diff --git a/doc/TopicLinearAlgebraDecompositions.dox b/doc/TopicLinearAlgebraDecompositions.dox new file mode 100644 index 000000000..5065be70a --- /dev/null +++ b/doc/TopicLinearAlgebraDecompositions.dox @@ -0,0 +1,223 @@ +namespace Eigen { + +/** \page TopicLinearAlgebraDecompositions Linear algebra and decompositions + + +\section TopicLinAlgBigTable Catalogue of decompositions offered by Eigen + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Generic information, not Eigen-specificEigen-specific
DecompositionRequirements on the matrixSpeedAlgorithm reliability and accuracyRank-revealingAllows to compute (besides linear solving)Linear solver provided by EigenMaturity of Eigen's implementation
PartialPivLUInvertibleFastDepends on condition number--YesExcellent
FullPivLU-SlowProvenYes-YesExcellent
HouseholderQR-FastAverageDepends on condition numberOrthogonalizationYesExcellent
ColPivHouseholderQR-FastGoodYesOrthogonalizationYesExcellent
FullPivHouseholderQR-SlowProvenYesOrthogonalizationYesAverage
LLTPositive definiteVery fastDepends on condition number--YesTODO Gael answer this
LDLTPositive or negative semidefiniteVery fastGood--YesTODO Gael answer this
SVD-AverageGoodYesSingular values/vectors, least squaresYesAverage
JacobiSVD-Slow (but fast for small matrices)ProvenYesSingular values/vectors, least squares-Excellent
SelfAdjointEigenSolverSelf-adjointAverageGoodYesEigenvalues/vectors-TODO Gael/Jitse answer this
ComplexEigenSolverSquareTODO Gael/Jitse answer thisTODO Gael/Jitse answer thisYesEigenvalues/vectors-TODO Gael/Jitse answer this
EigenSolverSquare and realTODO Gael/Jitse answer thisTODO Gael/Jitse answer thisYesEigenvalues/vectors-TODO Gael/Jitse answer this
GeneralizedSelfAdjointEigenSolverSquareTODO Gael/Jitse answer thisTODO Gael/Jitse answer this-Generalized eigenvalues/vectors-TODO Gael/Jitse answer this
RealSchurSquare and realTODO Gael/Jitse answer thisTODO Gael/Jitse answer thisYes--TODO Gael/Jitse answer this
UpperBidiagonalizationrows >= columnsFastGood---Good
TridiagonalizationSelf-adjointFastGood---Good
HessenbergDecomposition-TODO Gael/Jitse answer thisTODO Gael/Jitse answer this---TODO Gael/Jitse answer this
+ +\section TopicLinAlgTerminology Terminology + +TODO explain selfadjoint, positive definite/semidefinite, .... + + +*/ + +}