()
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| 208 | */
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| 209 | JacobianType& matrixR() {return m_rfactor; }
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| 210 |
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| 211 | /** the permutation used in the QR factorization
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| 212 | */
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| 213 | PermutationType permutation() {return m_permutation; }
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| 214 |
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| 215 | /**
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| 216 | * \brief Reports whether the minimization was successful
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| 217 | * \returns \c Success if the minimization was succesful,
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| 218 | * \c NumericalIssue if a numerical problem arises during the
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| 219 | * minimization process, for exemple during the QR factorization
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| 220 | * \c NoConvergence if the minimization did not converge after
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| 221 | * the maximum number of function evaluation allowed
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| 222 | * \c InvalidInput if the input matrix is invalid
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| 223 | */
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| 224 | ComputationInfo info() const
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| 225 | {
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| 226 |
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| 227 | return m_info;
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| 228 | }
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| 229 | private:
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| 230 | JacobianType m_fjac;
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| 231 | JacobianType m_rfactor; // The triangular matrix R from the QR of the jacobian matrix m_fjac
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| 232 | FunctorType &m_functor;
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| 233 | FVectorType m_fvec, m_qtf, m_diag;
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| 234 | Index n;
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| 235 | Index m;
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| 236 | Index m_nfev;
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| 237 | Index m_njev;
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| 238 | RealScalar m_fnorm; // Norm of the current vector function
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| 239 | RealScalar m_gnorm; //Norm of the gradient of the error
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| 240 | RealScalar m_factor; //
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| 241 | Index m_maxfev; // Maximum number of function evaluation
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| 242 | RealScalar m_ftol; //Tolerance in the norm of the vector function
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| 243 | RealScalar m_xtol; //
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| 244 | RealScalar m_gtol; //tolerance of the norm of the error gradient
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| 245 | RealScalar m_epsfcn; //
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| 246 | Index m_iter; // Number of iterations performed
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| 247 | RealScalar m_delta;
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| 248 | bool m_useExternalScaling;
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| 249 | PermutationType m_permutation;
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| 250 | FVectorType m_wa1, m_wa2, m_wa3, m_wa4; //Temporary vectors
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| 251 | RealScalar m_par;
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| 252 | bool m_isInitialized; // Check whether the minimization step has been called
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| 253 | ComputationInfo m_info;
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| 254 | };
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| 255 |
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| 256 | template<typename FunctorType>
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| 257 | LevenbergMarquardtSpace::Status
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| 258 | LevenbergMarquardt<FunctorType>::minimize(FVectorType &x)
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| 259 | {
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| 260 | LevenbergMarquardtSpace::Status status = minimizeInit(x);
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| 261 | if (status==LevenbergMarquardtSpace::ImproperInputParameters) {
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| 262 | m_isInitialized = true;
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| 263 | return status;
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| 264 | }
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| 265 | do {
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| 266 | // std::cout << " uv " << x.transpose() << "\n";
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| 267 | status = minimizeOneStep(x);
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| 268 | } while (status==LevenbergMarquardtSpace::Running);
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| 269 | m_isInitialized = true;
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| 270 | return status;
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| 271 | }
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| 272 |
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| 273 | template<typename FunctorType>
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| 274 | LevenbergMarquardtSpace::Status
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| 275 | LevenbergMarquardt<FunctorType>::minimizeInit(FVectorType &x)
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| 276 | {
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| 277 | n = x.size();
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| 278 | m = m_functor.values();
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| 279 |
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| 280 | m_wa1.resize(n); m_wa2.resize(n); m_wa3.resize(n);
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| 281 | m_wa4.resize(m);
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| 282 | m_fvec.resize(m);
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| 283 | //FIXME Sparse Case : Allocate space for the jacobian
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| 284 | m_fjac.resize(m, n);
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| 285 | // m_fjac.reserve(VectorXi::Constant(n,5)); // FIXME Find a better alternative
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| 286 | if (!m_useExternalScaling)
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| 287 | m_diag.resize(n);
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| 288 | eigen_assert( (!m_useExternalScaling || m_diag.size()==n) || "When m_useExternalScaling is set, the caller must provide a valid 'm_diag'");
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| 289 | m_qtf.resize(n);
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| 290 |
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| 291 | /* Function Body */
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| 292 | m_nfev = 0;
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| 293 | m_njev = 0;
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| 294 |
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| 295 | /* check the input parameters for errors. */
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| 296 | if (n <= 0 || m < n || m_ftol < 0. || m_xtol < 0. || m_gtol < 0. || m_maxfev <= 0 || m_factor <= 0.){
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| 297 | m_info = InvalidInput;
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| 298 | return LevenbergMarquardtSpace::ImproperInputParameters;
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| 299 | }
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| 300 |
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| 301 | if (m_useExternalScaling)
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| 302 | for (Index j = 0; j < n; ++j)
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| 303 | if (m_diag[j] <= 0.)
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| 304 | {
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| 305 | m_info = InvalidInput;
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| 306 | return LevenbergMarquardtSpace::ImproperInputParameters;
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| 307 | }
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| 308 |
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| 309 | /* evaluate the function at the starting point */
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| 310 | /* and calculate its norm. */
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| 311 | m_nfev = 1;
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| 312 | if ( m_functor(x, m_fvec) < 0)
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| 313 | return LevenbergMarquardtSpace::UserAsked;
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| 314 | m_fnorm = m_fvec.stableNorm();
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| 315 |
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| 316 | /* initialize levenberg-marquardt parameter and iteration counter. */
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| 317 | m_par = 0.;
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| 318 | m_iter = 1;
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| 319 |
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| 320 | return LevenbergMarquardtSpace::NotStarted;
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| 321 | }
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| 322 |
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| 323 | template<typename FunctorType>
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| 324 | LevenbergMarquardtSpace::Status
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| 325 | LevenbergMarquardt<FunctorType>::lmder1(
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| 326 | FVectorType &x,
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| 327 | const Scalar tol
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| 328 | )
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| 329 | {
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| 330 | n = x.size();
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| 331 | m = m_functor.values();
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| 332 |
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| 333 | /* check the input parameters for errors. */
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| 334 | if (n <= 0 || m < n || tol < 0.)
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| 335 | return LevenbergMarquardtSpace::ImproperInputParameters;
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| 336 |
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| 337 | resetParameters();
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| 338 | m_ftol = tol;
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| 339 | m_xtol = tol;
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| 340 | m_maxfev = 100*(n+1);
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| 341 |
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| 342 | return minimize(x);
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| 343 | }
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| 344 |
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| 345 |
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| 346 | template<typename FunctorType>
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| 347 | LevenbergMarquardtSpace::Status
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| 348 | LevenbergMarquardt<FunctorType>::lmdif1(
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| 349 | FunctorType &functor,
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| 350 | FVectorType &x,
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| 351 | Index *nfev,
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| 352 | const Scalar tol
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| 353 | )
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| 354 | {
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| 355 | Index n = x.size();
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| 356 | Index m = functor.values();
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| 357 |
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| 358 | /* check the input parameters for errors. */
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| 359 | if (n <= 0 || m < n || tol < 0.)
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| 360 | return LevenbergMarquardtSpace::ImproperInputParameters;
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| 361 |
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| 362 | NumericalDiff<FunctorType> numDiff(functor);
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| 363 | // embedded LevenbergMarquardt
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| 364 | LevenbergMarquardt<NumericalDiff<FunctorType> > lm(numDiff);
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| 365 | lm.setFtol(tol);
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| 366 | lm.setXtol(tol);
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| 367 | lm.setMaxfev(200*(n+1));
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| 368 |
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| 369 | LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x));
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| 370 | if (nfev)
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| 371 | * nfev = lm.nfev();
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| 372 | return info;
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| 373 | }
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| 374 |
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| 375 | } // end namespace Eigen
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| 376 |
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| 377 | #endif // EIGEN_LEVENBERGMARQUARDT_H
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