Doc: explain perf and multithreading issues in sparse iterative solvers

Eigen/src/IterativeLinearSolvers/BiCGSTAB.h

@@ -136,7 +136,11 @@ struct traits<BiCGSTAB<_MatrixType,_Preconditioner> >
   * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
   * and NumTraits<Scalar>::epsilon() for the tolerance.
   * 
-  * The tolerance is the relative residual error: |Ax-b|/|b|
+  * The tolerance corresponds to the relative residual error: |Ax-b|/|b|
+  * 
+  * \b Performance: when using sparse matrices, best performance is achied for a row-major sparse matrix format.
+  * Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
+  * See \ref TopicMultiThreading for details.
   * 
   * This class can be used as the direct solver classes. Here is a typical usage example:
   * \include BiCGSTAB_simple.cpp

Eigen/src/IterativeLinearSolvers/ConjugateGradient.h

@@ -114,14 +114,20 @@ struct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
   *
   * \tparam _MatrixType the type of the matrix A, can be a dense or a sparse matrix.
   * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower,
-  *               Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower.
+  *               \c Upper, or \c Lower|Upper in which the full matrix entries will be considered.
+  *               Default is \c Lower, best performance is \c Lower|Upper.
   * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner
   *
   * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
   * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
   * and NumTraits<Scalar>::epsilon() for the tolerance.
   * 
-  * The tolerance is the relative residual error: |Ax-b|/|b|
+  * The tolerance corresponds to the relative residual error: |Ax-b|/|b|
+  * 
+  * \b Performance: Even though the default value of \c _UpLo is \c Lower, significantly higher performance is
+  * achieved when using a complete matrix and \b Lower|Upper as the \a _UpLo template parameter. Moreover, in this
+  * case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
+  * See \ref TopicMultiThreading for details.
   * 
   * This class can be used as the direct solver classes. Here is a typical usage example:
     \code
@@ -129,7 +135,7 @@ struct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
     VectorXd x(n), b(n);
     SparseMatrix<double> A(n,n);
     // fill A and b
-    ConjugateGradient<SparseMatrix<double> > cg;
+    ConjugateGradient<SparseMatrix<double>, Lower|Upper> cg;
     cg.compute(A);
     x = cg.solve(b);
     std::cout << "#iterations:     " << cg.iterations() << std::endl;

doc/SparseLinearSystems.dox

@@ -21,7 +21,7 @@ They are summarized in the following table:
 <tr><td>ConjugateGradient</td><td>\link IterativeLinearSolvers_Module IterativeLinearSolvers \endlink</td><td>Classic iterative CG</td><td>SPD</td><td>Preconditionning</td>
     <td>built-in, MPL2</td>
     <td>Recommended for large symmetric problems (e.g., 3D Poisson eq.)</td></tr>
-<tr><td>LSCG</td><td>\link IterativeLinearSolvers_Module IterativeLinearSolvers \endlink</td><td>CG for rectangular least-square problem</td><td>Rectangular</td><td>Preconditionning</td>
+<tr><td>LeastSquaresConjugateGradient</td><td>\link IterativeLinearSolvers_Module IterativeLinearSolvers \endlink</td><td>CG for rectangular least-square problem</td><td>Rectangular</td><td>Preconditionning</td>
     <td>built-in, MPL2</td>
     <td>Solve for min |A'Ax-b|^2 without forming A'A</td></tr>
 <tr><td>BiCGSTAB</td><td>\link IterativeLinearSolvers_Module IterativeLinearSolvers \endlink</td><td>Iterative stabilized bi-conjugate gradient</td><td>Square</td><td>Preconditionning</td>

doc/TopicMultithreading.dox

@@ -22,8 +22,12 @@ n = Eigen::nbThreads( );
 You can disable Eigen's multi threading at compile time by defining the EIGEN_DONT_PARALLELIZE preprocessor token.
 
 Currently, the following algorithms can make use of multi-threading:
- * general matrix - matrix products
- * PartialPivLU
+ - general dense matrix - matrix products
+ - PartialPivLU
+ - row-major-sparse * dense vector/matrix products
+ - ConjugateGradient with \c Lower|Upper as the \c UpLo template parameter.
+ - BiCGSTAB with a row-major sparse matrix format.
+ - LeastSquaresConjugateGradient
 
 \section TopicMultiThreading_UsingEigenWithMT Using Eigen in a multi-threaded application