\section{mlpack\+:\+:math Namespace Reference} \label{namespacemlpack_1_1math}\index{mlpack\+::math@{mlpack\+::math}} Miscellaneous math routines. \subsection*{Classes} \begin{DoxyCompactItemize} \item class \textbf{ Columns\+To\+Blocks} \begin{DoxyCompactList}\small\item\em Transform the columns of the given matrix into a block format. \end{DoxyCompactList}\item class \textbf{ Range\+Type} \begin{DoxyCompactList}\small\item\em Simple real-\/valued range. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Typedefs} \begin{DoxyCompactItemize} \item typedef \textbf{ Range\+Type}$<$ double $>$ \textbf{ Range} \begin{DoxyCompactList}\small\item\em 3.\+0.\+0 T\+O\+DO\+: break reverse-\/compatibility by changing \doxyref{Range\+Type}{p.}{classmlpack_1_1math_1_1RangeType} to Range. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Functions} \begin{DoxyCompactItemize} \item {\footnotesize template$<$typename T $>$ }\\T\+::elem\+\_\+type \textbf{ Accu\+Log} (const T \&x) \begin{DoxyCompactList}\small\item\em Sum a vector of log values. \end{DoxyCompactList}\item void \textbf{ Center} (const arma\+::mat \&x, arma\+::mat \&x\+Centered) \begin{DoxyCompactList}\small\item\em Creates a centered matrix, where centering is done by subtracting the sum over the columns (a column vector) from each column of the matrix. \end{DoxyCompactList}\item double \textbf{ Clamp\+Non\+Negative} (const double d) \begin{DoxyCompactList}\small\item\em Forces a number to be non-\/negative, turning negative numbers into zero. \end{DoxyCompactList}\item double \textbf{ Clamp\+Non\+Positive} (const double d) \begin{DoxyCompactList}\small\item\em Forces a number to be non-\/positive, turning positive numbers into zero. \end{DoxyCompactList}\item double \textbf{ Clamp\+Range} (double value, const double range\+Min, const double range\+Max) \begin{DoxyCompactList}\small\item\em Clamp a number between a particular range. \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\void \textbf{ Clear\+Alias} (arma\+::\+Mat$<$ Elem\+Type $>$ \&mat) \begin{DoxyCompactList}\small\item\em Clear an alias so that no data is overwritten. \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\void \textbf{ Clear\+Alias} (arma\+::\+Sp\+Mat$<$ Elem\+Type $>$ \&) \begin{DoxyCompactList}\small\item\em Clear an alias for a sparse matrix. \end{DoxyCompactList}\item {\footnotesize template$<$typename eT $>$ }\\arma\+::\+Mat$<$ eT $>$ \textbf{ Column\+Covariance} (const arma\+::\+Mat$<$ eT $>$ \&A, const size\+\_\+t norm\+\_\+type=0) \item {\footnotesize template$<$typename T $>$ }\\arma\+::\+Mat$<$ std\+::complex$<$ T $>$ $>$ \textbf{ Column\+Covariance} (const arma\+::\+Mat$<$ std\+::complex$<$ T $>$ $>$ \&A, const size\+\_\+t norm\+\_\+type=0) \item void \textbf{ Custom\+Random\+Seed} (const size\+\_\+t seed) \item void \textbf{ Fixed\+Random\+Seed} () \begin{DoxyCompactList}\small\item\em Set the random seed to a fixed number. \end{DoxyCompactList}\item {\footnotesize template$<$typename T $>$ }\\T \textbf{ Log\+Add} (T x, T y) \begin{DoxyCompactList}\small\item\em Internal log-\/addition. \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\arma\+::\+Cube$<$ Elem\+Type $>$ \textbf{ Make\+Alias} (arma\+::\+Cube$<$ Elem\+Type $>$ \&input, const bool strict=true) \begin{DoxyCompactList}\small\item\em Make an alias of a dense cube. \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\arma\+::\+Mat$<$ Elem\+Type $>$ \textbf{ Make\+Alias} (arma\+::\+Mat$<$ Elem\+Type $>$ \&input, const bool strict=true) \begin{DoxyCompactList}\small\item\em Make an alias of a dense matrix. \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\arma\+::\+Row$<$ Elem\+Type $>$ \textbf{ Make\+Alias} (arma\+::\+Row$<$ Elem\+Type $>$ \&input, const bool strict=true) \begin{DoxyCompactList}\small\item\em Make an alias of a dense row. \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\arma\+::\+Col$<$ Elem\+Type $>$ \textbf{ Make\+Alias} (arma\+::\+Col$<$ Elem\+Type $>$ \&input, const bool strict=true) \begin{DoxyCompactList}\small\item\em Make an alias of a dense column. \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\arma\+::\+Sp\+Mat$<$ Elem\+Type $>$ \textbf{ Make\+Alias} (const arma\+::\+Sp\+Mat$<$ Elem\+Type $>$ \&input, const bool=true) \begin{DoxyCompactList}\small\item\em Make a copy of a sparse matrix (an alias is not possible). \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\arma\+::\+Sp\+Row$<$ Elem\+Type $>$ \textbf{ Make\+Alias} (const arma\+::\+Sp\+Row$<$ Elem\+Type $>$ \&input, const bool=true) \begin{DoxyCompactList}\small\item\em Make a copy of a sparse row (an alias is not possible). \end{DoxyCompactList}\item {\footnotesize template$<$typename Elem\+Type $>$ }\\arma\+::\+Sp\+Col$<$ Elem\+Type $>$ \textbf{ Make\+Alias} (const arma\+::\+Sp\+Col$<$ Elem\+Type $>$ \&input, const bool=true) \begin{DoxyCompactList}\small\item\em Make a copy of a sparse column (an alias is not possible). \end{DoxyCompactList}\item {\footnotesize template$<$typename Cube\+Type $>$ }\\Cube\+Type \textbf{ Multiply\+Cube2\+Cube} (const Cube\+Type \&cubeA, const Cube\+Type \&cubeB, const bool a\+Transpose=false, const bool b\+Transpose=false) \begin{DoxyCompactList}\small\item\em Matrix multiplication of slices of two cubes. \end{DoxyCompactList}\item {\footnotesize template$<$typename Cube\+Type , typename Mat\+Type $>$ }\\Cube\+Type \textbf{ Multiply\+Cube2\+Mat} (const Cube\+Type \&cubeA, const Mat\+Type \&matB, const bool a\+Transpose=false, const bool b\+Transpose=false) \begin{DoxyCompactList}\small\item\em Matrix multiplication of all slices of a cube with a matrix. \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type , typename Cube\+Type $>$ }\\Cube\+Type \textbf{ Multiply\+Mat2\+Cube} (const Mat\+Type \&matA, const Cube\+Type \&cubeB, const bool a\+Transpose=false, const bool b\+Transpose=false) \begin{DoxyCompactList}\small\item\em Matrix multiplication of a matrix and all the slices of a cube. \end{DoxyCompactList}\item void \textbf{ Obtain\+Distinct\+Samples} (const size\+\_\+t lo\+Inclusive, const size\+\_\+t hi\+Exclusive, const size\+\_\+t max\+Num\+Samples, arma\+::uvec \&distinct\+Samples) \begin{DoxyCompactList}\small\item\em Obtains no more than max\+Num\+Samples distinct samples. \end{DoxyCompactList}\item void \textbf{ Orthogonalize} (const arma\+::mat \&x, arma\+::mat \&W) \begin{DoxyCompactList}\small\item\em Orthogonalize x and return the result in W, using eigendecomposition. \end{DoxyCompactList}\item void \textbf{ Orthogonalize} (arma\+::mat \&x) \begin{DoxyCompactList}\small\item\em Orthogonalize x in-\/place. \end{DoxyCompactList}\item double \textbf{ Rand\+Bernoulli} (const double input) \begin{DoxyCompactList}\small\item\em Generates a 0/1 specified by the input. \end{DoxyCompactList}\item int \textbf{ Rand\+Int} (const int hi\+Exclusive) \begin{DoxyCompactList}\small\item\em Generates a uniform random integer. \end{DoxyCompactList}\item int \textbf{ Rand\+Int} (const int lo, const int hi\+Exclusive) \begin{DoxyCompactList}\small\item\em Generates a uniform random integer. \end{DoxyCompactList}\item double \textbf{ Rand\+Normal} () \begin{DoxyCompactList}\small\item\em Generates a normally distributed random number with mean 0 and variance 1. \end{DoxyCompactList}\item double \textbf{ Rand\+Normal} (const double mean, const double variance) \begin{DoxyCompactList}\small\item\em Generates a normally distributed random number with specified mean and variance. \end{DoxyCompactList}\item double \textbf{ Random} () \begin{DoxyCompactList}\small\item\em Generates a uniform random number between 0 and 1. \end{DoxyCompactList}\item double \textbf{ Random} (const double lo, const double hi) \begin{DoxyCompactList}\small\item\em Generates a uniform random number in the specified range. \end{DoxyCompactList}\item void \textbf{ Random\+Basis} (arma\+::mat \&basis, const size\+\_\+t d) \begin{DoxyCompactList}\small\item\em Create a random d-\/dimensional orthogonal basis, storing it in the given matrix. \end{DoxyCompactList}\item void \textbf{ Random\+Seed} (const size\+\_\+t seed) \begin{DoxyCompactList}\small\item\em Set the random seed used by the random functions (\doxyref{Random()}{p.}{namespacemlpack_1_1math_a305db122ade561ba1fe874bd51e9797d} and \doxyref{Rand\+Int()}{p.}{namespacemlpack_1_1math_aad090ac225728d74c1b66bcf52f3ab95}). \end{DoxyCompactList}\item void \textbf{ Rand\+Vector} (arma\+::vec \&v) \begin{DoxyCompactList}\small\item\em Overwrites a dimension-\/N vector to a random vector on the unit sphere in R$^\wedge$N. \end{DoxyCompactList}\item void \textbf{ Remove\+Rows} (const arma\+::mat \&input, const std\+::vector$<$ size\+\_\+t $>$ \&rows\+To\+Remove, arma\+::mat \&output) \begin{DoxyCompactList}\small\item\em Remove a certain set of rows in a matrix while copying to a second matrix. \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type , typename Labels\+Type $>$ }\\void \textbf{ Shuffle\+Data} (const Mat\+Type \&input\+Points, const Labels\+Type \&input\+Labels, Mat\+Type \&output\+Points, Labels\+Type \&output\+Labels, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$=0, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$=0) \begin{DoxyCompactList}\small\item\em Shuffle a dataset and associated labels (or responses). \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type , typename Labels\+Type $>$ }\\void \textbf{ Shuffle\+Data} (const Mat\+Type \&input\+Points, const Labels\+Type \&input\+Labels, Mat\+Type \&output\+Points, Labels\+Type \&output\+Labels, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$=0, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$=0) \begin{DoxyCompactList}\small\item\em Shuffle a sparse dataset and associated labels (or responses). \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type , typename Labels\+Type $>$ }\\void \textbf{ Shuffle\+Data} (const Mat\+Type \&input\+Points, const Labels\+Type \&input\+Labels, Mat\+Type \&output\+Points, Labels\+Type \&output\+Labels, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$=0, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$=0, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Cube$<$ Labels\+Type $>$\+::value $>$ $\ast$=0) \begin{DoxyCompactList}\small\item\em Shuffle a cube-\/shaped dataset and associated labels (or responses) which are also cube-\/shaped. \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type , typename Labels\+Type , typename Weights\+Type $>$ }\\void \textbf{ Shuffle\+Data} (const Mat\+Type \&input\+Points, const Labels\+Type \&input\+Labels, const Weights\+Type \&input\+Weights, Mat\+Type \&output\+Points, Labels\+Type \&output\+Labels, Weights\+Type \&output\+Weights, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$=0, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$=0) \begin{DoxyCompactList}\small\item\em Shuffle a dataset and associated labels (or responses) and weights. \end{DoxyCompactList}\item {\footnotesize template$<$typename Mat\+Type , typename Labels\+Type , typename Weights\+Type $>$ }\\void \textbf{ Shuffle\+Data} (const Mat\+Type \&input\+Points, const Labels\+Type \&input\+Labels, const Weights\+Type \&input\+Weights, Mat\+Type \&output\+Points, Labels\+Type \&output\+Labels, Weights\+Type \&output\+Weights, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$=0, const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$=0) \begin{DoxyCompactList}\small\item\em Shuffle a sparse dataset and associated labels (or responses) and weights. \end{DoxyCompactList}\item {\footnotesize template$<$typename T $>$ }\\T \textbf{ Sign} (const T x) \begin{DoxyCompactList}\small\item\em Signum function. \end{DoxyCompactList}\item void \textbf{ Smat} (const arma\+::vec \&input, arma\+::mat \&output) \begin{DoxyCompactList}\small\item\em The inverse of Svec. \end{DoxyCompactList}\item void \textbf{ Svec} (const arma\+::mat \&input, arma\+::vec \&output) \begin{DoxyCompactList}\small\item\em Upper triangular representation of a symmetric matrix, scaled such that, dot(Svec(\+A), Svec(\+B)) == dot(\+A, B) for symmetric A, B. \end{DoxyCompactList}\item void \textbf{ Svec} (const arma\+::sp\+\_\+mat \&input, arma\+::sp\+\_\+vec \&output) \item size\+\_\+t \textbf{ Svec\+Index} (size\+\_\+t i, size\+\_\+t j, size\+\_\+t n) \begin{DoxyCompactList}\small\item\em Return the index such that A[i,j] == factr(i, j) $\ast$ svec(\+A)[pos(i, j)], where factr(i, j) = sqrt(2) if i != j and 1 otherwise. \end{DoxyCompactList}\item void \textbf{ Sym\+Kron\+Id} (const arma\+::mat \&A, arma\+::mat \&op) \begin{DoxyCompactList}\small\item\em If A is a symmetric matrix, then Sym\+Kron\+Id returns an operator Op such that. \end{DoxyCompactList}\item void \textbf{ Vector\+Power} (arma\+::vec \&vec, const double power) \begin{DoxyCompactList}\small\item\em Auxiliary function to raise vector elements to a specific power. \end{DoxyCompactList}\item void \textbf{ Whiten\+Using\+S\+VD} (const arma\+::mat \&x, arma\+::mat \&x\+Whitened, arma\+::mat \&whitening\+Matrix) \begin{DoxyCompactList}\small\item\em Whitens a matrix using the singular value decomposition of the covariance matrix. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Variables} \begin{DoxyCompactItemize} \item M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT std\+::mt19937 \textbf{ rand\+Gen} \begin{DoxyCompactList}\small\item\em M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT is required for global variables; it exports the symbols correctly on Windows. \end{DoxyCompactList}\item M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT std\+::normal\+\_\+distribution \textbf{ rand\+Normal\+Dist} \item M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT std\+::uniform\+\_\+real\+\_\+distribution \textbf{ rand\+Uniform\+Dist} \end{DoxyCompactItemize} \subsection{Detailed Description} Miscellaneous math routines. \subsection{Typedef Documentation} \mbox{\label{namespacemlpack_1_1math_ad17d9cabd4fd82cbed4ccd5e53b47d70}} \index{mlpack\+::math@{mlpack\+::math}!Range@{Range}} \index{Range@{Range}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Range} {\footnotesize\ttfamily typedef \textbf{ Range\+Type}$<$double$>$ \textbf{ Range}} 3.\+0.\+0 T\+O\+DO\+: break reverse-\/compatibility by changing \doxyref{Range\+Type}{p.}{classmlpack_1_1math_1_1RangeType} to Range. Definition at line 19 of file range.\+hpp. \subsection{Function Documentation} \mbox{\label{namespacemlpack_1_1math_ae537d6afdea1348abf317d7761319a14}} \index{mlpack\+::math@{mlpack\+::math}!Accu\+Log@{Accu\+Log}} \index{Accu\+Log@{Accu\+Log}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Accu\+Log()} {\footnotesize\ttfamily T\+::elem\+\_\+type mlpack\+::math\+::\+Accu\+Log (\begin{DoxyParamCaption}\item[{const T \&}]{x }\end{DoxyParamCaption})} Sum a vector of log values. (T should be an Armadillo type.) \begin{DoxyParams}{Parameters} {\em x} & vector of log values \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} log(e$^\wedge$x0 + e$^\wedge$x1 + ...) \end{DoxyReturn} \mbox{\label{namespacemlpack_1_1math_af20ca29adeac02601e8f4386bda3588e}} \index{mlpack\+::math@{mlpack\+::math}!Center@{Center}} \index{Center@{Center}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Center()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Center (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{x, }\item[{arma\+::mat \&}]{x\+Centered }\end{DoxyParamCaption})} Creates a centered matrix, where centering is done by subtracting the sum over the columns (a column vector) from each column of the matrix. \begin{DoxyParams}{Parameters} {\em x} & Input matrix \\ \hline {\em x\+Centered} & Matrix to write centered output into \\ \hline \end{DoxyParams} Referenced by Nystroem\+Kernel\+Rule$<$ Kernel\+Type, Point\+Selection\+Policy $>$\+::\+Apply\+Kernel\+Matrix(), and H\+Rect\+Bound$<$ Metric\+Type $>$\+::\+Metric(). \mbox{\label{namespacemlpack_1_1math_a6d16c12e401f859c53595d709892b2a2}} \index{mlpack\+::math@{mlpack\+::math}!Clamp\+Non\+Negative@{Clamp\+Non\+Negative}} \index{Clamp\+Non\+Negative@{Clamp\+Non\+Negative}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Clamp\+Non\+Negative()} {\footnotesize\ttfamily double mlpack\+::math\+::\+Clamp\+Non\+Negative (\begin{DoxyParamCaption}\item[{const double}]{d }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Forces a number to be non-\/negative, turning negative numbers into zero. Avoids branching costs (this is a measurable improvement). \begin{DoxyParams}{Parameters} {\em d} & Double to clamp. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} 0 if d $<$ 0, d otherwise. \end{DoxyReturn} Definition at line 28 of file clamp.\+hpp. Referenced by Clamp\+Range(). \mbox{\label{namespacemlpack_1_1math_a10bd2254595feb073cdfd55e31c1231b}} \index{mlpack\+::math@{mlpack\+::math}!Clamp\+Non\+Positive@{Clamp\+Non\+Positive}} \index{Clamp\+Non\+Positive@{Clamp\+Non\+Positive}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Clamp\+Non\+Positive()} {\footnotesize\ttfamily double mlpack\+::math\+::\+Clamp\+Non\+Positive (\begin{DoxyParamCaption}\item[{const double}]{d }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Forces a number to be non-\/positive, turning positive numbers into zero. Avoids branching costs (this is a measurable improvement). \begin{DoxyParams}{Parameters} {\em d} & Double to clamp. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} 0 if d $>$ 0, d otherwise. \end{DoxyReturn} Definition at line 40 of file clamp.\+hpp. Referenced by Clamp\+Range(). \mbox{\label{namespacemlpack_1_1math_a0fa7f378ef122a2fc2b82009b436cdeb}} \index{mlpack\+::math@{mlpack\+::math}!Clamp\+Range@{Clamp\+Range}} \index{Clamp\+Range@{Clamp\+Range}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Clamp\+Range()} {\footnotesize\ttfamily double mlpack\+::math\+::\+Clamp\+Range (\begin{DoxyParamCaption}\item[{double}]{value, }\item[{const double}]{range\+Min, }\item[{const double}]{range\+Max }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Clamp a number between a particular range. \begin{DoxyParams}{Parameters} {\em value} & The number to clamp. \\ \hline {\em range\+Min} & The first of the range. \\ \hline {\em range\+Max} & The last of the range. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} max(range\+Min, min(range\+Max, d)). \end{DoxyReturn} Definition at line 53 of file clamp.\+hpp. References Clamp\+Non\+Negative(), and Clamp\+Non\+Positive(). Referenced by Reward\+Clipping$<$ Environment\+Type $>$\+::\+Sample(), Continuous\+Mountain\+Car\+::\+Sample(), Mountain\+Car\+::\+Sample(), Pendulum\+::\+Sample(), and Acrobot\+::\+Sample(). \mbox{\label{namespacemlpack_1_1math_a61d04fbb64cb618da2dc4305b1e7024f}} \index{mlpack\+::math@{mlpack\+::math}!Clear\+Alias@{Clear\+Alias}} \index{Clear\+Alias@{Clear\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Clear\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Clear\+Alias (\begin{DoxyParamCaption}\item[{arma\+::\+Mat$<$ Elem\+Type $>$ \&}]{mat }\end{DoxyParamCaption})} Clear an alias so that no data is overwritten. This resets the matrix if it is an alias (and does nothing otherwise). Definition at line 110 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_aa25733e8424870f1be6b1eb0492503a2}} \index{mlpack\+::math@{mlpack\+::math}!Clear\+Alias@{Clear\+Alias}} \index{Clear\+Alias@{Clear\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Clear\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Clear\+Alias (\begin{DoxyParamCaption}\item[{arma\+::\+Sp\+Mat$<$ Elem\+Type $>$ \&}]{ }\end{DoxyParamCaption})} Clear an alias for a sparse matrix. This does nothing because no sparse matrices can have aliases. Definition at line 121 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_a5b2ddc31187ec7a449b6ebcd71b2e52b}} \index{mlpack\+::math@{mlpack\+::math}!Column\+Covariance@{Column\+Covariance}} \index{Column\+Covariance@{Column\+Covariance}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Column\+Covariance()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily arma\+::\+Mat$<$eT$>$ mlpack\+::math\+::\+Column\+Covariance (\begin{DoxyParamCaption}\item[{const arma\+::\+Mat$<$ eT $>$ \&}]{A, }\item[{const size\+\_\+t}]{norm\+\_\+type = {\ttfamily 0} }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Referenced by P\+C\+A\+Whitening\+::\+Fit(). \mbox{\label{namespacemlpack_1_1math_afe55df16c60f2f3ae0a4e37320821e83}} \index{mlpack\+::math@{mlpack\+::math}!Column\+Covariance@{Column\+Covariance}} \index{Column\+Covariance@{Column\+Covariance}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Column\+Covariance()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily arma\+::\+Mat$<$ std\+::complex$<$T$>$ $>$ mlpack\+::math\+::\+Column\+Covariance (\begin{DoxyParamCaption}\item[{const arma\+::\+Mat$<$ std\+::complex$<$ T $>$ $>$ \&}]{A, }\item[{const size\+\_\+t}]{norm\+\_\+type = {\ttfamily 0} }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} \mbox{\label{namespacemlpack_1_1math_ac9cdbda323da580d360c4532db71f9f7}} \index{mlpack\+::math@{mlpack\+::math}!Custom\+Random\+Seed@{Custom\+Random\+Seed}} \index{Custom\+Random\+Seed@{Custom\+Random\+Seed}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Custom\+Random\+Seed()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Custom\+Random\+Seed (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{seed }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Definition at line 72 of file random.\+hpp. \mbox{\label{namespacemlpack_1_1math_a1ca2678f931cc4bba542a17136d98437}} \index{mlpack\+::math@{mlpack\+::math}!Fixed\+Random\+Seed@{Fixed\+Random\+Seed}} \index{Fixed\+Random\+Seed@{Fixed\+Random\+Seed}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Fixed\+Random\+Seed()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Fixed\+Random\+Seed (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Set the random seed to a fixed number. This function is used in binding tests to set a fixed random seed before calling mlpack(). In this way we can test whether a certain parameter makes a difference to execution of C\+LI binding. Refer to pull request \#1306 for discussion on this function. Definition at line 64 of file random.\+hpp. \mbox{\label{namespacemlpack_1_1math_a973f88fb3695c2d92af88f354742697e}} \index{mlpack\+::math@{mlpack\+::math}!Log\+Add@{Log\+Add}} \index{Log\+Add@{Log\+Add}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Log\+Add()} {\footnotesize\ttfamily T mlpack\+::math\+::\+Log\+Add (\begin{DoxyParamCaption}\item[{T}]{x, }\item[{T}]{y }\end{DoxyParamCaption})} Internal log-\/addition. \begin{DoxyParams}{Parameters} {\em x} & log value \\ \hline {\em y} & log value \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} log(e$^\wedge$x + e$^\wedge$y) \end{DoxyReturn} \mbox{\label{namespacemlpack_1_1math_ae977d6bbdbe1e2a26017645a7ee18433}} \index{mlpack\+::math@{mlpack\+::math}!Make\+Alias@{Make\+Alias}} \index{Make\+Alias@{Make\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Make\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [1/7]}} {\footnotesize\ttfamily arma\+::\+Cube$<$Elem\+Type$>$ mlpack\+::math\+::\+Make\+Alias (\begin{DoxyParamCaption}\item[{arma\+::\+Cube$<$ Elem\+Type $>$ \&}]{input, }\item[{const bool}]{strict = {\ttfamily true} }\end{DoxyParamCaption})} Make an alias of a dense cube. If strict is true, then the alias cannot be resized or pointed at new memory. Definition at line 24 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_a6611a3cfd0aad124d0ca5bf45b44801c}} \index{mlpack\+::math@{mlpack\+::math}!Make\+Alias@{Make\+Alias}} \index{Make\+Alias@{Make\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Make\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [2/7]}} {\footnotesize\ttfamily arma\+::\+Mat$<$Elem\+Type$>$ mlpack\+::math\+::\+Make\+Alias (\begin{DoxyParamCaption}\item[{arma\+::\+Mat$<$ Elem\+Type $>$ \&}]{input, }\item[{const bool}]{strict = {\ttfamily true} }\end{DoxyParamCaption})} Make an alias of a dense matrix. If strict is true, then the alias cannot be resized or pointed at new memory. Definition at line 37 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_ae0f2bc84fae09e2232931990bcb3fc08}} \index{mlpack\+::math@{mlpack\+::math}!Make\+Alias@{Make\+Alias}} \index{Make\+Alias@{Make\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Make\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [3/7]}} {\footnotesize\ttfamily arma\+::\+Row$<$Elem\+Type$>$ mlpack\+::math\+::\+Make\+Alias (\begin{DoxyParamCaption}\item[{arma\+::\+Row$<$ Elem\+Type $>$ \&}]{input, }\item[{const bool}]{strict = {\ttfamily true} }\end{DoxyParamCaption})} Make an alias of a dense row. If strict is true, then the alias cannot be resized or pointed at new memory. Definition at line 50 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_acd2b618f5a0ec77ccb94cf43a06846e9}} \index{mlpack\+::math@{mlpack\+::math}!Make\+Alias@{Make\+Alias}} \index{Make\+Alias@{Make\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Make\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [4/7]}} {\footnotesize\ttfamily arma\+::\+Col$<$Elem\+Type$>$ mlpack\+::math\+::\+Make\+Alias (\begin{DoxyParamCaption}\item[{arma\+::\+Col$<$ Elem\+Type $>$ \&}]{input, }\item[{const bool}]{strict = {\ttfamily true} }\end{DoxyParamCaption})} Make an alias of a dense column. If strict is true, then the alias cannot be resized or pointed at new memory. Definition at line 62 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_a327a59b10b6b84ea4c3eec3469644bec}} \index{mlpack\+::math@{mlpack\+::math}!Make\+Alias@{Make\+Alias}} \index{Make\+Alias@{Make\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Make\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [5/7]}} {\footnotesize\ttfamily arma\+::\+Sp\+Mat$<$Elem\+Type$>$ mlpack\+::math\+::\+Make\+Alias (\begin{DoxyParamCaption}\item[{const arma\+::\+Sp\+Mat$<$ Elem\+Type $>$ \&}]{input, }\item[{const bool}]{ = {\ttfamily true} }\end{DoxyParamCaption})} Make a copy of a sparse matrix (an alias is not possible). The strict parameter is ignored. Definition at line 74 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_a6b3f7eb08a72a99cd338824b85276e0f}} \index{mlpack\+::math@{mlpack\+::math}!Make\+Alias@{Make\+Alias}} \index{Make\+Alias@{Make\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Make\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [6/7]}} {\footnotesize\ttfamily arma\+::\+Sp\+Row$<$Elem\+Type$>$ mlpack\+::math\+::\+Make\+Alias (\begin{DoxyParamCaption}\item[{const arma\+::\+Sp\+Row$<$ Elem\+Type $>$ \&}]{input, }\item[{const bool}]{ = {\ttfamily true} }\end{DoxyParamCaption})} Make a copy of a sparse row (an alias is not possible). The strict parameter is ignored. Definition at line 86 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_a42a8a4c43e657af6d3557fdaa3082f93}} \index{mlpack\+::math@{mlpack\+::math}!Make\+Alias@{Make\+Alias}} \index{Make\+Alias@{Make\+Alias}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Make\+Alias()\hspace{0.1cm}{\footnotesize\ttfamily [7/7]}} {\footnotesize\ttfamily arma\+::\+Sp\+Col$<$Elem\+Type$>$ mlpack\+::math\+::\+Make\+Alias (\begin{DoxyParamCaption}\item[{const arma\+::\+Sp\+Col$<$ Elem\+Type $>$ \&}]{input, }\item[{const bool}]{ = {\ttfamily true} }\end{DoxyParamCaption})} Make a copy of a sparse column (an alias is not possible). The strict parameter is ignored. Definition at line 98 of file make\+\_\+alias.\+hpp. \mbox{\label{namespacemlpack_1_1math_a047dc14951af6707554936acb575ecdd}} \index{mlpack\+::math@{mlpack\+::math}!Multiply\+Cube2\+Cube@{Multiply\+Cube2\+Cube}} \index{Multiply\+Cube2\+Cube@{Multiply\+Cube2\+Cube}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Multiply\+Cube2\+Cube()} {\footnotesize\ttfamily Cube\+Type mlpack\+::math\+::\+Multiply\+Cube2\+Cube (\begin{DoxyParamCaption}\item[{const Cube\+Type \&}]{cubeA, }\item[{const Cube\+Type \&}]{cubeB, }\item[{const bool}]{a\+Transpose = {\ttfamily false}, }\item[{const bool}]{b\+Transpose = {\ttfamily false} }\end{DoxyParamCaption})} Matrix multiplication of slices of two cubes. This function expects both cubes to have the same number of slices. For example, a valid operation would be\+: cube A of shape (m, p, s) multiplied by cube B of shape (p, n, s) resulting in a cube of shape (m, n, s). \begin{DoxyParams}{Parameters} {\em cubeA} & First cube. \\ \hline {\em cubeB} & Second cube. \\ \hline {\em a\+Transpose} & Whether slices of first cube have to be transposed. \\ \hline {\em b\+Transpose} & Whether slices of second cube have to be transposed. \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a75d67d2fe4e1046bfdc903f32a4b0230}} \index{mlpack\+::math@{mlpack\+::math}!Multiply\+Cube2\+Mat@{Multiply\+Cube2\+Mat}} \index{Multiply\+Cube2\+Mat@{Multiply\+Cube2\+Mat}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Multiply\+Cube2\+Mat()} {\footnotesize\ttfamily Cube\+Type mlpack\+::math\+::\+Multiply\+Cube2\+Mat (\begin{DoxyParamCaption}\item[{const Cube\+Type \&}]{cubeA, }\item[{const Mat\+Type \&}]{matB, }\item[{const bool}]{a\+Transpose = {\ttfamily false}, }\item[{const bool}]{b\+Transpose = {\ttfamily false} }\end{DoxyParamCaption})} Matrix multiplication of all slices of a cube with a matrix. This function is used when the first object is a cube and the second object is a matrix. For example, a valid operation would be\+: cube A of shape (m, p, s) multiplied by a matrix of shape (p, n) resulting in a cube of shape (m, n, s). \begin{DoxyParams}{Parameters} {\em cubeA} & The cube as the first operand. \\ \hline {\em matB} & The matrix as the second operand. \\ \hline {\em a\+Transpose} & Whether slices of cube have to be transposed. \\ \hline {\em b\+Transpose} & Whether matrix has to be transposed. \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a6921a2dfaeb07fc6c47616b9fabdffce}} \index{mlpack\+::math@{mlpack\+::math}!Multiply\+Mat2\+Cube@{Multiply\+Mat2\+Cube}} \index{Multiply\+Mat2\+Cube@{Multiply\+Mat2\+Cube}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Multiply\+Mat2\+Cube()} {\footnotesize\ttfamily Cube\+Type mlpack\+::math\+::\+Multiply\+Mat2\+Cube (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{matA, }\item[{const Cube\+Type \&}]{cubeB, }\item[{const bool}]{a\+Transpose = {\ttfamily false}, }\item[{const bool}]{b\+Transpose = {\ttfamily false} }\end{DoxyParamCaption})} Matrix multiplication of a matrix and all the slices of a cube. This function is used when the first object is a matrix and the second object is a cube. For example, a valid operation would be\+: matrix A of shape (m, p) multiplied by cube B of shape (p, n, s) resulting in a cube of shape (m, n, s). \begin{DoxyParams}{Parameters} {\em matA} & The matrix as the first operand. \\ \hline {\em cubeB} & The cube as the second operand. \\ \hline {\em a\+Transpose} & Whether matrix has to be transposed. \\ \hline {\em b\+Transpose} & Whether slices of cube have to be transposed. \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a9f6fa0072288d9c1139394683e0c3636}} \index{mlpack\+::math@{mlpack\+::math}!Obtain\+Distinct\+Samples@{Obtain\+Distinct\+Samples}} \index{Obtain\+Distinct\+Samples@{Obtain\+Distinct\+Samples}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Obtain\+Distinct\+Samples()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Obtain\+Distinct\+Samples (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{lo\+Inclusive, }\item[{const size\+\_\+t}]{hi\+Exclusive, }\item[{const size\+\_\+t}]{max\+Num\+Samples, }\item[{arma\+::uvec \&}]{distinct\+Samples }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Obtains no more than max\+Num\+Samples distinct samples. Each sample belongs to [lo\+Inclusive, hi\+Exclusive). \begin{DoxyParams}{Parameters} {\em lo\+Inclusive} & The lower bound (inclusive). \\ \hline {\em hi\+Exclusive} & The high bound (exclusive). \\ \hline {\em max\+Num\+Samples} & The maximum number of samples to obtain. \\ \hline {\em distinct\+Samples} & The samples that will be obtained. \\ \hline \end{DoxyParams} Definition at line 153 of file random.\+hpp. References Rand\+Int(). \mbox{\label{namespacemlpack_1_1math_a33495d8fdb79a9b5783d683cf11b0d6b}} \index{mlpack\+::math@{mlpack\+::math}!Orthogonalize@{Orthogonalize}} \index{Orthogonalize@{Orthogonalize}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Orthogonalize()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Orthogonalize (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{x, }\item[{arma\+::mat \&}]{W }\end{DoxyParamCaption})} Orthogonalize x and return the result in W, using eigendecomposition. We will be using the formula $ W = x (x^T x)^{-0.5} $. \mbox{\label{namespacemlpack_1_1math_a532da68daa876aaa1060fbe54eaa3722}} \index{mlpack\+::math@{mlpack\+::math}!Orthogonalize@{Orthogonalize}} \index{Orthogonalize@{Orthogonalize}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Orthogonalize()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Orthogonalize (\begin{DoxyParamCaption}\item[{arma\+::mat \&}]{x }\end{DoxyParamCaption})} Orthogonalize x in-\/place. This could be sped up by a custom implementation. \mbox{\label{namespacemlpack_1_1math_a6b25c05d1e1c066d6b33aa55bdfd39f6}} \index{mlpack\+::math@{mlpack\+::math}!Rand\+Bernoulli@{Rand\+Bernoulli}} \index{Rand\+Bernoulli@{Rand\+Bernoulli}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Rand\+Bernoulli()} {\footnotesize\ttfamily double mlpack\+::math\+::\+Rand\+Bernoulli (\begin{DoxyParamCaption}\item[{const double}]{input }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Generates a 0/1 specified by the input. Definition at line 99 of file random.\+hpp. References Random(). \mbox{\label{namespacemlpack_1_1math_aad090ac225728d74c1b66bcf52f3ab95}} \index{mlpack\+::math@{mlpack\+::math}!Rand\+Int@{Rand\+Int}} \index{Rand\+Int@{Rand\+Int}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Rand\+Int()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily int mlpack\+::math\+::\+Rand\+Int (\begin{DoxyParamCaption}\item[{const int}]{hi\+Exclusive }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Generates a uniform random integer. Definition at line 110 of file random.\+hpp. References rand\+Uniform\+Dist. Referenced by Random\+Dimension\+Select\+::\+Begin(), Multiple\+Random\+Dimension\+Select\+::\+Begin(), Sample\+Initialization\+::\+Cluster(), Data\+Dependent\+Random\+Initializer\+::\+Initialize(), Random\+Acol\+Initialization$<$ columns\+To\+Average $>$\+::\+Initialize(), Obtain\+Distinct\+Samples(), Greedy\+Policy$<$ Environment\+Type $>$\+::\+Sample(), Random\+Selection\+::\+Select(), and Random\+Point\+Selection\+::\+Select(). \mbox{\label{namespacemlpack_1_1math_a2befbd48db5691a0ed3b87bb4b423095}} \index{mlpack\+::math@{mlpack\+::math}!Rand\+Int@{Rand\+Int}} \index{Rand\+Int@{Rand\+Int}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Rand\+Int()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily int mlpack\+::math\+::\+Rand\+Int (\begin{DoxyParamCaption}\item[{const int}]{lo, }\item[{const int}]{hi\+Exclusive }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Generates a uniform random integer. Definition at line 118 of file random.\+hpp. References rand\+Uniform\+Dist. \mbox{\label{namespacemlpack_1_1math_a4ad431d20545de6887998188074989af}} \index{mlpack\+::math@{mlpack\+::math}!Rand\+Normal@{Rand\+Normal}} \index{Rand\+Normal@{Rand\+Normal}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Rand\+Normal()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double mlpack\+::math\+::\+Rand\+Normal (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Generates a normally distributed random number with mean 0 and variance 1. Definition at line 127 of file random.\+hpp. References rand\+Normal\+Dist. Referenced by Gaussian\+Initialization\+::\+Initialize(). \mbox{\label{namespacemlpack_1_1math_a731e1fe0fb09c263299222a594a73e7f}} \index{mlpack\+::math@{mlpack\+::math}!Rand\+Normal@{Rand\+Normal}} \index{Rand\+Normal@{Rand\+Normal}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Rand\+Normal()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double mlpack\+::math\+::\+Rand\+Normal (\begin{DoxyParamCaption}\item[{const double}]{mean, }\item[{const double}]{variance }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Generates a normally distributed random number with specified mean and variance. \begin{DoxyParams}{Parameters} {\em mean} & Mean of distribution. \\ \hline {\em variance} & Variance of distribution. \\ \hline \end{DoxyParams} Definition at line 139 of file random.\+hpp. References rand\+Normal\+Dist. \mbox{\label{namespacemlpack_1_1math_a305db122ade561ba1fe874bd51e9797d}} \index{mlpack\+::math@{mlpack\+::math}!Random@{Random}} \index{Random@{Random}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Random()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double mlpack\+::math\+::\+Random (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Generates a uniform random number between 0 and 1. Definition at line 83 of file random.\+hpp. References rand\+Uniform\+Dist. Referenced by Continuous\+Mountain\+Car\+::\+Initial\+Sample(), Pendulum\+::\+Initial\+Sample(), Mock\+Categorical\+Data(), Rand\+Bernoulli(), Greedy\+Policy$<$ Environment\+Type $>$\+::\+Sample(), and Acrobot\+::\+Torque(). \mbox{\label{namespacemlpack_1_1math_a73063c4b5f50db033266cd16afaceca9}} \index{mlpack\+::math@{mlpack\+::math}!Random@{Random}} \index{Random@{Random}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Random()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double mlpack\+::math\+::\+Random (\begin{DoxyParamCaption}\item[{const double}]{lo, }\item[{const double}]{hi }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Generates a uniform random number in the specified range. Definition at line 91 of file random.\+hpp. References rand\+Uniform\+Dist. \mbox{\label{namespacemlpack_1_1math_ae197a3d057c10401e3a1f30f94ff0934}} \index{mlpack\+::math@{mlpack\+::math}!Random\+Basis@{Random\+Basis}} \index{Random\+Basis@{Random\+Basis}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Random\+Basis()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Random\+Basis (\begin{DoxyParamCaption}\item[{arma\+::mat \&}]{basis, }\item[{const size\+\_\+t}]{d }\end{DoxyParamCaption})} Create a random d-\/dimensional orthogonal basis, storing it in the given matrix. \begin{DoxyParams}{Parameters} {\em basis} & Matrix to store basis in. \\ \hline {\em d} & Desired number of dimensions in the basis. \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a99560c3cf9c2db393309a31933b8d480}} \index{mlpack\+::math@{mlpack\+::math}!Random\+Seed@{Random\+Seed}} \index{Random\+Seed@{Random\+Seed}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Random\+Seed()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Random\+Seed (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{seed }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Set the random seed used by the random functions (\doxyref{Random()}{p.}{namespacemlpack_1_1math_a305db122ade561ba1fe874bd51e9797d} and \doxyref{Rand\+Int()}{p.}{namespacemlpack_1_1math_aad090ac225728d74c1b66bcf52f3ab95}). The seed is casted to a 32-\/bit integer before being given to the random number generator, but a size\+\_\+t is taken as a parameter for A\+PI consistency. \begin{DoxyParams}{Parameters} {\em seed} & Seed for the random number generator. \\ \hline \end{DoxyParams} Definition at line 40 of file random.\+hpp. \mbox{\label{namespacemlpack_1_1math_a27732f0088e81d179a8e6c92c4f9c4b8}} \index{mlpack\+::math@{mlpack\+::math}!Rand\+Vector@{Rand\+Vector}} \index{Rand\+Vector@{Rand\+Vector}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Rand\+Vector()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Rand\+Vector (\begin{DoxyParamCaption}\item[{arma\+::vec \&}]{v }\end{DoxyParamCaption})} Overwrites a dimension-\/N vector to a random vector on the unit sphere in R$^\wedge$N. \mbox{\label{namespacemlpack_1_1math_ac03fe146911a97bef099efc9e99296ff}} \index{mlpack\+::math@{mlpack\+::math}!Remove\+Rows@{Remove\+Rows}} \index{Remove\+Rows@{Remove\+Rows}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Remove\+Rows()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Remove\+Rows (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{input, }\item[{const std\+::vector$<$ size\+\_\+t $>$ \&}]{rows\+To\+Remove, }\item[{arma\+::mat \&}]{output }\end{DoxyParamCaption})} Remove a certain set of rows in a matrix while copying to a second matrix. \begin{DoxyParams}{Parameters} {\em input} & Input matrix to copy. \\ \hline {\em rows\+To\+Remove} & Vector containing indices of rows to be removed. \\ \hline {\em output} & Matrix to copy non-\/removed rows into. \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a9fd573f30f3cd68f82f51ba57506d169}} \index{mlpack\+::math@{mlpack\+::math}!Shuffle\+Data@{Shuffle\+Data}} \index{Shuffle\+Data@{Shuffle\+Data}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Shuffle\+Data()\hspace{0.1cm}{\footnotesize\ttfamily [1/5]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Shuffle\+Data (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{input\+Points, }\item[{const Labels\+Type \&}]{input\+Labels, }\item[{Mat\+Type \&}]{output\+Points, }\item[{Labels\+Type \&}]{output\+Labels, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0}, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0} }\end{DoxyParamCaption})} Shuffle a dataset and associated labels (or responses). It is expected that input\+Points and input\+Labels have the same number of columns (so, be sure that input\+Labels, if it is a vector, is a row vector). Shuffled data will be output into output\+Points and output\+Labels. Definition at line 28 of file shuffle\+\_\+data.\+hpp. \mbox{\label{namespacemlpack_1_1math_a3d51da0ee510a507855d587b91645a2e}} \index{mlpack\+::math@{mlpack\+::math}!Shuffle\+Data@{Shuffle\+Data}} \index{Shuffle\+Data@{Shuffle\+Data}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Shuffle\+Data()\hspace{0.1cm}{\footnotesize\ttfamily [2/5]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Shuffle\+Data (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{input\+Points, }\item[{const Labels\+Type \&}]{input\+Labels, }\item[{Mat\+Type \&}]{output\+Points, }\item[{Labels\+Type \&}]{output\+Labels, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0}, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0} }\end{DoxyParamCaption})} Shuffle a sparse dataset and associated labels (or responses). It is expected that input\+Points and input\+Labels have the same number of columns (so, be sure that input\+Labels, if it is a vector, is a row vector). Shuffled data will be output into output\+Points and output\+Labels. Definition at line 51 of file shuffle\+\_\+data.\+hpp. \mbox{\label{namespacemlpack_1_1math_ae867d408a4e6bd4f6c6efa6ad46f699d}} \index{mlpack\+::math@{mlpack\+::math}!Shuffle\+Data@{Shuffle\+Data}} \index{Shuffle\+Data@{Shuffle\+Data}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Shuffle\+Data()\hspace{0.1cm}{\footnotesize\ttfamily [3/5]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Shuffle\+Data (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{input\+Points, }\item[{const Labels\+Type \&}]{input\+Labels, }\item[{Mat\+Type \&}]{output\+Points, }\item[{Labels\+Type \&}]{output\+Labels, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0}, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0}, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Cube$<$ Labels\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0} }\end{DoxyParamCaption})} Shuffle a cube-\/shaped dataset and associated labels (or responses) which are also cube-\/shaped. It is expected that input\+Points and input\+Labels have the same number of columns. Shuffled data will be output into output\+Points and output\+Labels. Definition at line 103 of file shuffle\+\_\+data.\+hpp. \mbox{\label{namespacemlpack_1_1math_a4e6818ee1202660968eeda80040b5d0e}} \index{mlpack\+::math@{mlpack\+::math}!Shuffle\+Data@{Shuffle\+Data}} \index{Shuffle\+Data@{Shuffle\+Data}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Shuffle\+Data()\hspace{0.1cm}{\footnotesize\ttfamily [4/5]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Shuffle\+Data (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{input\+Points, }\item[{const Labels\+Type \&}]{input\+Labels, }\item[{const Weights\+Type \&}]{input\+Weights, }\item[{Mat\+Type \&}]{output\+Points, }\item[{Labels\+Type \&}]{output\+Labels, }\item[{Weights\+Type \&}]{output\+Weights, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0}, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0} }\end{DoxyParamCaption})} Shuffle a dataset and associated labels (or responses) and weights. It is expected that input\+Points and input\+Labels and input\+Weights have the same number of columns (so, be sure that input\+Labels, if it is a vector, is a row vector). Shuffled data will be output into output\+Points and output\+Labels and output\+Weights. Definition at line 160 of file shuffle\+\_\+data.\+hpp. \mbox{\label{namespacemlpack_1_1math_a522c0905bf5015a7eebac8fdddb6452b}} \index{mlpack\+::math@{mlpack\+::math}!Shuffle\+Data@{Shuffle\+Data}} \index{Shuffle\+Data@{Shuffle\+Data}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Shuffle\+Data()\hspace{0.1cm}{\footnotesize\ttfamily [5/5]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Shuffle\+Data (\begin{DoxyParamCaption}\item[{const Mat\+Type \&}]{input\+Points, }\item[{const Labels\+Type \&}]{input\+Labels, }\item[{const Weights\+Type \&}]{input\+Weights, }\item[{Mat\+Type \&}]{output\+Points, }\item[{Labels\+Type \&}]{output\+Labels, }\item[{Weights\+Type \&}]{output\+Weights, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$ arma\+::is\+\_\+\+Sp\+Mat$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0}, }\item[{const \textbf{ std\+::enable\+\_\+if\+\_\+t}$<$!arma\+::is\+\_\+\+Cube$<$ Mat\+Type $>$\+::value $>$ $\ast$}]{ = {\ttfamily 0} }\end{DoxyParamCaption})} Shuffle a sparse dataset and associated labels (or responses) and weights. It is expected that input\+Points and input\+Labels and input\+Weights have the same number of columns (so, be sure that input\+Labels, if it is a vector, is a row vector). Shuffled data will be output into output\+Points and output\+Labels and output\+Weights. Definition at line 188 of file shuffle\+\_\+data.\+hpp. \mbox{\label{namespacemlpack_1_1math_a5a69e6e582ac415528f3a219e5336b83}} \index{mlpack\+::math@{mlpack\+::math}!Sign@{Sign}} \index{Sign@{Sign}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Sign()} {\footnotesize\ttfamily T mlpack\+::math\+::\+Sign (\begin{DoxyParamCaption}\item[{const T}]{x }\end{DoxyParamCaption})} Signum function. Return 1 if x$>$0; return 0 if x=0; return -\/1 if x$<$0. Return type are the same as input type. \begin{DoxyParams}{Parameters} {\em x} & Number of any type. \\ \hline \end{DoxyParams} Definition at line 128 of file lin\+\_\+alg.\+hpp. \mbox{\label{namespacemlpack_1_1math_acf1d819071707267cdce9c78abd32e2e}} \index{mlpack\+::math@{mlpack\+::math}!Smat@{Smat}} \index{Smat@{Smat}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Smat()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Smat (\begin{DoxyParamCaption}\item[{const arma\+::vec \&}]{input, }\item[{arma\+::mat \&}]{output }\end{DoxyParamCaption})} The inverse of Svec. That is, Smat(\+Svec(\+A)) == A. \begin{DoxyParams}{Parameters} {\em input} & \\ \hline {\em output} & A symmetric matrix \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a76535efa4f447182fed1a2ad789d5340}} \index{mlpack\+::math@{mlpack\+::math}!Svec@{Svec}} \index{Svec@{Svec}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Svec()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Svec (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{input, }\item[{arma\+::vec \&}]{output }\end{DoxyParamCaption})} Upper triangular representation of a symmetric matrix, scaled such that, dot(Svec(\+A), Svec(\+B)) == dot(\+A, B) for symmetric A, B. Specifically, Svec(\+K) = [ K\+\_\+11, sqrt(2) K\+\_\+12, ..., sqrt(2) K\+\_\+1n, K\+\_\+22, ..., sqrt(2) K\+\_\+2n, ..., K\+\_\+nn ]$^\wedge$T \begin{DoxyParams}{Parameters} {\em input} & A symmetric matrix \\ \hline {\em output} & \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a2e46372873806bdfef7d596dcc78a5ea}} \index{mlpack\+::math@{mlpack\+::math}!Svec@{Svec}} \index{Svec@{Svec}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Svec()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily void mlpack\+::math\+::\+Svec (\begin{DoxyParamCaption}\item[{const arma\+::sp\+\_\+mat \&}]{input, }\item[{arma\+::sp\+\_\+vec \&}]{output }\end{DoxyParamCaption})} \mbox{\label{namespacemlpack_1_1math_a630a16e49385717a8fef7d25d0093c37}} \index{mlpack\+::math@{mlpack\+::math}!Svec\+Index@{Svec\+Index}} \index{Svec\+Index@{Svec\+Index}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Svec\+Index()} {\footnotesize\ttfamily size\+\_\+t mlpack\+::math\+::\+Svec\+Index (\begin{DoxyParamCaption}\item[{size\+\_\+t}]{i, }\item[{size\+\_\+t}]{j, }\item[{size\+\_\+t}]{n }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Return the index such that A[i,j] == factr(i, j) $\ast$ svec(\+A)[pos(i, j)], where factr(i, j) = sqrt(2) if i != j and 1 otherwise. \begin{DoxyParams}{Parameters} {\em i} & \\ \hline {\em j} & \\ \hline {\em n} & \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a99efc34a8a0f9ed477baf86cb62adb3f}} \index{mlpack\+::math@{mlpack\+::math}!Sym\+Kron\+Id@{Sym\+Kron\+Id}} \index{Sym\+Kron\+Id@{Sym\+Kron\+Id}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Sym\+Kron\+Id()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Sym\+Kron\+Id (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{A, }\item[{arma\+::mat \&}]{op }\end{DoxyParamCaption})} If A is a symmetric matrix, then Sym\+Kron\+Id returns an operator Op such that. Op $\ast$ svec(\+X) == svec(0.\+5 $\ast$ (AX + XA)) for every symmetric matrix X \begin{DoxyParams}{Parameters} {\em A} & \\ \hline {\em op} & \\ \hline \end{DoxyParams} \mbox{\label{namespacemlpack_1_1math_a1afb9b62743ad2c961a4f240d8694e1e}} \index{mlpack\+::math@{mlpack\+::math}!Vector\+Power@{Vector\+Power}} \index{Vector\+Power@{Vector\+Power}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Vector\+Power()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Vector\+Power (\begin{DoxyParamCaption}\item[{arma\+::vec \&}]{vec, }\item[{const double}]{power }\end{DoxyParamCaption})} Auxiliary function to raise vector elements to a specific power. The sign is ignored in the power operation and then re-\/added. Useful for eigenvalues. \mbox{\label{namespacemlpack_1_1math_a9498ec73c0c6b0f151a10b2357a11468}} \index{mlpack\+::math@{mlpack\+::math}!Whiten\+Using\+S\+VD@{Whiten\+Using\+S\+VD}} \index{Whiten\+Using\+S\+VD@{Whiten\+Using\+S\+VD}!mlpack\+::math@{mlpack\+::math}} \subsubsection{Whiten\+Using\+S\+V\+D()} {\footnotesize\ttfamily void mlpack\+::math\+::\+Whiten\+Using\+S\+VD (\begin{DoxyParamCaption}\item[{const arma\+::mat \&}]{x, }\item[{arma\+::mat \&}]{x\+Whitened, }\item[{arma\+::mat \&}]{whitening\+Matrix }\end{DoxyParamCaption})} Whitens a matrix using the singular value decomposition of the covariance matrix. Whitening means the covariance matrix of the result is the identity matrix. \subsection{Variable Documentation} \mbox{\label{namespacemlpack_1_1math_a56ce900a37460cea29bd0359aeaaff34}} \index{mlpack\+::math@{mlpack\+::math}!rand\+Gen@{rand\+Gen}} \index{rand\+Gen@{rand\+Gen}!mlpack\+::math@{mlpack\+::math}} \subsubsection{rand\+Gen} {\footnotesize\ttfamily M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT std\+::mt19937 rand\+Gen} M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT is required for global variables; it exports the symbols correctly on Windows. \mbox{\label{namespacemlpack_1_1math_a109a494ed74138c2d02d64bb3ebe6f9f}} \index{mlpack\+::math@{mlpack\+::math}!rand\+Normal\+Dist@{rand\+Normal\+Dist}} \index{rand\+Normal\+Dist@{rand\+Normal\+Dist}!mlpack\+::math@{mlpack\+::math}} \subsubsection{rand\+Normal\+Dist} {\footnotesize\ttfamily M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT std\+::normal\+\_\+distribution rand\+Normal\+Dist} Referenced by Rand\+Normal(). \mbox{\label{namespacemlpack_1_1math_a7793dcf6af53048459e80aa26780afa0}} \index{mlpack\+::math@{mlpack\+::math}!rand\+Uniform\+Dist@{rand\+Uniform\+Dist}} \index{rand\+Uniform\+Dist@{rand\+Uniform\+Dist}!mlpack\+::math@{mlpack\+::math}} \subsubsection{rand\+Uniform\+Dist} {\footnotesize\ttfamily M\+L\+P\+A\+C\+K\+\_\+\+E\+X\+P\+O\+RT std\+::uniform\+\_\+real\+\_\+distribution rand\+Uniform\+Dist} Referenced by Rand\+Int(), and Random().