From d2dd5063b6f52e16e15790eac7c9d1f57a60c96f Mon Sep 17 00:00:00 2001
From: Desire NUENTSA <desire.nuentsa_wakam@inria.fr>
Date: Mon, 21 Jan 2013 15:37:47 +0100
Subject: Documentation for the ordering methods

---
 Eigen/OrderingMethods | 46 +++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 43 insertions(+), 3 deletions(-)

(limited to 'Eigen/OrderingMethods')

diff --git a/Eigen/OrderingMethods b/Eigen/OrderingMethods
index 8abc128b9..423cfb0cd 100644
--- a/Eigen/OrderingMethods
+++ b/Eigen/OrderingMethods
@@ -8,12 +8,52 @@
 /** 
   * \defgroup OrderingMethods_Module OrderingMethods module
   *
-  * This module is currently for internal use only.
-  *
-  *
+  * This module is currently for internal use only
+  * 
+  * It defines various built-in and external ordering methods for sparse matrices. 
+  * They are typically used to reduce the number of elements during 
+  * the sparse matrix decomposition (LLT, LU, QR).
+  * Precisely, in a preprocessing step, a permutation matrix P is computed using 
+  * those ordering methods and applied to the columns of the matrix. 
+  * Using for instance the sparse Cholesky decomposition, it is expected that 
+  * the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A).
+  * 
+  * 
+  * Usage : 
   * \code
   * #include <Eigen/OrderingMethods>
   * \endcode
+  * 
+  * A simple usage is as a template parameter in the sparse decomposition classes : 
+  * 
+  * \code 
+  * SparseLU<MatrixType, COLAMDOrdering<int> > solver;
+  * \endcode 
+  * 
+  * \code 
+  * SparseQR<MatrixType, COLAMDOrdering<int> > solver;
+  * \endcode
+  * 
+  * It is possible as well to call directly a particular ordering method for your own purpose, 
+  * \code 
+  * AMDOrdering<int> ordering;
+  * PermutationMatrix<Dynamic, Dynamic, int> perm;
+  * SparseMatrix<double> A; 
+  * //Fill the matrix ...
+  * 
+  * ordering(A, perm); // Call AMD
+  * \endcode
+  * 
+  * \note Some of these methods (like AMD or METIS), need the sparsity pattern 
+  * of the input matrix to be symmetric. When the matrix is structurally unsymmetric, 
+  * Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method.
+  * If your matrix is already symmetric (at leat in structure), you can avoid that
+  * by calling the method with a SelfAdjointView type.
+  * 
+  * \code
+  *  // Call the ordering on the pattern of the lower triangular matrix A
+  * ordering(A.selfadjointView<Lower>(), perm);
+  * \endcode
   */
 
 #include "src/OrderingMethods/Amd.h"
-- 
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