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Update decompositions tables

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This commit is contained in:
Gael Guennebaud 2014-06-17 09:37:07 +02:00
parent b0979b8598
commit 95ecd582a3
2 changed files with 23 additions and 7 deletions
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4
doc/TopicLinearAlgebraDecompositions.dox
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@ -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>

26
doc/TutorialLinearAlgebra.dox
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@ -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">