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128 lines
3.9 KiB
128 lines
3.9 KiB
2 years ago
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\chapter{Summary of Functions} \label{appx:function}
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\begin{center} \begin{tabular}{||l|l||}
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\hline
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\multicolumn{2}{||c||}{} \\
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\multicolumn{2}{||c||}{Standard \caps{FORTRAN} Functions} \\
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\multicolumn{2}{||c||}{} \\
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\hline
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\param{r} = \cmd{AINT} ($x$)
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& truncation: $|x|$ \\
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\param{r} = \cmd{ANINT} ($x$)
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& nearest integer: [$x + .5*$sign($x$)] \\
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\param{r} = \cmd{ABS} ($x$)
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& absolute value: $|x|$ \\
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\param{r} = \cmd{MOD} ($x$, $y$)
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& remainder: $x - y * [x/y]$ \\
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\param{r} = \cmd{SIGN} ($x$, $y$)
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& transfer of sign: $|x|$ sign $y$ \\
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\param{r} = \cmd{DIM} ($x$, $y$)
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& positive difference: $x - $min($x$,$y$) \\
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\param{r} = \cmd{MAX} ($x$, $y$, \ldots)
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& maximum of $x$, $y$, \ldots\ \\
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\param{r} = \cmd{MIN} ($x$, $y$, \ldots)
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& minimum of $x$, $y$, \ldots\ \\
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\param{r} = \cmd{SQRT} ($x$)
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& square root: $\sqrt{x}$ \\
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\param{r} = \cmd{EXP} ($x$)
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& exponentiation: e$^{x}$ \\
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\param{r} = \cmd{LOG} ($x$)
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& natural logarithm: log$_{e}x$ \\
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\param{r} = \cmd{LOG10} ($x$)
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& common logarithm: log$_{10}x$ \\
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\param{r} = \cmd{SIN} ($x$)
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& sine $x$ \\
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\param{r} = \cmd{COS} ($x$)
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& cosine $x$ \\
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\param{r} = \cmd{TAN} ($x$)
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& tangent $x$ \\
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\param{r} = \cmd{ASIN} ($x$)
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& arc sine $x$ \\
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\param{r} = \cmd{ACOS} ($x$)
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& arc cosine $x$ \\
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\param{r} = \cmd{ATAN} ($x$)
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& arc tangent $x$ \\
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\param{r} = \cmd{ATAN2} ($x$, $y$)
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& arc tangent $x/y$ \\
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\param{r} = \cmd{SINH} ($x$)
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& hyperbolic sine $x$ \\
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\param{r} = \cmd{COSH} ($x$)
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& hyperbolic cosine $x$ \\
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\param{r} = \cmd{TANH} ($x$)
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& hyperbolic tangent $x$ \\
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\hline
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\end{tabular} \end{center}
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\medskip
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\begin{center} \begin{tabular}{||l|l||}
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\hline
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\multicolumn{2}{||c||}{} \\
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\multicolumn{2}{||c||}{Tensor Principal Values and Magnitude Functions}
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\\
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\multicolumn{2}{||c||}{} \\
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\hline
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\param{r} = \cmd{PMAX}
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($T_{11}$, $T_{22}$, $T_{33}$, $T_{12}$, $T_{23}$, $T_{31}$)
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& maximum principal values \\
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\param{r} = \cmd{PMIN}
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($T_{11}$, $T_{22}$, $T_{33}$, $T_{12}$, $T_{23}$, $T_{31}$)
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& minimum principal values \\
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\param{r} = \cmd{PMAX2} ($T_{11}$, $T_{22}$, $T_{12}$)
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& maximum principal values (2D) \\
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\param{r} = \cmd{PMIN2} ($T_{11}$, $T_{22}$, $T_{12}$)
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& minimum principal values (2D) \\
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\param{r} = \cmd{TMAG}
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($T_{11}$, $T_{22}$, $T_{33}$, $T_{12}$, $T_{23}$, $T_{31}$)
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& magnitude of the deviatoric part \\
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\hline
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\end{tabular} \end{center}
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\medskip
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\begin{center} \begin{tabular}{||l|l||}
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\hline
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\multicolumn{2}{||c||}{} \\
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\multicolumn{2}{||c||}{IF Functions} \\
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\multicolumn{2}{||c||}{} \\
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\hline
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\param{r} = \cmd{IFLZ} (\param{cond}, \param{rtrue}, \param{rfalse})
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& if \param{cond} $<$ 0.0,
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\param{rtrue} else \param{rfalse} \\
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\param{r} = \cmd{IFEZ} (\param{cond}, \param{rtrue}, \param{rfalse})
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& if \param{cond} $=$ 0.0,
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\param{rtrue} else \param{rfalse} \\
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\param{r} = \cmd{IFGZ} (\param{cond}, \param{rtrue}, \param{rfalse})
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& if \param{cond} $>$ 0.0,
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\param{rtrue} else \param{rfalse} \\
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\hline
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\end{tabular} \end{center}
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\medskip
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\begin{center} \begin{tabular}{||l|l||}
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\hline
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\multicolumn{2}{||c||}{} \\
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\multicolumn{2}{||c||}{Array $\Rightarrow$ Global Variable Functions} \\
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\multicolumn{2}{||c||}{} \\
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\hline
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\param{r} = \cmd{SUM} (\param{x})
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& sum of \param{x} over all nodes or elements \\
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\param{r} = \cmd{SMAX} (\param{x})
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& maximum of \param{x} over all nodes or elements \\
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\param{r} = \cmd{SMIN} (\param{x})
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& minimum of \param{x} over all nodes or elements \\
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\hline
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\end{tabular} \end{center}
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\medskip
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\begin{center} \begin{tabular}{||l|l||}
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\hline
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\multicolumn{2}{||c||}{} \\
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\multicolumn{2}{||c||}{Envelope Functions} \\
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\multicolumn{2}{||c||}{} \\
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\hline
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\param{r} = \cmd{ENVMAX} (\param{x})
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& maximum of \param{x} over all previous time steps \\
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\param{r} = \cmd{ENVMIN} (\param{x})
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& minimum of \param{x} over all previous time steps \\
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\hline
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\end{tabular} \end{center}
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