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cs440-acg/ext/eigen/unsupported/Eigen/NonLinearOptimization

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+// 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_NONLINEAROPTIMIZATION_MODULE
+#define EIGEN_NONLINEAROPTIMIZATION_MODULE
+
+#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 (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