\section{Laplacian\+Kernel Class Reference} \label{classmlpack_1_1kernel_1_1LaplacianKernel}\index{Laplacian\+Kernel@{Laplacian\+Kernel}} The standard Laplacian kernel. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ Laplacian\+Kernel} () \begin{DoxyCompactList}\small\item\em Default constructor; sets bandwidth to 1.\+0. \end{DoxyCompactList}\item \textbf{ Laplacian\+Kernel} (double bandwidth) \begin{DoxyCompactList}\small\item\em Construct the Laplacian kernel with a custom bandwidth. \end{DoxyCompactList}\item double \textbf{ Bandwidth} () const \begin{DoxyCompactList}\small\item\em Get the bandwidth. \end{DoxyCompactList}\item double \& \textbf{ Bandwidth} () \begin{DoxyCompactList}\small\item\em Modify the bandwidth. \end{DoxyCompactList}\item {\footnotesize template$<$typename Vec\+TypeA , typename Vec\+TypeB $>$ }\\double \textbf{ Evaluate} (const Vec\+TypeA \&a, const Vec\+TypeB \&b) const \begin{DoxyCompactList}\small\item\em Evaluation of the Laplacian kernel. \end{DoxyCompactList}\item double \textbf{ Evaluate} (const double t) const \begin{DoxyCompactList}\small\item\em Evaluation of the Laplacian kernel given the distance between two points. \end{DoxyCompactList}\item double \textbf{ Gradient} (const double t) const \begin{DoxyCompactList}\small\item\em Evaluation of the gradient of the Laplacian kernel given the distance between two points. \end{DoxyCompactList}\item {\footnotesize template$<$typename Archive $>$ }\\void \textbf{ serialize} (Archive \&ar, const unsigned int) \begin{DoxyCompactList}\small\item\em Serialize the kernel. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} The standard Laplacian kernel. Given two vectors $ x $, $ y $, and a bandwidth $ \mu $ (set in the constructor), \[ K(x, y) = \exp(-\frac{|| x - y ||}{\mu}). \] The implementation is all in the header file because it is so simple. Definition at line 30 of file laplacian\+\_\+kernel.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_a8bfe7f6ab7ae7fc69ef672bd2a8caec8}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!Laplacian\+Kernel@{Laplacian\+Kernel}} \index{Laplacian\+Kernel@{Laplacian\+Kernel}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{Laplacian\+Kernel()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily \textbf{ Laplacian\+Kernel} (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Default constructor; sets bandwidth to 1.\+0. Definition at line 36 of file laplacian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_adad3af357ff4d5ea13e7a146437bde42}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!Laplacian\+Kernel@{Laplacian\+Kernel}} \index{Laplacian\+Kernel@{Laplacian\+Kernel}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{Laplacian\+Kernel()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily \textbf{ Laplacian\+Kernel} (\begin{DoxyParamCaption}\item[{double}]{bandwidth }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Construct the Laplacian kernel with a custom bandwidth. \begin{DoxyParams}{Parameters} {\em bandwidth} & The bandwidth of the kernel ( $\mu$). \\ \hline \end{DoxyParams} Definition at line 44 of file laplacian\+\_\+kernel.\+hpp. \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_ae9cbd816179d6c36036139ccc8fea8c8}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!Bandwidth@{Bandwidth}} \index{Bandwidth@{Bandwidth}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{Bandwidth()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Bandwidth (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the bandwidth. Definition at line 95 of file laplacian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_a202e9a76b6f5f948e98e68a374ae8ea4}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!Bandwidth@{Bandwidth}} \index{Bandwidth@{Bandwidth}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{Bandwidth()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double\& Bandwidth (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the bandwidth. Definition at line 97 of file laplacian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_a84c3aeba25ea7703bd2d4f85a54301da}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!Evaluate@{Evaluate}} \index{Evaluate@{Evaluate}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{Evaluate()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Evaluate (\begin{DoxyParamCaption}\item[{const Vec\+TypeA \&}]{a, }\item[{const Vec\+TypeB \&}]{b }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluation of the Laplacian kernel. This could be generalized to use any distance metric, not the Euclidean distance, but for now, the Euclidean distance is used. \begin{DoxyTemplParams}{Template Parameters} {\em Vec\+TypeA} & Type of first vector (likely arma\+::vec or arma\+::sp\+\_\+vec). \\ \hline {\em Vec\+TypeB} & Type of second vector (arma\+::vec / arma\+::sp\+\_\+vec). \\ \hline \end{DoxyTemplParams} \begin{DoxyParams}{Parameters} {\em a} & First vector. \\ \hline {\em b} & Second vector. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} K(a, b) using the bandwidth ( $\mu$) specified in the constructor. \end{DoxyReturn} Definition at line 61 of file laplacian\+\_\+kernel.\+hpp. References L\+Metric$<$ T\+Power, T\+Take\+Root $>$\+::\+Evaluate(). \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_a031ed73efe13c6e6bc805006bd249238}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!Evaluate@{Evaluate}} \index{Evaluate@{Evaluate}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{Evaluate()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double Evaluate (\begin{DoxyParamCaption}\item[{const double}]{t }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluation of the Laplacian kernel given the distance between two points. \begin{DoxyParams}{Parameters} {\em t} & The distance between the two points the kernel should be evaluated on. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} K(t) using the bandwidth ( $\mu$) specified in the constructor. \end{DoxyReturn} Definition at line 75 of file laplacian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_a6abdb9c6ceb3252af988ab5fb5f13764}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!Gradient@{Gradient}} \index{Gradient@{Gradient}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{Gradient()} {\footnotesize\ttfamily double Gradient (\begin{DoxyParamCaption}\item[{const double}]{t }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluation of the gradient of the Laplacian kernel given the distance between two points. \begin{DoxyParams}{Parameters} {\em t} & The distance between the two points the kernel should be evaluated on. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} K(t) using the bandwidth ( $\mu$) specified in the constructor. \end{DoxyReturn} Definition at line 90 of file laplacian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1LaplacianKernel_af0dd9205158ccf7bcfcd8ff81f79c927}} \index{mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::kernel\+::\+Laplacian\+Kernel@{mlpack\+::kernel\+::\+Laplacian\+Kernel}} \subsubsection{serialize()} {\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{ar, }\item[{const unsigned}]{int }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Serialize the kernel. Definition at line 101 of file laplacian\+\_\+kernel.\+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.\+0/src/mlpack/core/kernels/\textbf{ laplacian\+\_\+kernel.\+hpp}\end{DoxyCompactItemize}