1// This file is part of Eigen, a lightweight C++ template library
4// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10#ifndef EIGEN_NONLINEAROPTIMIZATION_MODULE
11#define EIGEN_NONLINEAROPTIMIZATION_MODULE
15#include "../../Eigen/Core"
16#include "../../Eigen/Jacobi"
17#include "../../Eigen/QR"
18#include "NumericalDiff"
21 * \defgroup NonLinearOptimization_Module Non linear optimization module
24 * #include <unsupported/Eigen/NonLinearOptimization>
27 * This module provides implementation of two important algorithms in non linear
28 * optimization. In both cases, we consider a system of non linear functions. Of
29 * course, this should work, and even work very well if those functions are
30 * actually linear. But if this is so, you should probably better use other
31 * methods more fitted to this special case.
33 * One algorithm allows to find a least-squares solution of such a system
34 * (Levenberg-Marquardt algorithm) and the second one is used to find
35 * a zero for the system (Powell hybrid "dogleg" method).
37 * This code is a port of minpack (http://en.wikipedia.org/wiki/MINPACK).
38 * Minpack is a very famous, old, robust and well renowned package, written in
39 * fortran. Those implementations have been carefully tuned, tested, and used
40 * for several decades.
42 * The original fortran code was automatically translated using f2c (http://en.wikipedia.org/wiki/F2c) in C,
43 * then c++, and then cleaned by several different authors.
44 * The last one of those cleanings being our starting point :
45 * http://devernay.free.fr/hacks/cminpack.html
47 * Finally, we ported this code to Eigen, creating classes and API
48 * coherent with Eigen. When possible, we switched to Eigen
49 * implementation, such as most linear algebra (vectors, matrices, stable norms).
51 * Doing so, we were very careful to check the tests we setup at the very
52 * beginning, which ensure that the same results are found.
54 * \section Tests Tests
56 * The tests are placed in the file unsupported/test/NonLinear.cpp.
58 * There are two kinds of tests : those that come from examples bundled with cminpack.
59 * They guaranty we get the same results as the original algorithms (value for 'x',
60 * for the number of evaluations of the function, and for the number of evaluations
61 * of the Jacobian if ever).
63 * Other tests were added by myself at the very beginning of the
64 * process and check the results for Levenberg-Marquardt using the reference data
65 * on http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml. Since then i've
66 * carefully checked that the same results were obtained when modifying the
67 * code. Please note that we do not always get the exact same decimals as they do,
68 * but this is ok : they use 128bits float, and we do the tests using the C type 'double',
69 * which is 64 bits on most platforms (x86 and amd64, at least).
70 * I've performed those tests on several other implementations of Levenberg-Marquardt, and
71 * (c)minpack performs VERY well compared to those, both in accuracy and speed.
73 * The documentation for running the tests is on the wiki
74 * http://eigen.tuxfamily.org/index.php?title=Tests
76 * \section API API: overview of methods
78 * Both algorithms needs a functor computing the Jacobian. It can be computed by
79 * hand, using auto-differentiation (see \ref AutoDiff_Module), or using numerical
80 * differences (see \ref NumericalDiff_Module). For instance:
83 * NumericalDiff<MyFunc> func_with_num_diff(func);
84 * LevenbergMarquardt<NumericalDiff<MyFunc> > lm(func_with_num_diff);
86 * For HybridNonLinearSolver, the method solveNumericalDiff() does the above wrapping for
89 * The methods LevenbergMarquardt.lmder1()/lmdif1()/lmstr1() and
90 * HybridNonLinearSolver.hybrj1()/hybrd1() are specific methods from the original
91 * minpack package that you probably should NOT use until you are porting a code that
92 * was previously using minpack. They just define a 'simple' API with default values
93 * for some parameters.
95 * All algorithms are provided using two APIs :
96 * - one where the user inits the algorithm, and uses '*OneStep()' as much as he wants :
97 * this way the caller have control over the steps
98 * - one where the user just calls a method (optimize() or solve()) which will
99 * handle the loop: init + loop until a stop condition is met. Those are provided for
102 * As an example, the method LevenbergMarquardt::minimize() is
103 * implemented as follow:
105 * Status LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x, const int mode)
107 * Status status = minimizeInit(x, mode);
109 * status = minimizeOneStep(x, mode);
110 * } while (status==Running);
115 * \section examples Examples
117 * The easiest way to understand how to use this module is by looking at the many examples in the file
118 * unsupported/test/NonLinearOptimization.cpp.
121#ifndef EIGEN_PARSED_BY_DOXYGEN
123#include "src/NonLinearOptimization/qrsolv.h"
124#include "src/NonLinearOptimization/r1updt.h"
125#include "src/NonLinearOptimization/r1mpyq.h"
126#include "src/NonLinearOptimization/rwupdt.h"
127#include "src/NonLinearOptimization/fdjac1.h"
128#include "src/NonLinearOptimization/lmpar.h"
129#include "src/NonLinearOptimization/dogleg.h"
130#include "src/NonLinearOptimization/covar.h"
132#include "src/NonLinearOptimization/chkder.h"
136#include "src/NonLinearOptimization/HybridNonLinearSolver.h"
137#include "src/NonLinearOptimization/LevenbergMarquardt.h"
140#endif // EIGEN_NONLINEAROPTIMIZATION_MODULE