\section{Gamma\+Distribution Class Reference} \label{classmlpack_1_1distribution_1_1GammaDistribution}\index{Gamma\+Distribution@{Gamma\+Distribution}} This class represents the Gamma distribution. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ Gamma\+Distribution} (const size\+\_\+t dimensionality=0) \begin{DoxyCompactList}\small\item\em Construct the Gamma distribution with the given number of dimensions (default 0); each parameter will be initialized to 0. \end{DoxyCompactList}\item \textbf{ Gamma\+Distribution} (const arma\+::mat \&data, const double tol=1e-\/8) \begin{DoxyCompactList}\small\item\em Construct the Gamma distribution, training on the given parameters. \end{DoxyCompactList}\item \textbf{ Gamma\+Distribution} (const arma\+::vec \&alpha, const arma\+::vec \&beta) \begin{DoxyCompactList}\small\item\em Construct the Gamma distribution given two vectors alpha and beta. \end{DoxyCompactList}\item \textbf{ $\sim$\+Gamma\+Distribution} () \begin{DoxyCompactList}\small\item\em Destructor. \end{DoxyCompactList}\item double \textbf{ Alpha} (const size\+\_\+t dim) const \begin{DoxyCompactList}\small\item\em Get the alpha parameter of the given dimension. \end{DoxyCompactList}\item double \& \textbf{ Alpha} (const size\+\_\+t dim) \begin{DoxyCompactList}\small\item\em Modify the alpha parameter of the given dimension. \end{DoxyCompactList}\item double \textbf{ Beta} (const size\+\_\+t dim) const \begin{DoxyCompactList}\small\item\em Get the beta parameter of the given dimension. \end{DoxyCompactList}\item double \& \textbf{ Beta} (const size\+\_\+t dim) \begin{DoxyCompactList}\small\item\em Modify the beta parameter of the given dimension. \end{DoxyCompactList}\item size\+\_\+t \textbf{ Dimensionality} () const \begin{DoxyCompactList}\small\item\em Get the dimensionality of the distribution. \end{DoxyCompactList}\item void \textbf{ Log\+Probability} (const arma\+::mat \&observations, arma\+::vec \&log\+Probabilities) const \begin{DoxyCompactList}\small\item\em This function returns the logarithm of the probability of a group of observations. \end{DoxyCompactList}\item double \textbf{ Log\+Probability} (double x, const size\+\_\+t dim) const \begin{DoxyCompactList}\small\item\em This function returns the logarithm of the probability of a single observation. \end{DoxyCompactList}\item void \textbf{ Probability} (const arma\+::mat \&observations, arma\+::vec \&probabilities) const \begin{DoxyCompactList}\small\item\em This function returns the probability of a group of observations. \end{DoxyCompactList}\item double \textbf{ Probability} (double x, const size\+\_\+t dim) const \begin{DoxyCompactList}\small\item\em This is a shortcut to the Probability(arma\+::mat\&, arma\+::vec\&) function for when we want to evaluate only the probability of one dimension of the gamma. \end{DoxyCompactList}\item arma\+::vec \textbf{ Random} () const \begin{DoxyCompactList}\small\item\em This function returns an observation of this distribution. \end{DoxyCompactList}\item void \textbf{ Train} (const arma\+::mat \&rdata, const double tol=1e-\/8) \begin{DoxyCompactList}\small\item\em This function trains (fits distribution parameters) to new data or the dataset the object owns. \end{DoxyCompactList}\item void \textbf{ Train} (const arma\+::mat \&observations, const arma\+::vec \&probabilities, const double tol=1e-\/8) \begin{DoxyCompactList}\small\item\em Fits an alpha and beta parameter according to observation probabilities. \end{DoxyCompactList}\item void \textbf{ Train} (const arma\+::vec \&log\+Meanx\+Vec, const arma\+::vec \&mean\+Logx\+Vec, const arma\+::vec \&meanx\+Vec, const double tol=1e-\/8) \begin{DoxyCompactList}\small\item\em This function trains (fits distribution parameters) to a dataset with pre-\/computed statistics log\+Meanx, mean\+Logx, meanx for each dimension. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Detailed Description} This class represents the Gamma distribution. It supports training a Gamma distribution on a given dataset and accessing the fitted alpha and beta parameters. This class supports multidimensional Gamma distributions; however, it is assumed that each dimension is independent; therefore, a multidimensional Gamma distribution here may be seen as a set of independent single-\/dimensional Gamma distributions---and the parameters are estimated under this assumption. The estimation algorithm used can be found in the following paper\+: \begin{DoxyCode} @techreport\{minka2002estimating, title=\{Estimating a \{G\}amma distribution\}, author=\{Minka, Thomas P.\}, institution=\{Microsoft Research\}, address=\{Cambridge, U.K.\}, year=\{2002\} \} \end{DoxyCode} Definition at line 52 of file gamma\+\_\+distribution.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_aad5c9deb1c53fda3075ce214ec9f68c2}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Gamma\+Distribution@{Gamma\+Distribution}} \index{Gamma\+Distribution@{Gamma\+Distribution}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Gamma\+Distribution()\hspace{0.1cm}{\footnotesize\ttfamily [1/3]}} {\footnotesize\ttfamily \textbf{ Gamma\+Distribution} (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dimensionality = {\ttfamily 0} }\end{DoxyParamCaption})} Construct the Gamma distribution with the given number of dimensions (default 0); each parameter will be initialized to 0. \begin{DoxyParams}{Parameters} {\em dimensionality} & Number of dimensions. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_ae89433aa9673a783c3da50e1c8370def}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Gamma\+Distribution@{Gamma\+Distribution}} \index{Gamma\+Distribution@{Gamma\+Distribution}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Gamma\+Distribution()\hspace{0.1cm}{\footnotesize\ttfamily [2/3]}} {\footnotesize\ttfamily \textbf{ Gamma\+Distribution} (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{data, }\item[{const double}]{tol = {\ttfamily 1e-\/8} }\end{DoxyParamCaption})} Construct the Gamma distribution, training on the given parameters. \begin{DoxyParams}{Parameters} {\em data} & Data to train the distribution on. \\ \hline {\em tol} & Convergence tolerance. This is {\itshape not} an absolute measure\+: It will stop the approximation once the {\itshape change} in the value is smaller than tol. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a9267054c34f06ce056eb9e1e76334199}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Gamma\+Distribution@{Gamma\+Distribution}} \index{Gamma\+Distribution@{Gamma\+Distribution}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Gamma\+Distribution()\hspace{0.1cm}{\footnotesize\ttfamily [3/3]}} {\footnotesize\ttfamily \textbf{ Gamma\+Distribution} (\begin{DoxyParamCaption}\item[{const arma\+::vec \&}]{alpha, }\item[{const arma\+::vec \&}]{beta }\end{DoxyParamCaption})} Construct the Gamma distribution given two vectors alpha and beta. \begin{DoxyParams}{Parameters} {\em alpha} & The vector of alphas, one per dimension. \\ \hline {\em beta} & The vector of betas, one per dimension. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a3dfc2487502db9fd91b7a16a44f0014e}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!````~Gamma\+Distribution@{$\sim$\+Gamma\+Distribution}} \index{````~Gamma\+Distribution@{$\sim$\+Gamma\+Distribution}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{$\sim$\+Gamma\+Distribution()} {\footnotesize\ttfamily $\sim$\textbf{ Gamma\+Distribution} (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Destructor. Definition at line 84 of file gamma\+\_\+distribution.\+hpp. References Gamma\+Distribution\+::\+Log\+Probability(), Gamma\+Distribution\+::\+Probability(), Gamma\+Distribution\+::\+Random(), and Gamma\+Distribution\+::\+Train(). \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_ab0770061da842c3d1ef78b6c13d6b324}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Alpha@{Alpha}} \index{Alpha@{Alpha}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Alpha()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Alpha (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dim }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the alpha parameter of the given dimension. Definition at line 197 of file gamma\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_af677766dff71e1394fb7531aa73ec755}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Alpha@{Alpha}} \index{Alpha@{Alpha}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Alpha()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double\& Alpha (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dim }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the alpha parameter of the given dimension. Definition at line 199 of file gamma\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a4a58618c95fbb488db0201f02d722d17}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Beta@{Beta}} \index{Beta@{Beta}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Beta()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Beta (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dim }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the beta parameter of the given dimension. Definition at line 202 of file gamma\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_aca929e6fd58776c990e0a59545283e4f}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Beta@{Beta}} \index{Beta@{Beta}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Beta()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double\& Beta (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dim }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the beta parameter of the given dimension. Definition at line 204 of file gamma\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a78eda6bfb9e9462afa0fc85e32abe1af}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Dimensionality@{Dimensionality}} \index{Dimensionality@{Dimensionality}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Dimensionality()} {\footnotesize\ttfamily size\+\_\+t Dimensionality (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the dimensionality of the distribution. Definition at line 207 of file gamma\+\_\+distribution.\+hpp. \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a10aa8675001ec75323be892d23b4a2cb}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Log\+Probability@{Log\+Probability}} \index{Log\+Probability@{Log\+Probability}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Log\+Probability()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily void Log\+Probability (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{observations, }\item[{arma\+::vec \&}]{log\+Probabilities }\end{DoxyParamCaption}) const} This function returns the logarithm of the probability of a group of observations. The logarithm of the probability of a value x is \[ \log(\frac{x^{(\alpha - 1)}}{\Gamma(\alpha) \beta^\alpha} e^ {-\frac{x}{\beta}}) \] for one dimension. This implementation assumes each dimension is independent, so the product rule is used. \begin{DoxyParams}{Parameters} {\em observations} & Matrix of observations, one per column. \\ \hline {\em log\+Probabilities} & Column vector of log probabilities, one per observation. \\ \hline \end{DoxyParams} Referenced by Gamma\+Distribution\+::$\sim$\+Gamma\+Distribution(). \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a61f67c6ba839aa711f4eb108b31dfc56}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Log\+Probability@{Log\+Probability}} \index{Log\+Probability@{Log\+Probability}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Log\+Probability()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double Log\+Probability (\begin{DoxyParamCaption}\item[{double}]{x, }\item[{const size\+\_\+t}]{dim }\end{DoxyParamCaption}) const} This function returns the logarithm of the probability of a single observation. \begin{DoxyParams}{Parameters} {\em x} & The 1-\/dimensional observation. \\ \hline {\em dim} & The dimension for which to calculate the probability. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_aea9691b5cbbb57e28db1de846a50b44e}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Probability@{Probability}} \index{Probability@{Probability}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Probability()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily void Probability (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{observations, }\item[{arma\+::vec \&}]{probabilities }\end{DoxyParamCaption}) const} This function returns the probability of a group of observations. The probability of the value x is \[ \frac{x^{(\alpha - 1)}}{\Gamma(\alpha) \beta^\alpha} e^{-\frac{x}{\beta}} \] for one dimension. This implementation assumes each dimension is independent, so the product rule is used. \begin{DoxyParams}{Parameters} {\em observations} & Matrix of observations, one per column. \\ \hline {\em probabilities} & Column vector of probabilities, one per observation. \\ \hline \end{DoxyParams} Referenced by Gamma\+Distribution\+::$\sim$\+Gamma\+Distribution(). \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a6f2d582a78ea604f0c682f81932ad539}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Probability@{Probability}} \index{Probability@{Probability}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Probability()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double Probability (\begin{DoxyParamCaption}\item[{double}]{x, }\item[{const size\+\_\+t}]{dim }\end{DoxyParamCaption}) const} This is a shortcut to the Probability(arma\+::mat\&, arma\+::vec\&) function for when we want to evaluate only the probability of one dimension of the gamma. \begin{DoxyParams}{Parameters} {\em x} & The 1-\/dimensional observation. \\ \hline {\em dim} & The dimension for which to calculate the probability. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a2c6f8d5bb4eacf7de767d2172b320756}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Random@{Random}} \index{Random@{Random}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Random()} {\footnotesize\ttfamily arma\+::vec Random (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const} This function returns an observation of this distribution. Referenced by Gamma\+Distribution\+::$\sim$\+Gamma\+Distribution(). \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_aa026c530ceb9b6eb76ffe66dcb8d257b}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Train@{Train}} \index{Train@{Train}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Train()\hspace{0.1cm}{\footnotesize\ttfamily [1/3]}} {\footnotesize\ttfamily void Train (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{rdata, }\item[{const double}]{tol = {\ttfamily 1e-\/8} }\end{DoxyParamCaption})} This function trains (fits distribution parameters) to new data or the dataset the object owns. \begin{DoxyParams}{Parameters} {\em rdata} & Reference data to fit parameters to. \\ \hline {\em tol} & Convergence tolerance. This is {\itshape not} an absolute measure\+: It will stop the approximation once the {\itshape change} in the value is smaller than tol. \\ \hline \end{DoxyParams} Referenced by Gamma\+Distribution\+::$\sim$\+Gamma\+Distribution(). \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a7585f30a098bb6b0ceac0ede43255eba}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Train@{Train}} \index{Train@{Train}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Train()\hspace{0.1cm}{\footnotesize\ttfamily [2/3]}} {\footnotesize\ttfamily void Train (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{observations, }\item[{const arma\+::vec \&}]{probabilities, }\item[{const double}]{tol = {\ttfamily 1e-\/8} }\end{DoxyParamCaption})} Fits an alpha and beta parameter according to observation probabilities. This method is not yet implemented. \begin{DoxyParams}{Parameters} {\em observations} & The reference data, one observation per column. \\ \hline {\em probabilities} & The probability of each observation. One value per column of the observations matrix. \\ \hline {\em tol} & Convergence tolerance. This is {\itshape not} an absolute measure\+: It will stop the approximation once the {\itshape change} in the value is smaller than tol. \\ \hline \end{DoxyParams} \mbox{\label{classmlpack_1_1distribution_1_1GammaDistribution_a6999bb3e85b101307b6c28d12aae0b4d}} \index{mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}!Train@{Train}} \index{Train@{Train}!mlpack\+::distribution\+::\+Gamma\+Distribution@{mlpack\+::distribution\+::\+Gamma\+Distribution}} \subsubsection{Train()\hspace{0.1cm}{\footnotesize\ttfamily [3/3]}} {\footnotesize\ttfamily void Train (\begin{DoxyParamCaption}\item[{const arma\+::vec \&}]{log\+Meanx\+Vec, }\item[{const arma\+::vec \&}]{mean\+Logx\+Vec, }\item[{const arma\+::vec \&}]{meanx\+Vec, }\item[{const double}]{tol = {\ttfamily 1e-\/8} }\end{DoxyParamCaption})} This function trains (fits distribution parameters) to a dataset with pre-\/computed statistics log\+Meanx, mean\+Logx, meanx for each dimension. \begin{DoxyParams}{Parameters} {\em log\+Meanx\+Vec} & Is each dimension\textquotesingle{}s logarithm of the mean (log(mean(x))). \\ \hline {\em mean\+Logx\+Vec} & Is each dimension\textquotesingle{}s mean of logarithms (mean(log(x))). \\ \hline {\em meanx\+Vec} & Is each dimension\textquotesingle{}s mean (mean(x)). \\ \hline {\em tol} & Convergence tolerance. This is {\itshape not} an absolute measure\+: It will stop the approximation once the {\itshape change} in the value is smaller than tol. \\ \hline \end{DoxyParams} 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/dists/\textbf{ gamma\+\_\+distribution.\+hpp}\end{DoxyCompactItemize}