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diff --git a/Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex b/Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex index 671c45e405d..bc3698732c9 100644 --- a/Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex +++ b/Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex @@ -1,448 +1,434 @@ -\documentclass[fleqn,10pt]{article} - -\usepackage{multicol} -\usepackage[a4paper,margin=1.5cm,includeheadfoot]{geometry} -\usepackage{fancyhdr} +%% $Id: pst-func-doc.tex 72 2009-01-08 22:00:47Z herbert $ +\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings + headexclude,footexclude,oneside]{pst-doc} +\usepackage[utf8]{inputenc} +\usepackage{pst-math} +\let\pstMathFV\fileversion +\usepackage{pstricks-add} \usepackage[baw,pstricks]{fvrb-ex} -\usepackage{pstricks} -\usepackage{pst-math,pst-plot} -\usepackage{amsmath,amssymb} -\makeatletter - -\renewcommand{\Begin@Example}{% -\parindent=0pt -\multiply\topsep by 2 \VerbatimEnvironment -\begin{VerbatimOut}[codes={\catcode`\£=12\catcode`\/=12\catcode`\&=12% - \catcode`\"=12}]{\jobname.tmp}} - -\renewcommand{\Below@Example}[1]{% -\VerbatimInput[gobble=0,commentchar=£,commandchars=/&",numbersep=3pt]% - {\jobname.tmp} -\catcode`\£=9\relax% -\NoHighlight@Attributes % To suppress possible highlighting -\ifFvrbEx@Grid\vspace{5pt}\fi -#1% -\ifFvrbEx@Grid\vspace{5pt}\fi -\par} - -\renewcommand{\SideBySide@Example}[1]{% -\@tempdimb=\FV@XRightMargin \advance\@tempdimb -5mm -\begin{minipage}[c]{\@tempdimb} - \fvset{xrightmargin=0pt} - \catcode`\£=9\relax% - \NoHighlight@Attributes % To suppress possible highlighting - #1 -\end{minipage}% -\@tempdimb=\textwidth \advance\@tempdimb -\FV@XRightMargin \advance\@tempdimb 5mm -\begin{minipage}[c]{\@tempdimb} - \VerbatimInput[gobble=0,commentchar=£,commandchars=/&",numbersep=3pt, - xleftmargin=5mm,xrightmargin=0pt]{\jobname.tmp} -\end{minipage}} - -% The \NoHighlight@Attributes from `hbaw' and `hcolors' packages -% must be modified too -\def\NoHighlight@Attributes{% -\catcode`\/=0\relax% -\catcode`\&=1\relax% -\catcode`\"=2\relax% -\def\HLa##1{##1}% -\def\HLb##1{##1}% -\def\HLc##1{##1}% -\def\HLd##1{##1}% -\def\HLe##1{##1}% -\def\HLf##1{##1}% -\def\HLBFa##1{##1}% -\def\HLBFb##1{##1}% -\def\HLBFc##1{##1}% -\def\HLBFd##1{##1}% -\def\HLBFe##1{##1}% -\def\HLBFf##1{##1}% -\def\HLITa##1{##1}% -\def\HLITb##1{##1}% -\def\HLITc##1{##1}% -\def\HLITd##1{##1}% -\def\HLITe##1{##1}% -\def\HLITf##1{##1}% -\def\HLCBBa##1{##1}% -\def\HLCBBb##1{##1}% -\def\HLCBBc##1{##1}% -\def\HLCBBd##1{##1}% -\def\HLCBBe##1{##1}% -\def\HLCBBf##1{##1}% -\def\HLCBBz##1{##1}% -\def\HLCBWa##1{##1}% -\def\HLCBWb##1{##1}% -\def\HLCBWc##1{##1}% -\def\HLCBWd##1{##1}% -\def\HLCBWe##1{##1}% -\def\HLCBWf##1{##1}% -\def\HLCBWz##1{##1}% -} - -\makeatother - -\fvset{numbers=none,frame=single,labelposition=topline,gobble=4} - -\DeclareRobustCommand\cs[1]{\texttt{\char`\\#1}} - -\newcommand{\MathPackage}{\textbf{`pst-math'}} - -\lhead{\MathPackage}\rhead{A PSTricks package for enhancing mathematical operators in PSTricks} -\pagestyle{fancy} - -\psset{subgriddiv=1,griddots=10}% -\showgrid - +\lstset{pos=t,wide=true,language=PSTricks, + morekeywords={psGammaDist,psChiIIDist,psTDist,psFDist,psBetaDist,psPlotImpl},basicstyle=\footnotesize\ttfamily} +% +\def\pshlabel#1{\footnotesize#1} +\def\psvlabel#1{\footnotesize#1} +% \makeatletter - \def\DefOfOperator{\@ifstar{\DefOfOperator@}{\DefOfOperator@@}} \def\DefOfOperator@#1#2#3#4{{\operator@font#1}:\left\{\begin{array}{ccc} #2&\to\\ x&\mapsto\end{array}\right.} \def\DefOfOperator@@#1#2#3{{\operator@font#1}:\left\{\begin{array}{ccc} #2&\to\\ x&\mapsto&{\operator@font#1}(x)\end{array}\right.} - \makeatother \begin{document} -\title{\MathPackage\\ A PSTricks package for enhancing mathematical operators in PSTricks\\ -\normalsize ver. 0.3} -\author{Christophe \textsc{Jorssen} \texttt{<christophe.jorssen@libre.fr.invalid>}\\ \footnotesize `libre' is the french word for `free'} +\title{\texttt{pst-math}} +\subtitle{Special mathematical PostScript functions; v.\pstMathFV} +\author{Christoph Jorssen\\Herbert Vo\ss} +\docauthor{Christoph Jorssen\\Herbert Vo\ss} \date{\today} \maketitle -\setlength{\columnseprule}{0.6pt} -\begin{multicols}{2} -{\parskip 0pt \tableofcontents} -\end{multicols} +\tableofcontents + +\clearpage + +\begin{abstract} +\noindent +\LPack{pst-math} is an extension to the PostScript language. The files \LFile{pst-math.sty} +and \LFile{pst-math.tex} are only wrapper files for the \LFile{pst-math.pro} file, which +defines all the new mathgematical functions for use with PostScript. + +\vfill\noindent +Thanks to: \\ +Jacques L'helgoualc'h; Dominik Rodriguez +\end{abstract} \section{Trigonometry} -\MathPackage{} introduces natural trigonometric postscript operators COS, SIN and TAN defined by +\LPack{pst-math} introduces natural trigonometric postscript operators COS, SIN and TAN defined by \[\DefOfOperator{cos}{\mathbb R}{[-1,1]}\] \[\DefOfOperator{sin}{\mathbb R}{[-1,1]}\] \[\DefOfOperator{tan}{\mathbb R\backslash\{k\frac{\pi}2,k\in\mathbb Z\}}{\mathbb R}\] where $x$ is in \emph{radians}. TAN does \emph{not} produce PS error\footnote{TAN is defined with Div PSTricks operator rather than with div PS operator.} when $x=k\frac{pi}{2}$. -\begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{COS}} & \textsf{\textsl{real}} & Return cosine of - \textsf{\textsl{num}} radians \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{SIN}} & \textsf{\textsl{real}} & Return sine of - \textsf{\textsl{num}} radians \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{TAN}} & \textsf{\textsl{real}} & Return tangent of - \textsf{\textsl{num}} radians -\end{tabular} -\end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture}*(-5,-2)(5,2) - \SpecialCoor % For label positionning - \psaxes[labels=y,Dx=/HLCBWz&\pstPI2"]{->}% - (0,0)(-5,-2)(5,2) - \uput[-90](!/HLCBWz&PI" 0){$\pi$} - \uput[-90](!/HLCBWz&PI" neg 0){$-\pi$} - \uput[-90](!/HLCBWz&PI" 2 div 0){$\frac{\pi}2$} - \uput[-90](!/HLCBWz&PI" 2 div neg 0)% - {$-\frac{\pi}2$} - \psplot[linecolor=blue]{-5}{5}{x /HLCBWz&COS"} - \psplot[linecolor=red]{-5}{5}{x /HLCBWz&SIN"} - \psplot[linecolor=green]{-5}{5}{x /HLCBWz&TAN"} - \end{pspicture} -\end{SideBySideExample} - -\MathPackage{} introduces natural trigonometric postscript operators SEC, COSEC and COTAN -defined by -\[\DefOfOperator{sec}{% - \mathbb R\backslash\{k\frac{\pi}{2},k\in\mathbb{Z}\}}{]-\infty,-1]\bigcup [1,+\infty[}\] -\[\DefOfOperator{cosec}% - {\mathbb R\backslash\{k\pi,k\in\mathbb Z\}}{]-\infty,-1]\bigcup [1,+\infty[}\] -\[\DefOfOperator{cotan}% - {\mathbb R\backslash\{k\pi,k\in\mathbb Z\}}{\mathbb R}\] -where $x$ is in \emph{radians}. \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{SEC}} & \textsf{\textsl{real}} & Return secant of - \textsf{\textsl{num}} radians \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{COSEC}} & \textsf{\textsl{real}} & Return cosecant of - \textsf{\textsl{num}} radians \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{COTAN}} & \textsf{\textsl{real}} & Return cotangent -of \textsf{\textsl{num}} radians +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num & \Lps{COS} & real & Return \Index{cosine} of \textsf{num} radians \\ +num & \Lps{SIN} & real & Return \Index{sine} of \textsf{num} radians \\ +num & \Lps{TAN} & real & Return \Index{tangent} of \textsf{num} radians\\\hline \end{tabular} \end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture}*(-5,-2)(5,2) - \SpecialCoor % For label positionning - \psaxes[labels=y,Dx=/HLCBWz&\pstPI2"]{->}% - (0,0)(-5,-2)(5,2) - \uput[-90](!/HLCBWz&PI" 0){$\pi$} - \uput[-90](!/HLCBWz&PI" neg 0){$-\pi$} - \uput[-90](!/HLCBWz&PI" 2 div 0)% - {$\frac{\pi}{2}$} - \uput[-90](!/HLCBWz&PI" 2 div neg 0)% - {$-\frac{\pi}{2}$} - \psplot[linecolor=blue]{-5}{5}{x /HLCBWz&SEC"} - \psplot[linecolor=red]{-5}{5}{x /HLCBWz&COSEC"} - \psplot[linecolor=green]{-5}{5}{x /HLCBWz&COTAN"} - \end{pspicture} -\end{SideBySideExample} - - -\MathPackage{} introduces natural trigonometric postscript operators ACOS, ASIN and ATAN defined by +\begin{LTXexample}[pos=t,wide=false] +\begin{pspicture}*(-5,-2)(5,2) +\SpecialCoor % For label positionning +\psaxes[labels=y,Dx=\pstPI2]{->}(0,0)(-5,-2)(5,2) +\uput[-90](!PI 0){$\pi$} \uput[-90](!PI neg 0){$-\pi$} +\uput[-90](!PI 2 div 0){$\frac{\pi}2$} +\uput[-90](!PI 2 div neg 0){$-\frac{\pi}2$} +\psplot[linewidth=1.5pt,linecolor=blue]{-5}{5}{x COS} +\psplot[linewidth=1.5pt,linecolor=red]{-5}{5}{x SIN} +\psplot[linewidth=1.5pt,linecolor=green]{-5}{5}{x TAN} +\end{pspicture} +\end{LTXexample} + +\LPack{pst-math} introduces natural trigonometric postscript +operators \Lps{ACOS}, \Lps{ASIN} and \Lps{ATAN} defined by + \[\DefOfOperator{acos}{[-1,1]}{[0,\pi]}\] \[\DefOfOperator{asin}{[-1,1]}{[-\frac{\pi}2,\frac{\pi}2]}\] \[\DefOfOperator{atan}{\mathbb R}{]-\frac{\pi}2,\frac{\pi}2[}\] \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{ACOS}} & \textsf{\textsl{angle}} & Return arccosine of - \textsf{\textsl{num}} in radians \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{ASIN}} & \textsf{\textsl{angle}} & Return arcsine of - \textsf{\textsl{num}} in radians \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{ATAN}} & \textsf{\textsl{angle}} & Return arctangent of - \textsf{\textsl{num}} in radians \\ +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num & \Lps{ACOS} & angle & Return \Index{arccosine} of \textsf{num} in radians \\ +num & \Lps{ASIN} & angle & Return \Index{arcsine} of \textsf{num} in radians \\ +num & \Lps{ATAN} & angle & Return \Index{arctangent} of \textsf{num} in radians \\\hline \end{tabular} \end{center} -\textbf{Important :} ATAN is \emph{not} defined as PS operator atan. ATAN needs only \emph{one} +\medskip\noindent +\begin{tabularx}{\linewidth}{!{\vrule width3pt}X} +\Lps{ATAN} is \emph{not} defined as PS operator \Lps{atan}. \Lps{ATAN} needs only \emph{one} argument on the stack. - -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture}(-5,-2)(5,4) - \SpecialCoor % For label positionning - \psaxes[labels=x,Dy=/HLCBWz&\pstPI2"]{->}% - (0,0)(-5,-2)(5,4) - \uput[0](!0 /HLCBWz&PI"){$\pi$} - \uput[0](!0 /HLCBWz&PI" 2 div){$\frac{\pi}2$} - \uput[0](!0 /HLCBWz&PI" 2 div neg)% - {$-\frac{\pi}2$} - \psplot[linecolor=blue]{-1}{1}% - {x /HLCBWz&ACOS"} - \psplot[linecolor=red]{-1}{1}% - {x /HLCBWz&ASIN"} - \psplot[linecolor=green]{-5}{5}% - {x /HLCBWz&ATAN"} - \end{pspicture} -\end{SideBySideExample} +\end{tabularx} + +\begin{LTXexample}[pos=t,wide=false] +\begin{pspicture}(-5,-2)(5,4) +\SpecialCoor % For label positionning +\psaxes[labels=x,Dy=\pstPI2]{->}(0,0)(-5,-2)(5,4) +\uput[0](!0 PI){$\pi$} \uput[0](!0 PI 2 div){$\frac{\pi}2$} +\uput[0](!0 PI 2 div neg){$-\frac{\pi}2$} +\psplot[linewidth=1.5pt,linecolor=blue]{-1}{1}{x ACOS} \psplot[linecolor=red]{-1}{1}{x ASIN} +\psplot[linewidth=1.5pt,linecolor=green]{-5}{5}{x ATAN} +\end{pspicture} +\end{LTXexample} \section{Hyperbolic trigonometry} -\MathPackage{} introduces hyperbolic trigonometric postscript operators COSH, SINH and TANH defined -by +\LPack{pst-math} introduces hyperbolic trigonometric postscript operators +\Lps{COSH}, \Lps{SINH} and \Lps{TANH} defined by + \[\DefOfOperator{cosh}{\mathbb R}{[1,+\infty[}\] \[\DefOfOperator{sinh}{\mathbb R}{\mathbb R}\] \[\DefOfOperator{tanh}{\mathbb R}{]-1,1[}\] + \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{COSH}} & \textsf{\textsl{real}} & Return hyperbolic cosine of - \textsf{\textsl{num}} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{SINH}} & \textsf{\textsl{real}} & Return hyperbolic sine of - \textsf{\textsl{num}} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{TANH}} & \textsf{\textsl{real}} & Return hyperbolic tangent of - \textsf{\textsl{num}} +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num & \Lps{COSH} & real & Return \Index{hyperbolic cosine} of \textsf{num} \\ +num & \Lps{SINH} & real & Return \Index{hyperbolic sine} of \textsf{num} \\ +num & \Lps{TANH} & real & Return \Index{hyperbolic tangent} of \textsf{num}\\\hline \end{tabular} \end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture}*(-5,-5)(5,5) - \psaxes{->}(0,0)(-5,-5)(5,5) - \psplot[linecolor=blue]{-5}{5}{x /HLCBWz&COSH"} - \psplot[linecolor=red]{-5}{5}{x /HLCBWz&SINH"} - \psplot[linecolor=green]{-5}{5}{x /HLCBWz&TANH"} - \end{pspicture} -\end{SideBySideExample} - -\MathPackage{} introduces reciprocal hyperbolic trigonometric postscript operators ACOSH, ASINH and -ATANH defined by +\begin{LTXexample}[pos=t,wide=false] +\begin{pspicture}*(-5,-5)(5,5) +\psaxes{->}(0,0)(-5,-5)(5,5) +\psplot[linewidth=1.5pt,linecolor=blue]{-5}{5}{x COSH} +\psplot[linewidth=1.5pt,linecolor=red]{-5}{5}{x SINH} +\psplot[linewidth=1.5pt,linecolor=green]{-5}{5}{x TANH} +\end{pspicture} +\end{LTXexample} + +\LPack{pst-math} introduces reciprocal hyperbolic trigonometric postscript operators \Lps{ACOSH}, \Lps{ASINH} and +\Lps{ATANH} defined by \[\DefOfOperator{acosh}{[1,+\infty[}{\mathbb R}\] \[\DefOfOperator{asinh}{\mathbb R}{\mathbb R}\] \[\DefOfOperator{atanh}{]-1,1[}{\mathbb R}\] + \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{ACOSH}} & \textsf{\textsl{real}} & Return reciprocal hyperbolic cosine of - \textsf{\textsl{num}} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{ASINH}} & \textsf{\textsl{real}} & Return reciprocal hyperbolic sine of - \textsf{\textsl{num}} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{ATANH}} & \textsf{\textsl{real}} & Return reciprocal hyperbolic tangent of - \textsf{\textsl{num}} +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num & \Lps{ACOSH} & real & Return \Index{reciprocal hyperbolic cosine} of \textsf{num} \\ +num & \Lps{ASINH} & real & Return \Index{reciprocal hyperbolic sine} of \textsf{num} \\ +num & \Lps{ATANH} & real & Return \Index{reciprocal hyperbolic tangent} of \textsf{num}\\\hline \end{tabular} \end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture}(-5,-4)(5,4) - \psaxes{->}(0,0)(-5,-4)(5,4) - \psplot[linecolor=blue]{1}{5}% - {x /HLCBWz&ACOSH"} - \psplot[linecolor=red]{-5}{5}% - {x /HLCBWz&ASINH"} - \psplot[linecolor=green]{-.999}{.999}% - {x /HLCBWz&ATANH"} - \end{pspicture} -\end{SideBySideExample} +\begin{LTXexample}[pos=t,wide=false] +\begin{pspicture}(-5,-4)(5,4) +\psaxes{->}(0,0)(-5,-4)(5,4) +\psplot[linewidth=1.5pt,linecolor=blue]{1}{5}{x ACOSH} +\psplot[linewidth=1.5pt,linecolor=red]{-5}{5}{x ASINH} +\psplot[linewidth=1.5pt,linecolor=green]{-.999}{.999}{x ATANH} +\end{pspicture} +\end{LTXexample} \section{Other operators} -\MathPackage{} introduces postscript operator EXP defined by +\LPack{pst-math} introduces postscript operator EXP defined by \[\DefOfOperator{exp}{\mathbb R}{\mathbb R}\] + \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{EXP}} & \textsf{\textsl{real}} & Return exponential of - \textsf{\textsl{num}} +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num & \Lps{EXP} & real & Return \Index{exponential} of \textsf{num}\\\hline \end{tabular} \end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture}*(-5,-1)(5,5) - \psaxes{->}(0,0)(-5,-0.5)(5,5) - \psplot[linecolor=blue, - plotpoints=1000]{-5}{5}{x /HLCBWz&EXP"} - \end{pspicture} -\end{SideBySideExample} +\begin{LTXexample}[pos=t,wide=false] +\begin{pspicture}*(-5,-1)(5,5) +\psaxes{->}(0,0)(-5,-0.5)(5,5) +\psplot[linecolor=blue,linewidth=1.5pt,plotpoints=1000]{-5}{5}{x EXP} +\end{pspicture} +\end{LTXexample} + +\LPack{pst-math} introduces postscript operator \Lps{GAUSS} defined by -\MathPackage{} introduces postscript operator GAUSS defined by \[\DefOfOperator*{gauss}{\mathbb R}{\mathbb R}{\displaystyle\frac{1}{\sqrt{2\pi\sigma^2}}\exp-\frac{(x-\overline x)^2}{2\sigma^2}}\] + \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}${}_1$} \textsf{\textsl{num}${}_2$} \textsf{\textsl{num}${}_3$} & - \textsf{\textbf{GAUSS}} & \textsf{\textsl{real}} & \parbox{4cm}{Return gaussian - of \textsf{\textsl{num}${}_1$} with mean \textsf{\textsl{num}${}_2$} and standart deviation \textsf{\textsl{num}${}_3$}} -\end{tabular} +\begin{tabularx}{\linewidth}{@{} >{\sffamily}l l >{\sffamily}l X @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num1 num2 num3 & \Lps{GAUSS} & real & Return gaussian of \textsf{num1} with + mean \textsf{num2} and \Index{standard deviation} \textsf{num3}\\\hline +\end{tabularx} \end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \psset{yunit=5} - \begin{pspicture}(-5,-.1)(5,1.1) - \psaxes{->}(0,0)(-5,-.1)(5,1.1) - \psplot[linecolor=blue, - plotpoints=1000]% - {-5}{5}{x 2 2 /HLCBWz&GAUSS"} - \psplot[linecolor=red, - plotpoints=1000]% - {-5}{5}{x 0 .5 /HLCBWz&GAUSS"} - \end{pspicture} -\end{SideBySideExample} - -\MathPackage{} introduces postscript operator SINC defined by +\begin{LTXexample}[pos=t,wide=false] +\psset{yunit=5} +\begin{pspicture}(-5,-.1)(5,1.1) +\psaxes{->}(0,0)(-5,-.1)(5,1.1) +\psplot[linecolor=blue,linewidth=1.5pt,plotpoints=1000]{-5}{5}{x 2 2 GAUSS} +\psplot[linecolor=red,linewidth=1.5pt,plotpoints=1000]{-5}{5}{x 0 .5 GAUSS} +\end{pspicture} +\end{LTXexample} + +\LPack{pst-math} introduces postscript operator \Index{SINC} defined by \[\DefOfOperator*{sinc}{\mathbb R}{\mathbb R}{\displaystyle\frac{\sin x}x}\] + \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ - \hline - \textsf{\textsl{num}} & \textsf{\textbf{SINC}} & \textsf{\textsl{real}} & Return cardinal sine of - \textsf{\textsl{num}} radians +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num & \Lps{SINC} & real & Return \Index{cardinal sine} of \textsf{num} radians\\\hline \end{tabular} \end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \psset{xunit=.25,yunit=3} - \begin{pspicture}(-20,-.5)(20,1.5) - \SpecialCoor % For label positionning - \psaxes[labels=y,Dx=/HLCBWz&\pstPI1"]{->}% - (0,0)(-20,-.5)(20,1.5) - \uput[-90](!/HLCBWz&PI" 0){$\pi$} - \uput[-90](!/HLCBWz&PI" neg 0){$-\pi$} - \psplot[linecolor=blue, - plotpoints=1000]{-20}{20}{x /HLCBWz&SINC"} - \end{pspicture} -\end{SideBySideExample} - -\MathPackage{} introduces postscript operator GAMMA and GAMMALN defined by +\begin{LTXexample}[pos=t,wide=false] +\psset{xunit=.25,yunit=3} +\begin{pspicture}(-20,-.5)(20,1.5) +\SpecialCoor % For label positionning +\psaxes[labels=y,Dx=\pstPI1]{->}(0,0)(-20,-.5)(20,1.5) +\uput[-90](!PI 0){$\pi$} \uput[-90](!PI neg 0){$-\pi$} +\psplot[linecolor=blue,linewidth=1.5pt,plotpoints=1000]{-20}{20}{x SINC} +\end{pspicture} +\end{LTXexample} + +\LPack{pst-math} introduces postscript operator \Lps{GAMMA} and \Lps{GAMMALN} defined by \[\DefOfOperator*{\Gamma}{\mathbb{R} \backslash\mathbb{Z}}{\mathbb R}{\displaystyle\int_0^\infty t^{x-1}\mathrm e^{-t}\,\mathrm d t}\] \[\DefOfOperator*{\ln\Gamma}{]0,+\infty[}{\mathbb R}{\ln\displaystyle\int_0^t t^{x-1}\mathrm e^{-t}\,\mathrm d t}\] + \begin{center} -\begin{tabular}{c|c|c|c} - \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\\hline - \textsf{\textsl{num}} & \textsf{\textbf{GAMMA}} & \textsf{\textsl{real}} & Return $\Gamma$ function of \textsf{\textsl{num}}\\ - \textsf{\textsl{num}} & \textsf{\textbf{GAMMALN}} & \textsf{\textsl{real}} & Return logarithm of - $\Gamma$ function of \textsf{\textsl{num}} +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num & \Lps{GAMMA} & real & Return $\Gamma$\index{Gamma func@$\Gamma$ function} function of \textsf{num}\\ +num & \Lps{GAMMALN} & real & Return \Index{logarithm} of $\Gamma$ function of \textsf{num}\\\hline \end{tabular} \end{center} -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture*}(-.5,-.5)(6.2,6.2) - \psaxes{->}(0,0)(-.5,-.5)(6,6) - \psplot[linecolor=blue, - plotpoints=200]{.1}{6}{x /HLCBWz&GAMMA"} - \psplot[linecolor=red, - plotpoints=200]{.1}{6}{x /HLCBWz&GAMMALN"} - \end{pspicture*} -\end{SideBySideExample} - -\begin{SideBySideExample}[xrightmargin=10.5cm] - \psset{xunit=.25,yunit=3} - \begin{pspicture}(-20,-.5)(20,1.5) - \psaxes[Dx=5,Dy=.5]{->}% - (0,0)(-20,-.5)(20,1.5) - \psplot[linecolor=blue, - plotpoints=1000]{-20}{20}% - {x /HLCBWz&BESSEL_J0"} - \psplot[linecolor=red, - plotpoints=1000]{-20}{20}% - {x /HLCBWz&BESSEL_J1"} - \end{pspicture} -\end{SideBySideExample} - -\begin{SideBySideExample}[xrightmargin=10.5cm] - \psset{xunit=.5,yunit=3} - \begin{pspicture}*(-1.5,-.75)(19,1.5) - \psaxes[Dx=5,Dy=.5]{->}% - (0,0)(-1,-.75)(19,1.5) - \psplot[linecolor=blue, - plotpoints=1000]{0.0001}{20}% - {x /HLCBWz&BESSEL_Y0"} - \psplot[linecolor=red, - plotpoints=1000]{0.0001}{20}% - {x /HLCBWz&BESSEL_Y1"} - % \psplot[linecolor=green, - % plotpoints=1000]{0.0001}{20}% - % {x 2 /HLCBWz&BESSEL_Yn"} - \end{pspicture} -\end{SideBySideExample} - -\section{Warnings} - -Since version 0.3, there is a new feature. When an argument of \textsf{\textbf{ACOS}}, -\textsf{\textbf{ASIN}}, \textsf{\textbf{ACOSH}} or \textsf{\textbf{ATANH}} is out of range, -the result of the calculation does not product a PS error: a zero value is substitued and a -warning message is printed on the postscript version of the document. - -\begin{SideBySideExample}[xrightmargin=10.5cm] - \begin{pspicture}(-1,-4)(5,4) - \psaxes{->}(0,0)(-1,-4)(5,4) - \psplot[linecolor=blue]{/HLCBWz&0"}{5}% - {x ACOSH} - \end{pspicture} -\end{SideBySideExample} - -\section{Credits} - -Many thanks to Jacques L'helgoualc'h, Herbert Voss and Martin Chicoine. +\begin{LTXexample}[pos=t,wide=false] +\begin{pspicture*}(-.5,-.5)(6.2,6.2) +\psaxes{->}(0,0)(-.5,-.5)(6,6) +\psplot[linecolor=blue,linewidth=1.5pt,plotpoints=200]{.1}{6}{x GAMMA} +\psplot[linecolor=red,linewidth=1.5pt,plotpoints=200]{.1}{6}{x GAMMALN} +\end{pspicture*} +\end{LTXexample} + +\begin{LTXexample}[pos=t,wide=false] +\psset{xunit=.25,yunit=3} +\begin{pspicture}(-20,-.5)(20,1.5) +\psaxes[Dx=5,Dy=.5]{->}(0,0)(-20,-.5)(20,1.5) +\psplot[linecolor=blue,linewidth=1.5pt,plotpoints=1000]{-20}{20}{x BESSEL_J0} +\psplot[linecolor=red,linewidth=1.5pt,plotpoints=1000]{-20}{20}{x BESSEL_J1} +\end{pspicture} +\end{LTXexample} + +\begin{LTXexample}[pos=t,wide=false] +\psset{xunit=.5,yunit=3} +\begin{pspicture}*(-1.5,-.75)(19,1.5) +\psaxes[Dx=5,Dy=.5]{->}(0,0)(-1,-.75)(19,1.5) +\psplot[linecolor=blue,linewidth=1.5pt,plotpoints=1000]{0.0001}{20}{x BESSEL_Y0} +\psplot[linecolor=red,linewidth=1.5pt,plotpoints=1000]{0.0001}{20}{x BESSEL_Y1} +%\psplot[linecolor=green,plotpoints=1000]{0.0001}{20}{x 2 BESSEL_Yn} +\end{pspicture} +\end{LTXexample} + +\section{Numerical integration} + +\begin{center} +\begin{tabular}{@{} >{\sffamily}l l >{\sffamily}l l @{} } +\emph{Stack} & \emph{Operator} & \emph{Result} & \emph{Description} \\\hline +num num /var $\lbrace$ function $\rbrace$ num & \Lps{SIMPSON} & real & Return $\displaystyle\int\limits_a^b f(t)\mathrm{d}t$ +\end{tabular} +\end{center} + +%a b var f Ierr + +the first two variables are the low and high boundary integral, both can be values or +\PS\ expressions. \verb+/var+ is the definition of the integrated variable (not x!), which is +used in the following function description, which must be inside of braces. The last +number is the tolerance for the step adjustment. The function \Lps{SIMPSON} can be +nested. + +\begin{LTXexample}[pos=t,wide=false] +\psset{xunit=.75} +\begin{pspicture*}[showgrid=true](-0.4,-3.4)(10,3) + \psplot[linestyle=dashed,linewidth=1.5pt]{.1}{10}{1 x div} + \psplot[linecolor=red,linewidth=1.5pt]{.1}{10}{ + 1 % start + x % end + /t % variable + { 1 t div } % function + .001 % tolerance + SIMPSON } % + \psplot[linecolor=blue,linewidth=1.5pt]{.1}{10}{1 x /t { 1 t div } 1 SIMPSON } +\end{pspicture*} +\end{LTXexample} + +\begin{LTXexample}[pos=t,wide=false] +%%% Gaussian and relative integral from -x to x to its value sqrt{pi} +\psset{unit=2} +\begin{pspicture}[showgrid=true](-3,-1)(3,1) + \psplot[linecolor=red,linewidth=1.5pt]{-3}{3}{Euler x dup mul neg exp } + \psplot[linecolor=green,linewidth=1.5pt]{-3}{3} + { x neg x /t { Euler t dup mul neg exp } .001 SIMPSON Pi sqrt div} +\end{pspicture} +\end{LTXexample} + + +\psset{unit=1.75cm} +%%% successive polynomial developments of sine-cosine +\begin{pspicture}[showgrid=true](-3,-2)(3,2) +\psaxes{->}(0,0)(-3,-2)(3,2) +\psset{linewidth=1.5pt} +\psplot[linecolor=green, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{0 x /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } +\psplot[linecolor=blue, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{1 0 x /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} +\psplot[linecolor=yellow, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{0 x /titi + {1 0 titi /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON } +\psplot[linecolor=red, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{1 0 x /tyty + {0 tyty /titi + {1 0 titi /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} +\psplot[linecolor=magenta, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{0 x /tete + {1 0 tete /tyty + {0 tyty /titi + {1 0 titi /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON }%%% FIVE nested calls +\end{pspicture} +\psset{unit=1cm} + +\begin{lstlisting} +\psset{unit=1.75cm} +%%% successive polynomial developments of sine-cosine +\begin{pspicture}[showgrid=true](-3,-2)(3,2) +\psaxes{->}(0,0)(-3,-2)(3,2) + \psplot[linecolor=green, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{0 x /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + \psplot[linecolor=blue, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{1 0 x /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + \psplot[linecolor=yellow, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{0 x /titi + {1 0 titi /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON } + \psplot[linecolor=red, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{1 0 x /tyty + {0 tyty /titi + {1 0 titi /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + \psplot[linecolor=magenta, algebraic=false, plotpoints=61, showpoints=true] + {-3}{3}{0 x /tete + {1 0 tete /tyty + {0 tyty /titi + {1 0 titi /tata + {0 tata /tutu + {1 0 tutu /toto { toto } .1 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON } + .01 SIMPSON sub} + .01 SIMPSON }%%% FIVE nested calls +\end{pspicture} +\end{lstlisting} + +\begin{LTXexample}[pos=t,wide=false] +% ce code definit la fonction [cos(2pix cos(t))-cos(2pix)]^2 / sin(t) avec x=h/lambda +\def\F{ + 0.01 3.1 + /t + { TwoPi x mul t COS mul COS TwoPi x mul COS sub 2 exp t SIN div } + .01 SIMPSON 60 mul } +% D = 2*(cos^2(2pix))/F +\def\fD{TwoPi x mul COS dup mul 2 mul \F\space div} +\psset{llx=-1.5cm,lly=-0.5cm,urx=0.2cm,ury=0.2cm, + xAxisLabel={$h/\lambda$},xAxisLabelPos={0.5,-45},yAxisLabel={$R_r$ en ohms}, + yAxisLabelPos={-0.1,150}} +\begin{psgraph}[Dy=50,Dx=0.1,xticksize=300 0,yticksize=1 0, + comma=true,axesstyle=frame](0,0)(1,300){10cm}{5cm} + \psplot{0}{1}{\F} + \psplot[linecolor=red]{0.01}{.1}{\fD}% +\end{psgraph} +\end{LTXexample} + + + +\bgroup +\raggedright +\nocite{*} +\bibliographystyle{plain} +\bibliography{pst-math-doc} +\egroup + +\printindex + + \end{document} |