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Doc: explain perf and multithreading issues in sparse iterative solvers

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This commit is contained in:
Gael Guennebaud
2015-06-26 10:49:40 +02:00
parent 53b930887d
commit 555b9c6843
4 changed files with 21 additions and 7 deletions
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6
Eigen/src/IterativeLinearSolvers/BiCGSTAB.h
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@@ -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

12
Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
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@@ -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;