\chapter{Summary of Functions} \label{appx:function}

\begin{center} \begin{tabular}{||l|l||}
\hline
\multicolumn{2}{||c||}{} \\
\multicolumn{2}{||c||}{Standard \caps{FORTRAN} Functions} \\
\multicolumn{2}{||c||}{} \\
\hline
\param{r} = \cmd{AINT} ($x$)
      & truncation: $|x|$ \\
\param{r} = \cmd{ANINT} ($x$)
      & nearest integer: [$x + .5*$sign($x$)] \\
\param{r} = \cmd{ABS} ($x$)
      & absolute value: $|x|$ \\
\param{r} = \cmd{MOD} ($x$, $y$)
      & remainder: $x - y * [x/y]$ \\
\param{r} = \cmd{SIGN} ($x$, $y$)
      & transfer of sign: $|x|$ sign $y$ \\
\param{r} = \cmd{DIM} ($x$, $y$)
      & positive difference: $x - $min($x$,$y$) \\
\param{r} = \cmd{MAX} ($x$, $y$, \ldots)
      & maximum of $x$, $y$, \ldots\ \\
\param{r} = \cmd{MIN} ($x$, $y$, \ldots)
      & minimum of $x$, $y$, \ldots\ \\
\param{r} = \cmd{SQRT} ($x$)
      & square root: $\sqrt{x}$ \\
\param{r} = \cmd{EXP} ($x$)
      & exponentiation: e$^{x}$ \\
\param{r} = \cmd{LOG} ($x$)
      & natural logarithm: log$_{e}x$ \\
\param{r} = \cmd{LOG10} ($x$)
      & common logarithm: log$_{10}x$ \\
\param{r} = \cmd{SIN} ($x$)
      & sine $x$ \\
\param{r} = \cmd{COS} ($x$)
      & cosine $x$ \\
\param{r} = \cmd{TAN} ($x$)
      & tangent $x$ \\
\param{r} = \cmd{ASIN} ($x$)
      & arc sine $x$ \\
\param{r} = \cmd{ACOS} ($x$)
      & arc cosine $x$ \\
\param{r} = \cmd{ATAN} ($x$)
      & arc tangent $x$ \\
\param{r} = \cmd{ATAN2} ($x$, $y$)
      & arc tangent $x/y$ \\
\param{r} = \cmd{SINH} ($x$)
      & hyperbolic sine $x$ \\
\param{r} = \cmd{COSH} ($x$)
      & hyperbolic cosine $x$ \\
\param{r} = \cmd{TANH} ($x$)
      & hyperbolic tangent $x$ \\
\hline
\end{tabular} \end{center}

\medskip
\begin{center} \begin{tabular}{||l|l||}
\hline
\multicolumn{2}{||c||}{} \\
\multicolumn{2}{||c||}{Tensor Principal Values and Magnitude Functions}
\\
\multicolumn{2}{||c||}{} \\
\hline
\param{r} = \cmd{PMAX}
   ($T_{11}$, $T_{22}$, $T_{33}$, $T_{12}$, $T_{23}$, $T_{31}$)
      & maximum principal values \\
\param{r} = \cmd{PMIN}
   ($T_{11}$, $T_{22}$, $T_{33}$, $T_{12}$, $T_{23}$, $T_{31}$)
      & minimum principal values \\
\param{r} = \cmd{PMAX2} ($T_{11}$, $T_{22}$, $T_{12}$)
      & maximum principal values (2D) \\
\param{r} = \cmd{PMIN2} ($T_{11}$, $T_{22}$, $T_{12}$)
      & minimum principal values (2D) \\
\param{r} = \cmd{TMAG}
   ($T_{11}$, $T_{22}$, $T_{33}$, $T_{12}$, $T_{23}$, $T_{31}$)
      & magnitude of the deviatoric part \\
\hline
\end{tabular} \end{center}

\medskip
\begin{center} \begin{tabular}{||l|l||}
\hline
\multicolumn{2}{||c||}{} \\
\multicolumn{2}{||c||}{IF Functions} \\
\multicolumn{2}{||c||}{} \\
\hline
\param{r} = \cmd{IFLZ} (\param{cond}, \param{rtrue}, \param{rfalse})
      & if \param{cond} $<$ 0.0,
         \param{rtrue} else \param{rfalse} \\
\param{r} = \cmd{IFEZ} (\param{cond}, \param{rtrue}, \param{rfalse})
      & if \param{cond} $=$ 0.0,
         \param{rtrue} else \param{rfalse} \\
\param{r} = \cmd{IFGZ} (\param{cond}, \param{rtrue}, \param{rfalse})
      & if \param{cond} $>$ 0.0,
         \param{rtrue} else \param{rfalse} \\
\hline
\end{tabular} \end{center}

\medskip
\begin{center} \begin{tabular}{||l|l||}
\hline
\multicolumn{2}{||c||}{} \\
\multicolumn{2}{||c||}{Array $\Rightarrow$ Global Variable Functions} \\
\multicolumn{2}{||c||}{} \\
\hline
\param{r} = \cmd{SUM} (\param{x})
      & sum of \param{x} over all nodes or elements \\
\param{r} = \cmd{SMAX} (\param{x})
      & maximum of \param{x} over all nodes or elements \\
\param{r} = \cmd{SMIN} (\param{x})
      & minimum of \param{x} over all nodes or elements \\
\hline
\end{tabular} \end{center}

\medskip
\begin{center} \begin{tabular}{||l|l||}
\hline
\multicolumn{2}{||c||}{} \\
\multicolumn{2}{||c||}{Envelope Functions} \\
\multicolumn{2}{||c||}{} \\
\hline
\param{r} = \cmd{ENVMAX} (\param{x})
      & maximum of \param{x} over all previous time steps \\
\param{r} = \cmd{ENVMIN} (\param{x})
      & minimum of \param{x} over all previous time steps \\
\hline
\end{tabular} \end{center}