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Diffstat (limited to 'doc/TopicLinearAlgebraDecompositions.dox')
-rw-r--r-- | doc/TopicLinearAlgebraDecompositions.dox | 32 |
1 files changed, 28 insertions, 4 deletions
diff --git a/doc/TopicLinearAlgebraDecompositions.dox b/doc/TopicLinearAlgebraDecompositions.dox index 491470627..402b3769e 100644 --- a/doc/TopicLinearAlgebraDecompositions.dox +++ b/doc/TopicLinearAlgebraDecompositions.dox @@ -4,7 +4,7 @@ namespace Eigen { This page presents a catalogue of the dense matrix decompositions offered by Eigen. For an introduction on linear solvers and decompositions, check this \link TutorialLinearAlgebra page \endlink. -To get an overview of the true relative speed of the different decomposition, check this \link DenseDecompositionBenchmark benchmark \endlink. +To get an overview of the true relative speed of the different decompositions, check this \link DenseDecompositionBenchmark benchmark \endlink. \section TopicLinAlgBigTable Catalogue of decompositions offered by Eigen @@ -72,7 +72,7 @@ To get an overview of the true relative speed of the different decomposition, ch <td>Orthogonalization</td> <td>Yes</td> <td>Excellent</td> - <td><em>Soon: blocking</em></td> + <td><em>-</em></td> </tr> <tr> @@ -88,6 +88,18 @@ To get an overview of the true relative speed of the different decomposition, ch </tr> <tr class="alt"> + <td>CompleteOrthogonalDecomposition</td> + <td>-</td> + <td>Fast</td> + <td>Good</td> + <td>Yes</td> + <td>Orthogonalization</td> + <td>Yes</td> + <td>Excellent</td> + <td><em>-</em></td> + </tr> + + <tr> <td>LLT</td> <td>Positive definite</td> <td>Very fast</td> @@ -99,7 +111,7 @@ To get an overview of the true relative speed of the different decomposition, ch <td>Blocking</td> </tr> - <tr> + <tr class="alt"> <td>LDLT</td> <td>Positive or negative semidefinite<sup><a href="#note1">1</a></sup></td> <td>Very fast</td> @@ -114,6 +126,18 @@ To get an overview of the true relative speed of the different decomposition, ch <tr><th class="inter" colspan="9">\n Singular values and eigenvalues decompositions</th></tr> <tr> + <td>BDCSVD (divide \& conquer)</td> + <td>-</td> + <td>One of the fastest SVD algorithms</td> + <td>Excellent</td> + <td>Yes</td> + <td>Singular values/vectors, least squares</td> + <td>Yes (and does least squares)</td> + <td>Excellent</td> + <td>Blocked bidiagonalization</td> + </tr> + + <tr> <td>JacobiSVD (two-sided)</td> <td>-</td> <td>Slow (but fast for small matrices)</td> @@ -248,7 +272,7 @@ To get an overview of the true relative speed of the different decomposition, ch <dt><b>Blocking</b></dt> <dd>Means the algorithm can work per block, whence guaranteeing a good scaling of the performance for large matrices.</dd> <dt><b>Implicit Multi Threading (MT)</b></dt> - <dd>Means the algorithm can take advantage of multicore processors via OpenMP. "Implicit" means the algortihm itself is not parallelized, but that it relies on parallelized matrix-matrix product rountines.</dd> + <dd>Means the algorithm can take advantage of multicore processors via OpenMP. "Implicit" means the algortihm itself is not parallelized, but that it relies on parallelized matrix-matrix product routines.</dd> <dt><b>Explicit Multi Threading (MT)</b></dt> <dd>Means the algorithm is explicitly parallelized to take advantage of multicore processors via OpenMP.</dd> <dt><b>Meta-unroller</b></dt> |