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start a topic page on decompositions, with a big table.

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still have to write the _tutorial_ on decompositions.
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Benoit Jacob 2010-06-28 10:43:11 -04:00
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namespace Eigen {
/** \page TopicLinearAlgebraDecompositions Linear algebra and decompositions
\section TopicLinAlgBigTable Catalogue of decompositions offered by Eigen
<table border="1">
<tr>
<td></td>
<td colspan="5" align="center">Generic information, not Eigen-specific</td>
<td colspan="2" align="center">Eigen-specific</td>
</tr>
<tr>
<td>Decomposition</td>
<td>Requirements on the matrix</td>
<td>Speed</td>
<td>Algorithm reliability and accuracy</td>
<td>Rank-revealing</td>
<td>Allows to compute (besides linear solving)</td>
<td>Linear solver provided by Eigen</td>
<td>Maturity of Eigen's implementation</td>
</tr>
<tr>
<td>PartialPivLU</td>
<td>Invertible</td>
<td>Fast</td>
<td>Depends on condition number</td>
<td>-</td>
<td>-</td>
<td>Yes</td>
<td>Excellent</td>
</tr>
<tr>
<td>FullPivLU</td>
<td>-</td>
<td>Slow</td>
<td>Proven</td>
<td>Yes</td>
<td>-</td>
<td>Yes</td>
<td>Excellent</td>
</tr>
<tr>
<td>HouseholderQR</td>
<td>-</td>
<td>Fast</td>
<td>Average</td>
<td>Depends on condition number</td>
<td>Orthogonalization</td>
<td>Yes</td>
<td>Excellent</td>
</tr>
<tr>
<td>ColPivHouseholderQR</td>
<td>-</td>
<td>Fast</td>
<td>Good</td>
<td>Yes</td>
<td>Orthogonalization</td>
<td>Yes</td>
<td>Excellent</td>
</tr>
<tr>
<td>FullPivHouseholderQR</td>
<td>-</td>
<td>Slow</td>
<td>Proven</td>
<td>Yes</td>
<td>Orthogonalization</td>
<td>Yes</td>
<td>Average</td>
</tr>
<tr>
<td>LLT</td>
<td>Positive definite</td>
<td>Very fast</td>
<td>Depends on condition number</td>
<td>-</td>
<td>-</td>
<td>Yes</td>
<td>TODO Gael answer this</td>
</tr>
<tr>
<td>LDLT</td>
<td>Positive or negative semidefinite</td>
<td>Very fast</td>
<td>Good</td>
<td>-</td>
<td>-</td>
<td>Yes</td>
<td>TODO Gael answer this</td>
</tr>
<tr>
<td>SVD</td>
<td>-</td>
<td>Average</td>
<td>Good</td>
<td>Yes</td>
<td>Singular values/vectors, least squares</td>
<td>Yes</td>
<td>Average</td>
</tr>
<tr>
<td>JacobiSVD</td>
<td>-</td>
<td>Slow (but fast for small matrices)</td>
<td>Proven</td>
<td>Yes</td>
<td>Singular values/vectors, least squares</td>
<td>-</td>
<td>Excellent</td>
</tr>
<tr>
<td>SelfAdjointEigenSolver</td>
<td>Self-adjoint</td>
<td>Average</td>
<td>Good</td>
<td>Yes</td>
<td>Eigenvalues/vectors</td>
<td>-</td>
<td>TODO Gael/Jitse answer this</td>
</tr>
<tr>
<td>ComplexEigenSolver</td>
<td>Square</td>
<td>TODO Gael/Jitse answer this</td>
<td>TODO Gael/Jitse answer this</td>
<td>Yes</td>
<td>Eigenvalues/vectors</td>
<td>-</td>
<td>TODO Gael/Jitse answer this</td>
</tr>
<tr>
<td>EigenSolver</td>
<td>Square and real</td>
<td>TODO Gael/Jitse answer this</td>
<td>TODO Gael/Jitse answer this</td>
<td>Yes</td>
<td>Eigenvalues/vectors</td>
<td>-</td>
<td>TODO Gael/Jitse answer this</td>
</tr>
<tr>
<td>GeneralizedSelfAdjointEigenSolver</td>
<td>Square</td>
<td>TODO Gael/Jitse answer this</td>
<td>TODO Gael/Jitse answer this</td>
<td>-</td>
<td>Generalized eigenvalues/vectors</td>
<td>-</td>
<td>TODO Gael/Jitse answer this</td>
</tr>
<tr>
<td>RealSchur</td>
<td>Square and real</td>
<td>TODO Gael/Jitse answer this</td>
<td>TODO Gael/Jitse answer this</td>
<td>Yes</td>
<td>-</td>
<td>-</td>
<td>TODO Gael/Jitse answer this</td>
</tr>
<tr>
<td>UpperBidiagonalization</td>
<td>rows >= columns</td>
<td>Fast</td>
<td>Good</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>Good</td>
</tr>
<tr>
<td>Tridiagonalization</td>
<td>Self-adjoint</td>
<td>Fast</td>
<td>Good</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>Good</td>
</tr>
<tr>
<td>HessenbergDecomposition</td>
<td>-</td>
<td>TODO Gael/Jitse answer this</td>
<td>TODO Gael/Jitse answer this</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>TODO Gael/Jitse answer this</td>
</tr>
</table>
\section TopicLinAlgTerminology Terminology
TODO explain selfadjoint, positive definite/semidefinite, ....
*/
}