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bug #1071: improve doc on lpNorm and add example for some operator norms

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Gael Guennebaud
2015-09-28 11:55:36 +02:00
parent 8c1ee3629f
commit 02e940fc9f
3 changed files with 35 additions and 4 deletions
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13
doc/TutorialReductionsVisitorsBroadcasting.dox
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@@ -32,7 +32,7 @@ Eigen also provides the \link MatrixBase::norm() norm() \endlink method, which r
These operations can also operate on matrices; in that case, a n-by-p matrix is seen as a vector of size (n*p), so for example the \link MatrixBase::norm() norm() \endlink method returns the "Frobenius" or "Hilbert-Schmidt" norm. We refrain from speaking of the \f$\ell^2\f$ norm of a matrix because that can mean different things.
If you want other \f$\ell^p\f$ norms, use the \link MatrixBase::lpNorm() lpNorm<p>() \endlink method. The template parameter \a p can take the special value \a Infinity if you want the \f$\ell^\infty\f$ norm, which is the maximum of the absolute values of the coefficients.
If you want other coefficient-wise \f$\ell^p\f$ norms, use the \link MatrixBase::lpNorm() lpNorm<p>() \endlink method. The template parameter \a p can take the special value \a Infinity if you want the \f$\ell^\infty\f$ norm, which is the maximum of the absolute values of the coefficients.
The following example demonstrates these methods.
@@ -45,6 +45,17 @@ The following example demonstrates these methods.
\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.out
</td></tr></table>
\b Operator \b norm: The 1-norm and \f$\infty\f$-norm <a href="https://en.wikipedia.org/wiki/Operator_norm">matrix operator norms</a> can easily be computed as follows:
<table class="example">
<tr><th>Example:</th><th>Output:</th></tr>
<tr><td>
\include Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp
</td>
<td>
\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.out
</td></tr></table>
See below for more explanations on the syntax of these expressions.
\subsection TutorialReductionsVisitorsBroadcastingReductionsBool Boolean reductions
The following reductions operate on boolean values: