NonLinearOptimization

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// This file is part of Eugenio, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
//
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// modify it under the terms of the GNU Lesser General Public
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// version 3 of the License, or (at your option) any later version.
//
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// modify it under the terms of the GNU General Public License as
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#ifndef EIGEN_NONLINEAROPTIMIZATION_MODULE
#define EIGEN_NONLINEAROPTIMIZATION_MODULE

#include <vector>

#include <Eigen/Core>
#include <Eigen/Jacobi>
#include <Eigen/QR>
#include <unsupported/Eigen/NumericalDiff>

namespace Eigen {

/** \ingroup Unsupported_modules
  * \defgroup NonLinearOptimization_Module Non linear optimization module  
 * \ingroup eigen_grp
 * \ingroup eigen_grp
  *
  * \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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/F2c) in C,
  * then c++, and then cleaned by several different authors.
  * The last one of those cleanings being our starting point : 
  * http://devernay.free.fr/hacks/cminpack.html
  * 
  * 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 http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml. 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
  * http://eigen.tuxfamily.org/index.php?title=Tests
  * 
  * \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.
  */

#ifndef EIGEN_PARSED_BY_DOXYGEN

#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"

#endif

#include "src/NonLinearOptimization/HybridNonLinearSolver.h"
#include "src/NonLinearOptimization/LevenbergMarquardt.h"

}



#endif // EIGEN_NONLINEAROPTIMIZATION_MODULE