\section{Epanechnikov\+Kernel Class Reference} \label{classmlpack_1_1kernel_1_1EpanechnikovKernel}\index{Epanechnikov\+Kernel@{Epanechnikov\+Kernel}} The Epanechnikov kernel, defined as. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ Epanechnikov\+Kernel} (const double bandwidth=1.\+0) \begin{DoxyCompactList}\small\item\em Instantiate the Epanechnikov kernel with the given bandwidth (default 1.\+0). \end{DoxyCompactList}\item {\footnotesize template$<$typename Vec\+TypeA , typename Vec\+TypeB $>$ }\\double \textbf{ Convolution\+Integral} (const Vec\+TypeA \&a, const Vec\+TypeB \&b) \begin{DoxyCompactList}\small\item\em Obtains the convolution integral [integral of K($\vert$$\vert$x-\/a$\vert$$\vert$) K($\vert$$\vert$b-\/x$\vert$$\vert$) dx] for the two vectors. \end{DoxyCompactList}\item {\footnotesize template$<$typename Vec\+TypeA , typename Vec\+TypeB $>$ }\\double \textbf{ Evaluate} (const Vec\+TypeA \&a, const Vec\+TypeB \&b) const \begin{DoxyCompactList}\small\item\em Evaluate the Epanechnikov kernel on the given two inputs. \end{DoxyCompactList}\item double \textbf{ Evaluate} (const double distance) const \begin{DoxyCompactList}\small\item\em Evaluate the Epanechnikov kernel given that the distance between the two input points is known. \end{DoxyCompactList}\item double \textbf{ Gradient} (const double distance) const \begin{DoxyCompactList}\small\item\em Evaluate the Gradient of Epanechnikov kernel given that the distance between the two input points is known. \end{DoxyCompactList}\item double \textbf{ Gradient\+For\+Squared\+Distance} (const double distance\+Squared) const \begin{DoxyCompactList}\small\item\em Evaluate the Gradient of Epanechnikov kernel given that the squared distance between the two input points is known. \end{DoxyCompactList}\item double \textbf{ Normalizer} (const size\+\_\+t dimension) \begin{DoxyCompactList}\small\item\em Compute the normalizer of this Epanechnikov kernel for the given dimension. \end{DoxyCompactList}\item {\footnotesize template$<$typename Archive $>$ }\\void \textbf{ serialize} (Archive \&ar, const unsigned int version) \begin{DoxyCompactList}\small\item\em Serialize the kernel. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} The Epanechnikov kernel, defined as. \[ K(x, y) = \max \{0, 1 - || x - y ||^2_2 / b^2 \} \] where $ b $ is the bandwidth the of the kernel (defaults to 1.\+0). Definition at line 30 of file epanechnikov\+\_\+kernel.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_ad3880022e464ae367ed9b7342f0cdf37}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!Epanechnikov\+Kernel@{Epanechnikov\+Kernel}} \index{Epanechnikov\+Kernel@{Epanechnikov\+Kernel}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}} \subsubsection{Epanechnikov\+Kernel()} {\footnotesize\ttfamily \textbf{ Epanechnikov\+Kernel} (\begin{DoxyParamCaption}\item[{const double}]{bandwidth = {\ttfamily 1.0} }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Instantiate the Epanechnikov kernel with the given bandwidth (default 1.\+0). \begin{DoxyParams}{Parameters} {\em bandwidth} & Bandwidth of the kernel. \\ \hline \end{DoxyParams} Definition at line 38 of file epanechnikov\+\_\+kernel.\+hpp. References Epanechnikov\+Kernel\+::\+Convolution\+Integral(), Epanechnikov\+Kernel\+::\+Evaluate(), Epanechnikov\+Kernel\+::\+Gradient(), Epanechnikov\+Kernel\+::\+Gradient\+For\+Squared\+Distance(), Epanechnikov\+Kernel\+::\+Normalizer(), and Epanechnikov\+Kernel\+::serialize(). \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_af3077f924263d1932950f4f7176c93eb}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!Convolution\+Integral@{Convolution\+Integral}} \index{Convolution\+Integral@{Convolution\+Integral}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}} \subsubsection{Convolution\+Integral()} {\footnotesize\ttfamily double Convolution\+Integral (\begin{DoxyParamCaption}\item[{const Vec\+TypeA \&}]{a, }\item[{const Vec\+TypeB \&}]{b }\end{DoxyParamCaption})} Obtains the convolution integral [integral of K($\vert$$\vert$x-\/a$\vert$$\vert$) K($\vert$$\vert$b-\/x$\vert$$\vert$) dx] for the two vectors. \begin{DoxyTemplParams}{Template Parameters} {\em Vec\+Type} & Type of vector (arma\+::vec, arma\+::spvec should be expected). \\ \hline \end{DoxyTemplParams} \begin{DoxyParams}{Parameters} {\em a} & First vector. \\ \hline {\em b} & Second vector. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} the convolution integral value. \end{DoxyReturn} Referenced by Epanechnikov\+Kernel\+::\+Epanechnikov\+Kernel(). \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_a84c3aeba25ea7703bd2d4f85a54301da}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!Evaluate@{Evaluate}} \index{Evaluate@{Evaluate}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+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} Evaluate the Epanechnikov kernel on the given two inputs. \begin{DoxyTemplParams}{Template Parameters} {\em Vec\+TypeA} & Type of first vector. \\ \hline {\em Vec\+TypeB} & Type of second vector. \\ \hline \end{DoxyTemplParams} \begin{DoxyParams}{Parameters} {\em a} & One input vector. \\ \hline {\em b} & The other input vector. \\ \hline \end{DoxyParams} Referenced by Epanechnikov\+Kernel\+::\+Epanechnikov\+Kernel(). \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_a5602dee5d3ad98a183b9a11d9e0ed225}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!Evaluate@{Evaluate}} \index{Evaluate@{Evaluate}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}} \subsubsection{Evaluate()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double Evaluate (\begin{DoxyParamCaption}\item[{const double}]{distance }\end{DoxyParamCaption}) const} Evaluate the Epanechnikov kernel given that the distance between the two input points is known. \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_ac83f017e98c3f23c603fb26b50b82cfd}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!Gradient@{Gradient}} \index{Gradient@{Gradient}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}} \subsubsection{Gradient()} {\footnotesize\ttfamily double Gradient (\begin{DoxyParamCaption}\item[{const double}]{distance }\end{DoxyParamCaption}) const} Evaluate the Gradient of Epanechnikov kernel given that the distance between the two input points is known. Referenced by Epanechnikov\+Kernel\+::\+Epanechnikov\+Kernel(). \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_aa993982e3ab29e7c8a299012dbe42cc5}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!Gradient\+For\+Squared\+Distance@{Gradient\+For\+Squared\+Distance}} \index{Gradient\+For\+Squared\+Distance@{Gradient\+For\+Squared\+Distance}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}} \subsubsection{Gradient\+For\+Squared\+Distance()} {\footnotesize\ttfamily double Gradient\+For\+Squared\+Distance (\begin{DoxyParamCaption}\item[{const double}]{distance\+Squared }\end{DoxyParamCaption}) const} Evaluate the Gradient of Epanechnikov kernel given that the squared distance between the two input points is known. Referenced by Epanechnikov\+Kernel\+::\+Epanechnikov\+Kernel(). \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_aa500736f2a5dac08fa9027543c2b05cb}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!Normalizer@{Normalizer}} \index{Normalizer@{Normalizer}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}} \subsubsection{Normalizer()} {\footnotesize\ttfamily double Normalizer (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dimension }\end{DoxyParamCaption})} Compute the normalizer of this Epanechnikov kernel for the given dimension. \begin{DoxyParams}{Parameters} {\em dimension} & Dimension to calculate the normalizer for. \\ \hline \end{DoxyParams} Referenced by Epanechnikov\+Kernel\+::\+Epanechnikov\+Kernel(). \mbox{\label{classmlpack_1_1kernel_1_1EpanechnikovKernel_a68e832cb064e3b7ca978d8e5911cf700}} \index{mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::kernel\+::\+Epanechnikov\+Kernel@{mlpack\+::kernel\+::\+Epanechnikov\+Kernel}} \subsubsection{serialize()} {\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{ar, }\item[{const unsigned int}]{version }\end{DoxyParamCaption})} Serialize the kernel. Referenced by Epanechnikov\+Kernel\+::\+Epanechnikov\+Kernel(). 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{ epanechnikov\+\_\+kernel.\+hpp}\end{DoxyCompactItemize}