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| -rw-r--r-- | doc/TopicLinearAlgebraDecompositions.dox | 4 | ||||
| -rw-r--r-- | doc/TutorialLinearAlgebra.dox | 26 |
2 files changed, 23 insertions, 7 deletions
diff --git a/doc/TopicLinearAlgebraDecompositions.dox b/doc/TopicLinearAlgebraDecompositions.dox index 77f2c92ab..5bcff2c96 100644 --- a/doc/TopicLinearAlgebraDecompositions.dox +++ b/doc/TopicLinearAlgebraDecompositions.dox @@ -116,7 +116,7 @@ For an introduction on linear solvers and decompositions, check this \link Tutor <td>JacobiSVD (two-sided)</td> <td>-</td> <td>Slow (but fast for small matrices)</td> - <td>Excellent-Proven<sup><a href="#note3">3</a></sup></td> + <td>Proven<sup><a href="#note3">3</a></sup></td> <td>Yes</td> <td>Singular values/vectors, least squares</td> <td>Yes (and does least squares)</td> @@ -132,7 +132,7 @@ For an introduction on linear solvers and decompositions, check this \link Tutor <td>Yes</td> <td>Eigenvalues/vectors</td> <td>-</td> - <td>Good</td> + <td>Excellent</td> <td><em>Closed forms for 2x2 and 3x3</em></td> </tr> diff --git a/doc/TutorialLinearAlgebra.dox b/doc/TutorialLinearAlgebra.dox index e6c41fd70..cb92ceeae 100644 --- a/doc/TutorialLinearAlgebra.dox +++ b/doc/TutorialLinearAlgebra.dox @@ -40,8 +40,9 @@ depending on your matrix and the trade-off you want to make: <tr> <th>Decomposition</th> <th>Method</th> - <th>Requirements on the matrix</th> - <th>Speed</th> + <th>Requirements<br/>on the matrix</th> + <th>Speed<br/> (small-to-medium)</th> + <th>Speed<br/> (large)</th> <th>Accuracy</th> </tr> <tr> @@ -49,6 +50,7 @@ depending on your matrix and the trade-off you want to make: <td>partialPivLu()</td> <td>Invertible</td> <td>++</td> + <td>++</td> <td>+</td> </tr> <tr class="alt"> @@ -56,6 +58,7 @@ depending on your matrix and the trade-off you want to make: <td>fullPivLu()</td> <td>None</td> <td>-</td> + <td>- -</td> <td>+++</td> </tr> <tr> @@ -63,20 +66,23 @@ depending on your matrix and the trade-off you want to make: <td>householderQr()</td> <td>None</td> <td>++</td> + <td>++</td> <td>+</td> </tr> <tr class="alt"> <td>ColPivHouseholderQR</td> <td>colPivHouseholderQr()</td> <td>None</td> - <td>+</td> <td>++</td> + <td>-</td> + <td>+++</td> </tr> <tr> <td>FullPivHouseholderQR</td> <td>fullPivHouseholderQr()</td> <td>None</td> <td>-</td> + <td>- -</td> <td>+++</td> </tr> <tr class="alt"> @@ -84,21 +90,31 @@ depending on your matrix and the trade-off you want to make: <td>llt()</td> <td>Positive definite</td> <td>+++</td> + <td>+++</td> <td>+</td> </tr> <tr> <td>LDLT</td> <td>ldlt()</td> - <td>Positive or negative semidefinite</td> + <td>Positive or negative<br/> semidefinite</td> <td>+++</td> + <td>+</td> <td>++</td> </tr> + <tr class="alt"> + <td>JacobiSVD</td> + <td>jacobiSvd()</td> + <td>None</td> + <td>- -</td> + <td>- - -</td> + <td>+++</td> + </tr> </table> All of these decompositions offer a solve() method that works as in the above example. For example, if your matrix is positive definite, the above table says that a very good -choice is then the LDLT decomposition. Here's an example, also demonstrating that using a general +choice is then the LLT or LDLT decomposition. Here's an example, also demonstrating that using a general matrix (not a vector) as right hand side is possible. <table class="example"> |