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author | Gael Guennebaud <g.gael@free.fr> | 2015-06-26 10:49:40 +0200 |
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committer | Gael Guennebaud <g.gael@free.fr> | 2015-06-26 10:49:40 +0200 |
commit | 555b9c684346129057b14d73db64a75274fdfe0f (patch) | |
tree | d35749e34b390790a9cd12c7e9309391baf69309 | |
parent | 53b930887d118af5204840231f08b3307addce4e (diff) |
Doc: explain perf and multithreading issues in sparse iterative solvers
-rw-r--r-- | Eigen/src/IterativeLinearSolvers/BiCGSTAB.h | 6 | ||||
-rw-r--r-- | Eigen/src/IterativeLinearSolvers/ConjugateGradient.h | 12 | ||||
-rw-r--r-- | doc/SparseLinearSystems.dox | 2 | ||||
-rw-r--r-- | doc/TopicMultithreading.dox | 8 |
4 files changed, 21 insertions, 7 deletions
diff --git a/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h b/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h index f6d54c5e7..a34ee7628 100644 --- a/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h +++ b/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 diff --git a/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h b/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h index 5f0159e52..8f33c446d 100644 --- a/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h +++ b/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; diff --git a/doc/SparseLinearSystems.dox b/doc/SparseLinearSystems.dox index 13741280a..48c18f46f 100644 --- a/doc/SparseLinearSystems.dox +++ b/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> diff --git a/doc/TopicMultithreading.dox b/doc/TopicMultithreading.dox index e22e1c613..66028d7a8 100644 --- a/doc/TopicMultithreading.dox +++ b/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 |