diff options
| -rw-r--r-- | Eigen/src/Core/Dot.h | 8 | ||||
| -rw-r--r-- | doc/TutorialReductionsVisitorsBroadcasting.dox | 13 | ||||
| -rw-r--r-- | doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp | 18 |
3 files changed, 35 insertions, 4 deletions
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h index 94b058466..003450f1a 100644 --- a/Eigen/src/Core/Dot.h +++ b/Eigen/src/Core/Dot.h @@ -178,9 +178,11 @@ struct lpNorm_selector<Derived, Infinity> } // end namespace internal -/** \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values - * of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$ - * norm, that is the maximum of the absolute values of the coefficients of *this. +/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values + * of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$ + * norm, that is the maximum of the absolute values of the coefficients of \c *this. + * + * \note For matrices, this function does not compute the <a href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink. * * \sa norm() */ diff --git a/doc/TutorialReductionsVisitorsBroadcasting.dox b/doc/TutorialReductionsVisitorsBroadcasting.dox index eb6787dbc..908a1b4b2 100644 --- a/doc/TutorialReductionsVisitorsBroadcasting.dox +++ b/doc/TutorialReductionsVisitorsBroadcasting.dox @@ -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: diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp new file mode 100644 index 000000000..62e28fc31 --- /dev/null +++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp @@ -0,0 +1,18 @@ +#include <Eigen/Dense> +#include <iostream> + +using namespace Eigen; +using namespace std; + +int main() +{ + MatrixXf m(2,2); + m << 1,-2, + -3,4; + + cout << "1-norm(m) = " << m.cwiseAbs().colwise().sum().maxCoeff() + << " == " << m.colwise().lpNorm<1>().maxCoeff() << endl; + + cout << "infty-norm(m) = " << m.cwiseAbs().rowwise().sum().maxCoeff() + << " == " << m.rowwise().lpNorm<1>().maxCoeff() << endl; +} |