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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
// Copyright (C) 2009 Thomas Capricelli <>
// 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
#include <vector>
#include <Eigen/Core>
#include <Eigen/Jacobi>
#include <Eigen/QR>
#include <unsupported/Eigen/NumericalDiff>
* \defgroup NonLinearOptimization_Module Non linear optimization module
* \code
* #include <unsupported/Eigen/NonLinearOptimization>
* \endcode
* This module provides implementation of two important algorithms in non linear
* optimization. In both cases, we consider a system of non linear functions. Of
* course, this should work, and even work very well if those functions are
* actually linear. But if this is so, you should probably better use other
* methods more fitted to this special case.
* One algorithm allows to find an extremum of such a system (Levenberg
* Marquardt algorithm) and the second one is used to find
* a zero for the system (Powell hybrid "dogleg" method).
* This code is a port of minpack (
* Minpack is a very famous, old, robust and well-reknown package, written in
* fortran. Those implementations have been carefully tuned, tested, and used
* for several decades.
* The original fortran code was automatically translated using f2c ( in C,
* then c++, and then cleaned by several different authors.
* The last one of those cleanings being our starting point :
* Finally, we ported this code to Eigen, creating classes and API
* coherent with Eigen. When possible, we switched to Eigen
* implementation, such as most linear algebra (vectors, matrices, stable norms).
* Doing so, we were very careful to check the tests we setup at the very
* beginning, which ensure that the same results are found.
* \section Tests Tests
* The tests are placed in the file unsupported/test/NonLinear.cpp.
* There are two kinds of tests : those that come from examples bundled with cminpack.
* They guaranty we get the same results as the original algorithms (value for 'x',
* for the number of evaluations of the function, and for the number of evaluations
* of the jacobian if ever).
* Other tests were added by myself at the very beginning of the
* process and check the results for levenberg-marquardt using the reference data
* on Since then i've
* carefully checked that the same results were obtained when modifiying the
* code. Please note that we do not always get the exact same decimals as they do,
* but this is ok : they use 128bits float, and we do the tests using the C type 'double',
* which is 64 bits on most platforms (x86 and amd64, at least).
* I've performed those tests on several other implementations of levenberg-marquardt, and
* (c)minpack performs VERY well compared to those, both in accuracy and speed.
* The documentation for running the tests is on the wiki
* \section API API : overview of methods
* Both algorithms can use either the jacobian (provided by the user) or compute
* an approximation by themselves (actually using Eigen \ref NumericalDiff_Module).
* The part of API referring to the latter use 'NumericalDiff' in the method names
* (exemple: LevenbergMarquardt.minimizeNumericalDiff() )
* The methods LevenbergMarquardt.lmder1()/lmdif1()/lmstr1() and
* HybridNonLinearSolver.hybrj1()/hybrd1() are specific methods from the original
* minpack package that you probably should NOT use until you are porting a code that
* was previously using minpack. They just define a 'simple' API with default values
* for some parameters.
* All algorithms are provided using Two APIs :
* - one where the user inits the algorithm, and uses '*OneStep()' as much as he wants :
* this way the caller have control over the steps
* - one where the user just calls a method (optimize() or solve()) which will
* handle the loop: init + loop until a stop condition is met. Those are provided for
* convenience.
* As an example, the method LevenbergMarquardt::minimize() is
* implemented as follow :
* \code
* Status LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x, const int mode)
* {
* Status status = minimizeInit(x, mode);
* do {
* status = minimizeOneStep(x, mode);
* } while (status==Running);
* return status;
* }
* \endcode
* \section examples Examples
* The easiest way to understand how to use this module is by looking at the many examples in the file
* unsupported/test/NonLinearOptimization.cpp.
#include "src/NonLinearOptimization/qrsolv.h"
#include "src/NonLinearOptimization/r1updt.h"
#include "src/NonLinearOptimization/r1mpyq.h"
#include "src/NonLinearOptimization/rwupdt.h"
#include "src/NonLinearOptimization/fdjac1.h"
#include "src/NonLinearOptimization/lmpar.h"
#include "src/NonLinearOptimization/dogleg.h"
#include "src/NonLinearOptimization/covar.h"
#include "src/NonLinearOptimization/chkder.h"
#include "src/NonLinearOptimization/HybridNonLinearSolver.h"
#include "src/NonLinearOptimization/LevenbergMarquardt.h"