\section{Softplus\+Function Class Reference}
\label{classmlpack_1_1ann_1_1SoftplusFunction}\index{Softplus\+Function@{Softplus\+Function}}


The softplus function, defined by.  


\subsection*{Static Public Member Functions}
\begin{DoxyCompactItemize}
\item 
static double \textbf{ Deriv} (const double y)
\begin{DoxyCompactList}\small\item\em Computes the first derivative of the softplus function. \end{DoxyCompactList}\item 
{\footnotesize template$<$typename Input\+Type , typename Output\+Type $>$ }\\static void \textbf{ Deriv} (const Input\+Type \&y, Output\+Type \&x)
\begin{DoxyCompactList}\small\item\em Computes the first derivatives of the softplus function. \end{DoxyCompactList}\item 
static double \textbf{ Fn} (const double x)
\begin{DoxyCompactList}\small\item\em Computes the softplus function. \end{DoxyCompactList}\item 
{\footnotesize template$<$typename Input\+Type , typename Output\+Type $>$ }\\static void \textbf{ Fn} (const Input\+Type \&x, Output\+Type \&y)
\begin{DoxyCompactList}\small\item\em Computes the softplus function. \end{DoxyCompactList}\item 
static double \textbf{ Inv} (const double y)
\begin{DoxyCompactList}\small\item\em Computes the inverse of the softplus function. \end{DoxyCompactList}\item 
{\footnotesize template$<$typename Input\+Type , typename Output\+Type $>$ }\\static void \textbf{ Inv} (const Input\+Type \&y, Output\+Type \&x)
\begin{DoxyCompactList}\small\item\em Computes the inverse of the softplus function. \end{DoxyCompactList}\end{DoxyCompactItemize}


\subsection{Detailed Description}
The softplus function, defined by. 

\begin{eqnarray*} f(x) &=& \ln(1 + e^{x}) \\ f'(x) &=& \frac{1}{1 + e^{-x}} \\ f^{-1}(y) &=& \ln(e^{y} - 1) \end{eqnarray*} 

Definition at line 43 of file softplus\+\_\+function.\+hpp.



\subsection{Member Function Documentation}
\mbox{\label{classmlpack_1_1ann_1_1SoftplusFunction_a163d34fd09f8edf457164f5033c635cf}} 
\index{mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}!Deriv@{Deriv}}
\index{Deriv@{Deriv}!mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}}
\subsubsection{Deriv()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}}
{\footnotesize\ttfamily static double Deriv (\begin{DoxyParamCaption}\item[{const double}]{y }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}



Computes the first derivative of the softplus function. 


\begin{DoxyParams}{Parameters}
{\em y} & Input data. \\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}
f\textquotesingle{}(x) 
\end{DoxyReturn}


Definition at line 81 of file softplus\+\_\+function.\+hpp.

\mbox{\label{classmlpack_1_1ann_1_1SoftplusFunction_ac7573a8739be4400959956c5cc42d19b}} 
\index{mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}!Deriv@{Deriv}}
\index{Deriv@{Deriv}!mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}}
\subsubsection{Deriv()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}}
{\footnotesize\ttfamily static void Deriv (\begin{DoxyParamCaption}\item[{const Input\+Type \&}]{y,  }\item[{Output\+Type \&}]{x }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}



Computes the first derivatives of the softplus function. 


\begin{DoxyParams}{Parameters}
{\em y} & Input data. \\
\hline
{\em x} & The resulting derivatives. \\
\hline
\end{DoxyParams}


Definition at line 93 of file softplus\+\_\+function.\+hpp.

\mbox{\label{classmlpack_1_1ann_1_1SoftplusFunction_a11bd9a1195e6b107f9fee73643bc328b}} 
\index{mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}!Fn@{Fn}}
\index{Fn@{Fn}!mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}}
\subsubsection{Fn()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}}
{\footnotesize\ttfamily static double Fn (\begin{DoxyParamCaption}\item[{const double}]{x }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}



Computes the softplus function. 


\begin{DoxyParams}{Parameters}
{\em x} & Input data. \\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}
f(x). 
\end{DoxyReturn}


Definition at line 52 of file softplus\+\_\+function.\+hpp.



Referenced by Softplus\+Function\+::\+Fn().

\mbox{\label{classmlpack_1_1ann_1_1SoftplusFunction_a5b84b986e495fe1b922b2f4d06f19c06}} 
\index{mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}!Fn@{Fn}}
\index{Fn@{Fn}!mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}}
\subsubsection{Fn()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}}
{\footnotesize\ttfamily static void Fn (\begin{DoxyParamCaption}\item[{const Input\+Type \&}]{x,  }\item[{Output\+Type \&}]{y }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}



Computes the softplus function. 


\begin{DoxyParams}{Parameters}
{\em x} & Input data. \\
\hline
{\em y} & The resulting output activation. \\
\hline
\end{DoxyParams}


Definition at line 67 of file softplus\+\_\+function.\+hpp.



References Softplus\+Function\+::\+Fn().

\mbox{\label{classmlpack_1_1ann_1_1SoftplusFunction_a32d503b167c9646569a202e8c134ef76}} 
\index{mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}!Inv@{Inv}}
\index{Inv@{Inv}!mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}}
\subsubsection{Inv()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}}
{\footnotesize\ttfamily static double Inv (\begin{DoxyParamCaption}\item[{const double}]{y }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}



Computes the inverse of the softplus function. 


\begin{DoxyParams}{Parameters}
{\em y} & Input data. \\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}
f$^\wedge$\{-\/1\}(y) 
\end{DoxyReturn}


Definition at line 104 of file softplus\+\_\+function.\+hpp.



Referenced by Softplus\+Function\+::\+Inv().

\mbox{\label{classmlpack_1_1ann_1_1SoftplusFunction_a3ea6c0a5538ecd48a07d3e2043a7a43b}} 
\index{mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}!Inv@{Inv}}
\index{Inv@{Inv}!mlpack\+::ann\+::\+Softplus\+Function@{mlpack\+::ann\+::\+Softplus\+Function}}
\subsubsection{Inv()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}}
{\footnotesize\ttfamily static void Inv (\begin{DoxyParamCaption}\item[{const Input\+Type \&}]{y,  }\item[{Output\+Type \&}]{x }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}, {\ttfamily [static]}}



Computes the inverse of the softplus function. 


\begin{DoxyParams}{Parameters}
{\em y} & Input data. \\
\hline
{\em x} & The resulting inverse of the input data. \\
\hline
\end{DoxyParams}


Definition at line 119 of file softplus\+\_\+function.\+hpp.



References Softplus\+Function\+::\+Inv().



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.\+2/src/mlpack/methods/ann/activation\+\_\+functions/\textbf{ softplus\+\_\+function.\+hpp}\end{DoxyCompactItemize}