%\documentclass[final,harvardcite]{ltugboat} \documentclass[final]{ltugboat} \PrelimDraftfalse \InputIfFileExists{tugboat.dates}% {}{} \InputIfFileExists{tb72pages.tex}% {}{\def\TBpstplot{1001}} \setcounter{page}{\TBpstplot} \overfullrule=6pt \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} \usepackage[scaled=0.96]{helvet} \usepackage{mathptmx} \usepackage{courier} \usepackage{comment} \usepackage{tabularx} \usepackage{graphicx} %\usepackage{pstcol} %\usepackage{pst-plot}% % \newcommand\verbI[1]{{\small\texttt{#1}}} \newcommand\CMD[1]{{\small\textbackslash\texttt{#1}}} \setlength{\belowcaptionskip}{\abovecaptionskip} % \usepackage{listings} \lstset{language=[LaTeX]TEX,basicstyle=\ttfamily\footnotesize,% extendedchars=true,numbers=left,numberstyle=\tiny,% xleftmargin=2em,breaklines=true} % \usepackage{ifpdf} \ifpdf% \usepackage[% pdftex,% pdfauthor={Jana and Herbert Voss},% pdftitle={2D Plots},% linktocpage,% colorlinks]{hyperref} \hypersetup{% colorlinks,linkcolor={black}, citecolor={black}, pagecolor={black}, urlcolor={black} } \else \usepackage[% ps2pdf,% pdfauthor={Jana and Herbert Voss},% pdftitle={2D Plots},% linktocpage,% colorlinks]{hyperref} \fi \makeatletter \usepackage{url} \begin{document} \sectitle{Graphics} \title{The plot functions of \texttt{pst-plot}\thanks{Translated from ``Die Plot-Funktionen von pst-plot,'' \textsl{Die TeXnische Kom\"odie} \textbf{2/02}, June 2002, pages 27-34, with permission.}} \author{Jana Voß} \address{Wasgenstr. 21\\14129 Berlin \textsc{GERMANY}} \netaddress{Jana@perce.de} % \author{Herbert Voß} \address{Wasgenstr. 21\\14129 Berlin \textsc{GERMANY}} \personalURL{http://www.perce.de} \netaddress{voss@perce.de} \maketitle \begin{abstract} Plotting of external data records is one of the standard problems of technical and industrial publications. One common approach is importing the data files into an external program, such as \verbI{gnuplot}, provided with axes of coordinates and further references, and finally exported to \LaTeX. By contrast, in this article we explain ways to get proper data plotting without using external applications. \end{abstract} \section{Introduction} The history and the meaning of \PS{} have been covered sufficiently in many articles. For the programming language \PS{} have a look at \cite{PostScript,ThinkPostScript}. The package \verbI{pst-plot} \cite{pst-plot} under consideration here is part of the \verbI{pstricks} project. It must be loaded into a \LaTeX{} document as usual with \CMD{usepackage\{pst-plot\}} or alternatively, for documents written in Plain\TeX, with \CMD{input pst-plot.tex}. \verbI{pst-plot} provides three plot macros for the representation of external data, with the following syntax: {\small\begin{verbatim} \listplot*[]{} \dataplot*[]{} \fileplot*[]{} \end{verbatim}} The starred forms have the same meaning as with all macros of \verbI{pstricks}: to plot the data in a reversed mode. Thus, for a default black-on-white diagram one produces the negative with the starred command form, namely white-on-black. Additionally, a negative plot implies that \PS{} closes the path of the points from the last to the first one and fills all points inside this closed path with the actual fillcolor. For our purposes in this article there will be no real sense in this negative view; therefore, all of the following examples are plotted with the normal (unstarred) form only. For further information about the package \verbI{pstricks} have a look at the (more or less) official documentation \cite{pstricks}, or the extensive description in the ``standard \LaTeX'' book \cite{companion} or in \cite{girou:01:,girou:02:}. Altogether, however, these do not fully describe the substantial differences between these three plot macros. For all of the examples in this article, the complete \verbI{pspicture} environment is indicated, so that the examples may be directly copied. The Documentation of the \verbI{multido} macro used here can be found in the package itself \cite{multido}; macros not otherwise mentioned are described in the \verbI{pstricks} documentation \cite{pstricks}. The general \verbI{plotstyle} parameter is particularly important, and can take the values shown in table \ref{tab:options}. \begin{table} \caption{Possible options}\label{tab:options} \begin{tabularx}{1.0\linewidth}{r|X} style option& meaning\\ \hline \verbI{plotstyle=dots} & plot $(x,y)$ as a dot\\ \verbI{=line} & draw a line from a dot to the following one\\ \verbI{=polygon} & nearly the same as \verbI{line}, but with a line from the last to the first dot\\ \verbI{=curve} & interpolation between three dots, whereby the curve can go beyond the point of origin and/or termination point\\ \verbI{=ecurve} & like \verbI{curve}, but ends at the first/last dot\\ \verbI{=ccurve} & like \verbI{curve}, but closed\\ \end{tabularx} \end{table} By default, the \verbI{line} option is selected. The following general commands are also useful in conjunction with the plot commands. They are also defined by the \verbI{pst-plot} package: {\small\begin{verbatim} \readdata{}{} \savedata{}{} \end{verbatim}} In the following examples only the \CMD{readdata} macro is used, but it would be straightforward to create examples with \CMD{savedata}. \section{Examples for \CMD{listplot}} The syntax of \CMD{listplot} is : {\small\begin{verbatim} \listplot{} \end{verbatim}} The data macro may contain any additional \AllTeX- or \PS-commands. The \AllTeX{} macros are expanded first before they are passed as a \textbf{list} of $x|y$ values to \PS. The data records can be defined inside the document like {\small\begin{verbatim} \newcommand{\dataA}{ 1.00000000 1.00000000 0.56000000 0.31000000 0.85841600 0.17360000 ... \end{verbatim}} \noindent or can be read from an external data file with the \CMD{readdata} macro: {\small\begin{verbatim} \readdata{\dataA}{/anyPath/data.dat} \end{verbatim}} The example in figure \ref{fig:listplot1} shows the Henon attractor, a typical graphic of a system with chaotic behavior\cite{voss:chaos}. Figure \ref{fig:listplot2} is nearly the same as figure~\ref{fig:listplot1}, with the addition of \PS{} code to get the "Draft" watermark. (Some familiarity with \PS{} is needed to fully understand its operation.) To save space, listing \ref{lst:listplot2} does not contain the data, which is nothing more than a sequence of pairs of floats, each value separated by a space, as shown above. \begin{figure}[htb] \centering \begin{comment} \PSforPDF{% \readdata{\henon}{henon.dat} \psset{xunit=1.5cm, yunit=3cm} \begin{pspicture}(-2,-0.5)(2.25,1.25) \psaxes{->}(0,0)(-2,-0.5)(1.5,1.25) \listplot[% showpoints=true,% plotstyle=curve]{\henon} \end{pspicture}% } \end{comment} \includegraphics{fig4} \caption{Example for \CMD{listplot}}\label{fig:listplot1} \end{figure} \begin{figure}[htb] \centering \begin{comment} \newcommand{\dataA}{ 1.00000000 1.00000000 0.56000000 0.31000000 0.85841600 0.17360000 0.11249564 0.26610896 1.24788537 0.03487365 -1.20752013 0.38684447 -0.71282656 -0.37433124 -0.10602649 -0.22097623 0.76283584 -0.03286821 0.12916912 0.23647911 1.21245320 0.04004243 -1.07681914 0.37586049 -0.29387634 -0.33381393 0.54182291 -0.09110166 0.48615456 0.16796510 0.82762650 0.15070791 0.16435741 0.25656422 1.21766498 0.05095080 -1.08414872 0.37747614 -0.31506881 -0.33608610 0.52096746 -0.09767133 0.51150245 0.16149991 0.78474587 0.15856576 0.27177620 0.24327122 1.13690951 0.08425062 -0.77704042 0.35244195 0.48298173 -0.24088253 0.42320673 0.14972434 0.89181467 0.13119409 -0.01408602 0.27646255 1.27617683 -0.00436667 -1.34958997 0.39561482 -1.22719125 -0.41837289 -1.58701052 -0.38042929 gsave /Helvetica findfont 40 scalefont setfont 45 rotate 0.9 setgray -60 10 moveto (DRAFT) show grestore } \psset{xunit=1.5cm, yunit=3cm} \begin{pspicture}(-2,-0.5)(2.25,1.25) \psaxes{->}(0,0)(-2,-0.5)(1.5,1.25) \listplot[% showpoints=true,% linecolor=red,% plotstyle=curve]{\dataA} \end{pspicture}% \end{comment} \includegraphics{fig5} \caption{Example for modified \CMD{listplot}}\label{fig:listplot2} \end{figure} \begin{lstlisting}[caption={\LaTeX\ source for figure \ref{fig:listplot1}},% label={lst:listplot1}] \readdata{\henon}{henon.dat} \psset{xunit=1.5cm, yunit=3cm} \begin{pspicture}(-3,-0.5)(2.25,1.25) \psaxes{->}(0,0)(-2,-0.5)(1.5,1.25) \listplot[% showpoints=true,% linecolor=red,% plotstyle=curve]{\dataA} \end{pspicture} \end{lstlisting} \begin{lstlisting}[caption={\LaTeX\ source for figure \ref{fig:listplot2}},% label={lst:listplot2}] \newcommand{\DataA}{% [ ... data ... ] gsave % save graphic status /Helvetica findfont 40 scalefont setfont 45 rotate % rotate by 45 degrees 0.9 setgray % 1 is color white -60 10 moveto (DRAFT) show grestore } \psset{xunit=1.5cm, yunit=3cm} \begin{pspicture}(-3,-0.5)(2.25,1.25) \psaxes{->}(0,0)(-2,-0.5)(1.5,1.25) \listplot[% showpoints=true,% plotstyle=curve]{\dataA} \end{pspicture} \end{lstlisting} Naturally, \verbI{[... data ...]} is replaced by all the $x|y$-values; they're omitted here only to save space. As an alternative to direct modification of the data set passed to \CMD{listplot}, one can redefine the macro \verbI{defScalePoints} from \verbI{pst-plot}. For example, to change the $x|y$ values and then rotate the whole plotted graphic (don't ask why!), the redefinition is as shown in listing \ref{lst:listplot3}. \begin{lstlisting}[% caption={\LaTeX\ source for figure \ref{fig:listplot3}},% label={lst:listplot3}] \makeatletter \pst@def{ScalePoints}<% %------------------------------------- 45 rotate % rotate the whole object %------------------------------------- /y ED /x ED counttomark dup dup cvi eq not { exch pop } if /m exch def /n m 2 div cvi def n { %------------------------------------- exch % exchange the last two elements %------------------------------------- y mul m 1 roll x mul m 1 roll /m m 2 sub def } repeat> \makeatother \end{lstlisting} \noindent This gives figure \ref{fig:listplot3}. \begin{figure}[htb] \centering \begin{comment} \makeatletter \pst@def{ScalePoints}<% %----------------------------------------------- 45 rotate % rotate the whole object %----------------------------------------------- /y ED /x ED counttomark dup dup cvi eq not { exch pop } if /m exch def /n m 2 div cvi def n { %----------------------------------------------- exch % exchange the last two elements %----------------------------------------------- y mul m 1 roll x mul m 1 roll /m m 2 sub def } repeat> \makeatother \readdata{\henon}{henon.dat} \begin{pspicture}(-0.5,-2.75)(3,3) \psset{xunit=3cm, yunit=1.5cm} \psaxes{->}(0,0)(-0.5,-2)(1.25,2) \listplot[% showpoints=true,% plotstyle=curve]{\henon} \end{pspicture}% \end{comment} \includegraphics{fig6} \caption{Example for \CMD{listplot} with a redefined \verbI{ScalePoints}}\label{fig:listplot3} \end{figure} Thus, the advantage of \CMD{listplot} is that one can easily modify the data values without any external program. Here is one more example---suppose you have the following data records: {\small\begin{verbatim} 1050, 0.368 1100, 0.371 1200, 0.471 1250, 0.428 1300, 0.391 1350, 0.456 1400, 0.499 1500, 1.712 1550, 0.475 1600, 0.497 \end{verbatim}} \noindent which perhaps came automatically from a technical device. The unit of the x-values is micrometer but it makes more sense to use millimeter for the plot. A redefinition of \verbI{ScalePoints} makes it very easy to plot the data with this change of scale: \begin{lstlisting}[caption={Rescale all x values},label={lst:lstplot}] \makeatletter \pst@def{ScalePoints}<% /y ED /x ED counttomark dup dup cvi eq not { exch pop } if /m exch def /n m 2 div cvi def n { y mul m 1 roll x mul 1000 div m 1 roll% <-- divide by 1000 /m m 2 sub def } repeat> \makeatother \end{lstlisting} \begin{figure}[htb] \centering \begin{comment} \makeatletter \begin{pdfpic} \pst@def{ScalePoints}<% /y ED /x ED counttomark dup dup cvi eq not { exch pop } if /m exch def /n m 2 div cvi def n { y mul m 1 roll x mul 1000 div m 1 roll% <-- divide by 1000 /m m 2 sub def } repeat> \makeatother \def\dataA{% 1050 0.368 1100 0.371 1200 0.471 1250 0.428 1300 0.391 1350 0.456 1400 0.499 1500 1.712 1550 0.475 1600 0.497 }% \psset{xunit=5} \begin{pspicture}(1,-0.25)(2,2.25) \psaxes[Dx=0.25,Ox=1]{->}(1,0)(2,2) \psaxes[Dx=0.05,Ox=1,labels=none,ticksize=0.05](1,0)(2,0) \listplot[plotstyle=dots,linecolor=red]{\dataA} \end{pspicture}% \end{pdfpic} \end{comment} \includegraphics{fig7} \caption{Example for modified data values with a redefined \verbI{ScalePoints}} \label{fig:lstplot4} \end{figure} \section{Examples for \CMD{dataplot}} \CMD{dataplot} has the same syntax as \CMD{listplot}, so the first question is, what is the difference between the two? \CMD{listplot} builds a list of all the data and then multiplies all values with the length unit. This takes some time, so you may prefer a so-called ``quick plot'', where the data can be passed more quickly to \PS, depending on the plotstyle and especially the option \verbI{showpoints}. Table \ref{tab:quickplot} shows whether this is possible. A quick plot is not possible with \CMD{listplot}, whereas \CMD{dataplot} uses it whenever possible. When it is not possible, \CMD{dataplot} simply calls \CMD{listplot}. \def\hI{\hangindent=3em} \begin{table}[htb] \caption{Possible options for a ''quick plot``}\label{tab:quickplot} \begin{tabularx}{\columnwidth}{lX|l} plotstyle & options & macro\\\hline \verbI{line} & all, except & quick plot\\ & \verbI{linearc}, \verbI{showpoints}, \verbI{arrows}, & \CMD{listplot}\\ \verbI{polygon} & all, except & quick plot\\ & \verbI{linearc}, \verbI{showpoints} & \CMD{listplot}\\ \verbI{dots} & all & quick plot\\ \verbI{bezier} & all, except & quick plot\\ &\verbI{arrows}, \verbI{showpoints} & \CMD{listplot}\\ \hI\verbI{cbezier} & all, except& \CMD{listplot}\\ &\verbI{showpoints} & quick plot\\ \verbI{curve} & all & \CMD{listplot}\\ \verbI{ecurve} & all & \CMD{listplot}\\ \verbI{ccurve} & all & \CMD{listplot} \end{tabularx} \end{table} \CMD{dataplot} needs to be passed a macro holding the data. The data is typically saved in an external file, which can be read by (for instance) the \CMD{readdata} macro, as follows: {\small\begin{verbatim} \readdata{}{} \end{verbatim}} \noindent For example: {\small\begin{verbatim} \readdata{\feigenbaum}{feigenbaum.data} \end{verbatim}} The amount of data is limited only by \TeX's memory. The above example can be plotted with: {\small\begin{verbatim} \dataplot{\feigenbaum} \end{verbatim}} Overlays with different data files are also possible. For example, figure~\ref{fig:dataplot} shows the use of two different data files which are plotted using one coordinate system. It shows the sorting time for ``Bubble-Sort'' and ``Select-Sort{}'' as a function of the number of the elements. \begin{figure} \centering \begin{comment}% \psset{xunit=0.0005cm,yunit=0.005cm} \begin{pspicture}(0,-50)(10000,1100) \readdata{\bubble}{bubble.data} \readdata{\select}{select.data} \dataplot[% plotstyle=line,% linecolor=blue]{\bubble} \dataplot[% plotstyle=line,% linecolor=red,% linewidth=2pt]{\select} \psline{->}(0,0)(10000,0) \psline{->}(0,0)(0,1000) \rput[l](40,920){time} \rput[r](9990,-30){elements} \rput[l](4500,800){Bubble-Sort} \rput[l](7500,200){Select-Sort} \end{pspicture}% \end{comment} \includegraphics{fig0} \caption{Example for \CMD{dataplot}}\label{fig:dataplot} \end{figure} \begin{lstlisting}[caption={\LaTeX\ source for figure \ref{fig:dataplot}}] \psset{xunit=0.0005cm,yunit=0.005cm} \begin{pspicture}(0,-50)(10000,1100) \readdata{\bubble}{bubble.data} \readdata{\select}{select.data} \dataplot[% plotstyle=line,% linecolor=blue]{\bubble} \dataplot[% plotstyle=line,% linecolor=red,% linewidth=2pt]{\select} \psline{->}(0,0)(10000,0) \psline{->}(0,0)(0,1000) \rput[l](20,995){time} \rput[r](9990,-20){elements} \rput[l](4500,800){Bubble-Sort} \rput[l](7500,200){Select-Sort} \end{pspicture} \end{lstlisting} In summary, the advantage of \CMD{dataplot} is the possibility of a ''quick plot``, and the advantage of \CMD{listplot} is that it is easy to manipulate the data values before they are plotted. \section{Examples for \CMD{fileplot}} \CMD{fileplot} can be used whenever $(x|y)$ data that is saved in a file is to be plotted. The values must be given as pure numerical values in pairs, one pair on each line, and may have spaces, commas, parentheses, and braces as punctuation, as follows: \begin{verbatim} x y x,y (x,y) {x,y} \end{verbatim} The tab character (\CMD{t} or \acro{ASCII} \CMD{009}) is often used as a separator, but tab is \emph{not} valid here. Tabs may be converted to spaces in many ways, for example with the standard Unix utility \texttt{tr}: {\small\begin{verbatim} tr '\t' ' ' outFile \end{verbatim}} The data files may also contain \% characters, but no other characters are allowed. Our first example for \CMD{fileplot} is shown in figure~\ref{fig:fileplot1}, which is an \acro{UV/VIS} absorber spectrum $A=\lg \frac{I_{0}}{I}$ as a function of the wavelength. The second example (figure~\ref{fig:fileplot2}) shows the evolution of a population as a function of the spawn factor (Feigenbaum diagram \cite{voss:chaos}). The source code for these images is shown in listings~\ref{lst:fileplot1} and~\ref{lst:fileplot2}. \begin{figure}[htb] \centering \begin{comment}% \psset{xunit=0.0025cm,yunit=1.1cm} \begin{pspicture}(-25,-.25)(1950,4) \fileplot[plotstyle=line, linewidth=1.5pt]{fileplot.data} \psaxes[dx=400,Dx=400]{->}(1900,4) \multido{\n=200+200}{9}{% \psline[linestyle=dotted](\n,0)(\n,4) } \multido{\n=+1}{5}{% \psline[linestyle=dotted](0,\n)(1800,\n)% } \end{pspicture}% \end{comment} \includegraphics{fig1} \caption{Example for \CMD{fileplot}}\label{fig:fileplot1} \end{figure} \begin{lstlisting}[caption={\LaTeX\ source for figure \ref{fig:fileplot1}},label={lst:fileplot1}] \psset{xunit=0.0025cm,yunit=1.1cm} \begin{pspicture}(-25,-.25)(1950,4) \fileplot[plotstyle=line]{fileplot.data} \psaxes[dx=400,Dx=400]{->}(1900,4) \multido{\n=200+200}{9}{% \psline[linestyle=dotted](\n,0)(\n,4)% } \multido{\n=+1}{5}{% \psline[linestyle=dotted]% (0,\n)(1800,\n)% } \end{pspicture} \end{lstlisting} \begin{figure}[htb] \centering \begin{comment}% \psset{xunit=1.25cm,yunit=5cm} \begin{pspicture}(-0.25,-0.05)(4.25,1.2) \fileplot[plotstyle=dots]{feigenbaum.data} \psaxes{->}(0,0)(4.05,1) \rput(4,-0.05){$x$} \rput(0.2,1.05){$y$} \rput[l](0.2,3.75){Feigenbaum-Diagram} \end{pspicture}% \end{comment} \includegraphics{fig2} \caption{Another example for \CMD{fileplot}}\label{fig:fileplot2} \end{figure} \begin{lstlisting}[caption={\LaTeX\ source for figure \ref{fig:fileplot2}},label={lst:fileplot2}] \psset{xunit=1.5cm,yunit=6cm} \begin{pspicture}(-0.25,-0.05)(4.25,1) \fileplot[plotstyle=dots]{% feigenbaum.data} \psaxes{->}(0,0)(4.05,1) \end{pspicture} \end{lstlisting} As you may see in listing \ref{lst:fileplot}, \CMD{fileplot} does little of its own. It first calls \CMD{readdata} to read the data, and then, depending on the kind of data and specified options, \CMD{fileplot} uses \CMD{dataplot} for a quick plot if possible. Otherwise, it falls back to \CMD{listplot}. \begin{lstlisting}[caption={The source of the \CMD{fileplot} macro},label={lst:fileplot}] \def\fileplot{\def\pst@par{}\pst@object{fileplot}} \def\fileplot@i#1{% \pst@killglue \begingroup \use@par \@pstfalse \@nameuse{testqp@\psplotstyle}% \if@pst \dataplot@ii{\pst@readfile{#1}}% \else \listplot@ii{\pst@altreadfile{#1}}% \fi \endgroup \ignorespaces% } \end{lstlisting} \CMD{fileplot} has the advantage of being easy to use, but the disadvantage of needing a lot of memory: \TeX{} has to read the all the data values before it can process anything. As a rule of thumb, when there are more than 1000 data entries \TeX{}'s main menory must be increased. Furthermore, the running time may be enormous, especially on slow machines. To prevent such problems, one can use the \CMD{PSTtoEPS} macro to create an \texttt{eps} file. For more information, see the documentation of \verbI{pstricks} \cite{pstricks}. \bibliographystyle{plain} \bibliography{\jobname} %\bibliographystyle{ltugbib} \makesignature \end{document}