\section{L\+Metric$<$ T\+Power, T\+Take\+Root $>$ Class Template Reference} \label{classmlpack_1_1metric_1_1LMetric}\index{L\+Metric$<$ T\+Power, T\+Take\+Root $>$@{L\+Metric$<$ T\+Power, T\+Take\+Root $>$}} The L\+\_\+p metric for arbitrary integer p, with an option to take the root. Inheritance diagram for L\+Metric$<$ T\+Power, T\+Take\+Root $>$\+: \nopagebreak \begin{figure}[H] \begin{center} \leavevmode \includegraphics[width=200pt]{classmlpack_1_1metric_1_1LMetric__inherit__graph} \end{center} \end{figure} \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ L\+Metric} () \begin{DoxyCompactList}\small\item\em Default constructor does nothing, but is required to satisfy the Metric policy. \end{DoxyCompactList}\item {\footnotesize template$<$typename Archive $>$ }\\void \textbf{ serialize} (Archive \&, const unsigned int) \begin{DoxyCompactList}\small\item\em Serialize the metric (nothing to do). \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Static Public Member Functions} \begin{DoxyCompactItemize} \item {\footnotesize template$<$typename Vec\+TypeA , typename Vec\+TypeB $>$ }\\static Vec\+Type\+A\+::elem\+\_\+type \textbf{ Evaluate} (const Vec\+TypeA \&a, const Vec\+TypeB \&b) \begin{DoxyCompactList}\small\item\em Computes the distance between two points. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Static Public Attributes} \begin{DoxyCompactItemize} \item static const int \textbf{ Power} = T\+Power \begin{DoxyCompactList}\small\item\em The power of the metric. \end{DoxyCompactList}\item static const bool \textbf{ Take\+Root} = T\+Take\+Root \begin{DoxyCompactList}\small\item\em Whether or not the root is taken. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} \subsubsection*{template$<$int T\+Power, bool T\+Take\+Root = true$>$\newline class mlpack\+::metric\+::\+L\+Metric$<$ T\+Power, T\+Take\+Root $>$} The L\+\_\+p metric for arbitrary integer p, with an option to take the root. This class implements the standard L\+\_\+p metric for two arbitrary vectors $ x $ and $ y $ of dimensionality $ n $\+: \[ d(x, y) = \left( \sum_{i = 1}^{n} | x_i - y_i |^p \right)^{\frac{1}{p}}. \] The value of p is given as a template parameter. In addition, the function $ d(x, y) $ can be simplified, neglecting the p-\/root calculation. This is done by specifying the Take\+Root template parameter to be false. Then, \[ d(x, y) = \sum_{i = 1}^{n} | x_i - y_i |^p \] It is faster to compute that distance, so Take\+Root is by default off. However, when Take\+Root is false, the distance given is not actually a true metric -- it does not satisfy the triangle inequality. Some mlpack methods do not require the triangle inequality to operate correctly (such as the Binary\+Space\+Tree), but setting Take\+Root = false in some cases will cause incorrect results. A few convenience typedefs are given\+: \begin{DoxyItemize} \item Manhattan\+Distance \item Euclidean\+Distance \item Squared\+Euclidean\+Distance \end{DoxyItemize} \begin{DoxyTemplParams}{Template Parameters} {\em Power} & Power of metric; i.\+e. Power = 1 gives the L1-\/norm (Manhattan distance). \\ \hline {\em Take\+Root} & If true, the Power\textquotesingle{}th root of the result is taken before it is returned. Setting this to false causes the metric to not satisfy the Triangle Inequality (be careful!). \\ \hline \end{DoxyTemplParams} Definition at line 63 of file lmetric.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1metric_1_1LMetric_ad296b4c8538551ddcef38a49d0842ca7}} \index{mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}!L\+Metric@{L\+Metric}} \index{L\+Metric@{L\+Metric}!mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}} \subsubsection{L\+Metric()} {\footnotesize\ttfamily \textbf{ L\+Metric} (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Default constructor does nothing, but is required to satisfy the Metric policy. Definition at line 70 of file lmetric.\+hpp. \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1metric_1_1LMetric_af39380107875eb94f0efef7d37cc57df}} \index{mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}!Evaluate@{Evaluate}} \index{Evaluate@{Evaluate}!mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}} \subsubsection{Evaluate()} {\footnotesize\ttfamily static Vec\+Type\+A\+::elem\+\_\+type Evaluate (\begin{DoxyParamCaption}\item[{const Vec\+TypeA \&}]{a, }\item[{const Vec\+TypeB \&}]{b }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [static]}} Computes the distance between two points. \begin{DoxyTemplParams}{Template Parameters} {\em Vec\+TypeA} & Type of first vector (generally arma\+::vec or arma\+::sp\+\_\+vec). \\ \hline {\em Vec\+TypeB} & Type of second vector. \\ \hline \end{DoxyTemplParams} \begin{DoxyParams}{Parameters} {\em a} & First vector. \\ \hline {\em b} & Second vector. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} Distance between vectors a and b. \end{DoxyReturn} Referenced by Spherical\+Kernel\+::\+Convolution\+Integral(), Gaussian\+Kernel\+::\+Convolution\+Integral(), Spherical\+Kernel\+::\+Evaluate(), Triangular\+Kernel\+::\+Evaluate(), Laplacian\+Kernel\+::\+Evaluate(), Gaussian\+Kernel\+::\+Evaluate(), Cauchy\+Kernel\+::\+Evaluate(), and L\+Metric$<$ T\+Power, true $>$\+::\+L\+Metric(). \mbox{\label{classmlpack_1_1metric_1_1LMetric_aa5b3dd8336182f751ebec27167c22415}} \index{mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}} \subsubsection{serialize()} {\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{, }\item[{const unsigned}]{int }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Serialize the metric (nothing to do). Definition at line 88 of file lmetric.\+hpp. \subsection{Member Data Documentation} \mbox{\label{classmlpack_1_1metric_1_1LMetric_add828b673634e896b13f47cc7fb331f5}} \index{mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}!Power@{Power}} \index{Power@{Power}!mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}} \subsubsection{Power} {\footnotesize\ttfamily const int Power = T\+Power\hspace{0.3cm}{\ttfamily [static]}} The power of the metric. Definition at line 91 of file lmetric.\+hpp. \mbox{\label{classmlpack_1_1metric_1_1LMetric_a0615e7186f9a9847e2f71d2d2622579d}} \index{mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}!Take\+Root@{Take\+Root}} \index{Take\+Root@{Take\+Root}!mlpack\+::metric\+::\+L\+Metric@{mlpack\+::metric\+::\+L\+Metric}} \subsubsection{Take\+Root} {\footnotesize\ttfamily const bool Take\+Root = T\+Take\+Root\hspace{0.3cm}{\ttfamily [static]}} Whether or not the root is taken. Definition at line 93 of file lmetric.\+hpp. The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize} \item /var/www/mlpack.\+ratml.\+org/mlpack.\+org/\+\_\+src/mlpack-\/3.\+3.\+1/src/mlpack/core/metrics/\textbf{ lmetric.\+hpp}\end{DoxyCompactItemize}