From b347eb0b1c6fd0c9ee09d3493e72d68a2d514db5 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Thu, 12 Jul 2018 11:56:18 +0200
Subject: Fix doc

---
 unsupported/Eigen/NonLinearOptimization | 32 +++++++++++++++++++-------------
 1 file changed, 19 insertions(+), 13 deletions(-)

(limited to 'unsupported/Eigen/NonLinearOptimization')

diff --git a/unsupported/Eigen/NonLinearOptimization b/unsupported/Eigen/NonLinearOptimization
index c22b89054..28eaa5f29 100644
--- a/unsupported/Eigen/NonLinearOptimization
+++ b/unsupported/Eigen/NonLinearOptimization
@@ -30,8 +30,8 @@
   * 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 
+  * One algorithm allows to find a least-squares solution 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).
@@ -58,35 +58,41 @@
   * 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).
+  * 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 
+  * 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 modifying 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
+  * 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
+  * \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() ) 
+  * Both algorithms needs a functor computing the Jacobian. It can be computed by
+  * hand, using auto-differentiation (see \ref AutoDiff_Module), or using numerical
+  * differences (see \ref NumericalDiff_Module). For instance:
+  *\code
+  * MyFunc func;
+  * NumericalDiff<MyFunc> func_with_num_diff(func);
+  * LevenbergMarquardt<NumericalDiff<MyFunc> > lm(func_with_num_diff);
+  * \endcode
+  * For HybridNonLinearSolver, the method solveNumericalDiff() does the above wrapping for
+  * you.
   * 
   * 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 
+  * was previously using minpack. They just define a 'simple' API with default values 
   * for some parameters.
   * 
-  * All algorithms are provided using Two APIs :
+  * 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 
@@ -94,7 +100,7 @@
   *  convenience.
   * 
   * As an example, the method LevenbergMarquardt::minimize() is 
-  * implemented as follow : 
+  * implemented as follow: 
   * \code
   * Status LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType  &x, const int mode)
   * {
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