%% This is the package dsptricks %% %% (c) Paolo Prandoni %% %% This program can be redistributed and/or modified under the terms %% of the LaTeX Project Public License Distributed from CTAN archives %% in directory macros/latex/base/lppl.txt. %% %% DESCRIPTION: %% `dsptricks' is a LaTeX package based on PSTricks to plot discrete- and continuous-time %% signals, pole-zero plots and DSP block diagrams. The package has been developed %% while writing the textbook "Signal Processing for Communication" by P. Prandoni %% and M. Vetterli, freely available at www.sp4comm.org %% %% v1.0, July 2014 %% \RequirePackage{pstricks} \RequirePackage{pstricks-add} \RequirePackage{pst-xkey} \RequirePackage{calc} \RequirePackage{fp} \RequirePackage{ifthen} % \ProvidesPackage{dsptricks}[2014/07/24 package for signal processing graphics] % turn off FP messages \FPmessagesfalse \makeatletter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Sizes and units: %% %% default values for plot size %% \newlength{\dspWidth}\setlength{\dspWidth}{0.7\textwidth} \newlength{\dspHeight}\setlength{\dspHeight}{0.43\dspWidth} \def\dspAxisColor{black} % %% Actual size (this is the size of the chart's frame, labels are extra) \newlength{\dspW} \newlength{\dspH} %% Basic Unit is a function of plot size \newlength{\dspBU} %% Derived units: \newlength{\dspLineWidth} \newlength{\dspStemWidth} \newlength{\dspDotSize} \newlength{\dspTickLen} \newlength{\dspXTickGap} \newlength{\dspYTickGap} \newlength{\dspTickLineWidth} \newlength{\dspFrameLineWidth} %% psTricks units \newlength{\dspUnitX} \newlength{\dspUnitY} \newlength{\dspTmpLen} %% booleans \newif\ifXTicks \newif\ifDoXTicks \newif\ifYTicks \newif\ifDoYTicks \newif\ifXLabel \newif\ifYLabel \newif\ifXAxisExp \newif\ifYAxisExp \newif\ifXAxisFreq \newif\ifXInside %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% dspPlot environment: %% %% \begin{dspPlot}[OPTIONS]{xMin, xMax}{yMin, yMAx} %% %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Keys for data plots : %% \define@key{dspDP}{width}{\setlength{\dspW}{#1}} \define@key{dspDP}{height}{\setlength{\dspH}{#1}} \define@key{dspDP}{xlabel}{\def\dspXLabel{#1}\XLabeltrue} \define@key{dspDP}{ylabel}{\def\dspYLabel{#1}\YLabeltrue} \define@key{dspDP}{rlabel}{\def\dspYLabelR{#1}\YLabeltrue} % right-side y-axis label \define@key{dspDP}{sidegap}{\def\sg{#1}} \define@choicekey*+{dspDP}{xtype}[\ll\ln]{time,freq}[time]{% \ifcase\ln\relax \XAxisFreqfalse \or \XAxisFreqtrue \fi}{} \define@choicekey*+{dspDP}{xticks}[\ll\ln]{auto,none,custom}[auto]{% \DoXTickstrue\XTickstrue\def\incX{-1}\def\piFrac{2} \ifcase\ln\relax \relax \or \DoXTicksfalse\XTicksfalse \or \DoXTicksfalse \fi}{% \DoXTickstrue\XTickstrue \def\incX{#1}\def\piFrac{#1}} \define@choicekey*+{dspDP}{yticks}[\ll\ln]{auto,none,custom}[auto]{% \DoYTickstrue\YTickstrue\def\incY{-1} \ifcase\ln\relax \relax \or \DoYTicksfalse\YTicksfalse \or \DoYTicksfalse \fi}{% \DoYTickstrue\YTickstrue \def\incY{#1}} \newif\ifXTicksOut \define@key{dspDP}{xout}{\XTicksOuttrue} \define@key{dspDP}{inticks}{\XInsidetrue} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% dspPlot environment %% \newenvironment{dspPlot}[3][]{% % default values \def\dspXlabel{}\XLabelfalse% \def\dspYLabel{}\def\dspYLabelR{}\YLabelfalse% \XAxisFreqfalse% \XTicksOutfalse% \setlength{\dspW}{\dspWidth}\setlength{\dspH}{\dspHeight}% \presetkeys{dspDP}{xticks=auto,yticks=auto}{}% \presetkeys{dspDP}{sidegap=-1}{}% \setkeys{dspDP}{#1}% %% %% set up \ifXAxisFreq\def\sg{0} \fi% \dspSetDims#2,#3,\sg\relax% \dspSetupAxes %% %% special x-axis for frequency plots \ifXAxisFreq\FPset\incX{1}% \ifXAxisExp% % x-axis is not on bottom; skip last values \FPupn\stX{\dspMinX{} \piFrac{} * 1 + 0 trunc}% \FPupn\tlimX{\stX{} \dspMaxX{} \piFrac{} * - 0 trunc}% \else% \FPupn\stX{\dspMinX{} \piFrac{} * 0 trunc}% \FPupn\tlimX{\stX{} \dspMaxX{} \piFrac{} * - 1 + 0 trunc}\relax\fi% % \ifXTicksOut% undo above if ticks explicitly out \FPupn\stX{\dspMinX{} \piFrac{} * 0 trunc}% \FPupn\tlimX{\stX{} \dspMaxX{} \piFrac{} * - 1 + 0 trunc}\relax\fi % \def\thisTickX##1{% \FPupn\u{\piFrac{} ##1 /}% \psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](\u,\haY)(\u,\tickEndX)} \def\thisTickLabelX##1##2{% \FPupn\u{\piFrac{} ##1 /}% \rput*[B]{{0}}(\u,\tickTxtX){{\simplifyPiFrac{##1}{\piFrac}}}}% \else \def\thisTickX{\dspTickX}\def\thisTickLabelX{\dspTickLabelX}\relax\fi %% %% start the plot \begin{pspicture}(\LX,\BY)(\RX,\TY) %\showpointstrue %\psframe[dimen=middle,linewidth=1pt,linecolor=red](\LX,\BY)(\RX,\TY)% \ifXAxisExp\psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](\dspMinX,0)(\dspMaxX,0)\fi \dspPlotFrame %% %% draw ticks selectively according to user options \ifDoXTicks\multido{\n=\stX+\incX}{\tlimX}{\thisTickX{\n}}\fi \ifDoYTicks\multido{\n=\stY+\incY}{\tlimY}{\dspTickY{\n}}\fi }{% %% tick labels \psset{xunit=\dspUnitX,yunit=\dspUnitY} %user may have changed those \ifDoXTicks\multido{\n=\stX+\incX}{\tlimX}{\thisTickLabelX{\n}{$\n$}}\fi \ifDoYTicks\multido{\n=\stY+\incY}{\tlimY}{\dspTickLabelY{\n}{$\n$}}\fi \dspLabels \end{pspicture}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Custom ticks %% %% \dspCustomTicks[axis={x|y}]{value label ...} %% %% if using macros for values, enclose them in curly braces: %% \def\a{1 } %% \dspCustomTicks{{\a} 1} %% \define@choicekey*{dspCT}{axis}[\ll\ln]{x,y,ry}[x]{% \def\dspCA{\ln}} \define@key{dspCT}{color}{\def\tickColor{#1}} \newcommand{\dspCustomTicks}[2][]{% \presetkeys{dspCT}{axis=x,color=black}{}% \setkeys{dspCT}{#1}% \ifcase\dspCA\relax% \def\dspMkTk##1##2{\dspTickX{##1}{\dspTickLabelX{##1}{##2}}}% \or \def\dspMkTk##1##2{\dspTickY{##1}{\dspTickLabelY{##1}{##2}}}% \or \def\dspMkTk##1##2{{\dspTickLabelYR{##1}{##2}}}% \fi \def\dspMakeTicks##1 ##2 ##3\relax{% \ifx&##3& \dspMkTk{##1}{##2} % \else \dspMkTk{##1}{##2} \relax % \dspMakeTicks##3\relax% \fi}% \dspMakeTicks#2 \relax} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Draw legend %% %% \dspLegend(x,y){color label color label ...} %% \def\dspLegend(#1,#2)#3{% \rput[lt](#1,#2){\fbox{% \begin{tabular}{ll} \@dsplegend#3 \@empty \end{tabular}}}} \def\@dsplegend#1 #2 #3{% {\color{#1}\rule[0.5ex]{2em}{2pt}} & #2\\ \space % fbox here to have a visual test \ifx #3\@empty\else \expandafter\@dsplegend \fi #3} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Redraw frame around plot %% \newcommand{\dspPlotFrame}{ \psframe[dimen=middle,linewidth=\dspFrameLineWidth,linecolor=black]% (\dspMinX,\dspMinY)(\dspMaxX,\dspMaxY)} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Environment to clip plots to within the frame box. Do not leave %% spaces in the environment's body otherwise graph will shift %% \newenvironment{dspClip}{% \psclip{\psframe[dimen=middle,linestyle=none](\dspMinX,\dspMinY)(\dspMaxX,\dspMaxY)}}{% \endpsclip} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plotting discrete-time signals in the dspPlot environment: %% %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Keys for plotting functions (these are set together with pstricks keys %% so they must use the [psset] prefix and be declared) %% %% xmin=N, %% xmax=N range for the plotted signal %% \define@key[psset]{dspData}{xmin}{\def\dspXmin{#1}} \define@key[psset]{dspData}{xmax}{\def\dspXmax{#1}} \pst@addfams{dspData} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot discrete-time points %% %% \dspTaps[OPTIONS]{x1 y1 x2 y2 ...} %% \newcommand{\dspTaps}[2][]{% \listplot[plotstyle=LineToXAxis, linestyle=solid,% showpoints=true, dotstyle=*, linewidth=\dspStemWidth,% dotsize=\dspDotSize, #1]{\expandafter\m@keList#2 \relax}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot discrete-time points starting at a given abscissa %% Data in this case is only ordinates %% %% \dspTapsAt{x0}{y0 y1 y2,...} %% \newcommand{\dspTapsAt}[3][]{% % use postscript to iterate over space-separated list and create indices \listplot[plotstyle=LineToXAxis, linestyle=solid,% showpoints=true, dotstyle=*, linewidth=\dspStemWidth,% dotsize=\dspDotSize, #1]{% #2 [#3] { % n [] % n a0 1 index % n a0 n 1 add } forall pop }} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot discrete-time signal from a data file %% %% \dspTapsFile[OPTIONS]{FILE} %% \newcommand{\dspTapsFile}[2][]{% \readdata{\data}{#2}% \listplot[plotstyle=LineToXAxis, linestyle=solid,% showpoints=true, dotstyle=*,% linewidth=\dspStemWidth, dotsize=\dspDotSize,% #1]{\data}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot discrete-time signal %% %% \dspSignal[OPTIONS]{PS code} %% \newcommand{\dspSignal}[2][]{% \presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}% \setkeys*[psset]{dspData}{#1}% \FPupn\mn{{\dspXmin} 0 trunc clip }% \FPupn\mx{{\dspXmax} 0 trunc clip }% \FPupn\ntaps{\mn{} \mx{} - 1 + 0 trunc clip}% \psplot[plotstyle=LineToXAxis, linestyle=solid,% showpoints=true, dotstyle=*,% linewidth=\dspStemWidth, dotsize=\dspDotSize,% plotpoints=\ntaps, #1]% {\mn}{\mx}{#2}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot discrete-time signal with postscript initialization options %% %\dspSignalOpt[OPTIONS]{PS init code}{PS code} %% \newcommand{\dspSignalOpt}[3][]{% \presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}% \setkeys*[psset]{dspData}{#1}% \FPupn\ntaps{\dspXmin{} \dspXmax{} - 1 + 0 trunc}% \psplot[plotstyle=LineToXAxis, linestyle=solid,% showpoints=true, dotstyle=*,% linewidth=\dspStemWidth, dotsize=\dspDotSize,% plotpoints=\ntaps, #1]% {\dspXmin}{\dspXmax}[{#2}]{#3}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plotting continuous-time signals in the dspPlot environment: %% %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot smooth function %% %% \dspFunc[OPTIONS]{PS code} %% \newcommand{\dspFunc}[2][]{% \presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}% \setkeys*[psset]{dspData}{#1}% \psplot[linewidth=\dspLineWidth, plotpoints=\dspPSPoints,% linejoin=1,#1]{\dspXmin}{\dspXmax}{#2}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot smooth function with postscript initialization options %% %% \dspFuncOpt[OPTIONS]{PS init code}{PS code} %% \newcommand{\dspFuncOpt}[3][]{% \presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}% \setkeys*[psset]{dspData}{#1}% \psplot[linewidth=\dspLineWidth, plotpoints=\dspPSPoints,% linejoin=1,#1]{\dspXmin}{\dspXmax}[{#2}]{#3}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot smooth function from a set of points %% %% \dspFuncData[OPTIONS]{x1 y1 x2 y2 ...} %% \newcommand{\dspFuncData}[2][]{% \listplot[linewidth=\dspLineWidth,linejoin=1,plotstyle=line,#1]{\expandafter\m@keList#2 \relax}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot smooth function from a set of points starting at a given point %% Data in this case is only ordinates %% %% \dspFuncDataAt[OPTIONS]{x1}{y1 y2 ...} %% \newcommand{\dspFuncDataAt}[3][]{% \listplot[linewidth=\dspLineWidth,linejoin=1,plotstyle=line,#1]{% #2 [#3] { % n [] % n a0 1 index % n a0 n 1 add } forall pop }} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot smooth function from a data file %% file must contain a list of space-separated abscissa and ordinate pairs %% %% \dspFuncFile[OPTIONS]{FILE} %% \newcommand{\dspFuncFile}[2][]{% \readdata{\data}{#2}% \listplot[linewidth=\dspLineWidth,linejoin=1,plotstyle=line,#1]{\data}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% Plot Dirac deltas %% %% \dspDiracs[OPTIONS]{x1 y1 x2 y2 ...} %% \newcommand{\dspDiracs}[2][]{% \def\dirac##1##2{\psline[linestyle=solid,linewidth=\dspLineWidth,#1]{->}(! ##1 0)(! ##1 ##2)} \doOnPairs{dirac}{#2}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Periodize function over the [-1, 1] interval % \newcommand{\dspPeriod}[1]{ #1 sub #1 2 mul div dup floor sub #1 2 mul mul #1 sub } \newcommand{\dspPeriodize}{ \dspPeriod{1} } \newcommand{\dspMainPeriod}[1][]{% \psframe[linecolor=lightgray,linewidth=0.4pt,#1](-1,\dspMinY)(1,\dspMaxY)} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Plot text % \dspText(x,y){text} \newcommand{\dspText}[2]{% \rput*[B]{0}#1{#2}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Pole-Zero Plots % % Specialized options: % % circle=["true" | "false"] draw unit circle % clabel="text" set a label at circle unit % roc % \define@key{dspPZ}{width}{\setlength{\dspW}{#1}\setlength{\dspH}{#1}} \define@key{dspPZ}{height}{\setlength{\dspH}{#1}} \define@key{dspPZ}{circle}{\def\dspCircle{#1}} \define@key{dspPZ}{clabel}{\def\dspCircleLabel{#1}} \define@choicekey*+{dspPZ}{xticks}[\ll\ln]{auto,none}[auto]{% \DoXTickstrue\def\incX{-1} \ifcase\ln\relax \relax \or \DoXTicksfalse \fi}{% \DoXTickstrue \def\incX{#1}} \define@choicekey*+{dspPZ}{yticks}[\ll\ln]{auto,none}[auto]{% \DoYTickstrue\def\incY{-1} \ifcase\ln\relax \relax \or \DoYTicksfalse \fi}{% \DoYTickstrue \def\incY{#1}} \newif\ifComplexLabels \define@choicekey*{dspPZ}{cunits}[\ll\ln]{true,false}[true]{% \ifcase\ln\relax \ComplexLabelstrue \or \ComplexLabelsfalse \fi} \define@key{dspPZ}{roc}{\def\PZCROC{#1}} \define@key{dspPZ}{antiroc}{\def\PZAROC{#1}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newenvironment{dspPZPlot}[2][]{% \setlength{\dspW}{\dspHeight}\setlength{\dspH}{\dspHeight}% \ComplexLabelstrue% \presetkeys{dspPZ}{xticks=auto,yticks=auto,circle=1,clabel={ },roc=-1,antiroc=-1}{}% \setkeys{dspPZ}{#1}% % %% set up \dspSetDims{-#2},{#2},{-#2},{#2},0\relax% \dspSetupAxes% % \gdef\dspTickX##1{\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,-\tickEndX)(##1,\tickEndX)}% \gdef\dspTickY##1{\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](-\tickEndY,##1)(\tickEndY,##1)}% \gdef\dspTickLabelY##1##2{\uput{{2\dspYTickGap}}[0]{{0}}(\tickEndY,##1){{##2}}}% \gdef\dspTickLabelX##1##2{\rput[B]{{0}}(##1,\tickTxtX){{##2}}}% % %% start the plot \begin{pspicture}(\LX,\BY)(\RX,\TY) \FPifpos\PZCROC% \pscustom[fillstyle=vlines,hatchcolor=lightgray,linecolor=lightgray,linewidth=0]{% \psarc(0,0){\PZCROC\dspUnitX}{0}{360}% \psline[linecolor=\dspAxisColor](\dspMaxX,0)(\dspMaxX,\dspMinY)(\dspMinX,\dspMinY)% (\dspMinX,\dspMaxY)(\dspMaxX,\dspMaxY)(\dspMaxX,0)} \pscircle[linecolor=lightgray,dimen=middle]{\PZCROC\dspUnitX}\relax\fi \FPifpos\PZAROC% \pscircle[fillstyle=vlines,hatchcolor=lightgray,linecolor=lightgray,dimen=middle]{\PZAROC\dspUnitX}\relax\fi %% \psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](\dspMinX,0)(\dspMaxX,0)% \psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](0,\dspMinY,0)(0,\dspMaxY)% \dspPlotFrame% \FPifgt\dspCircle{0}% \FPmul\r\dspCircle{\strip@pt\dspUnitX}% \pscircle[linewidth=\dspFrameLineWidth,dimen=middle](0,0){{\r}pt}% \ifx\@empty\dspCircleLabel% \def\dspCircleLabel{\dspCircle}\relax\fi \FPupn\r{0.6 \dspTSX{} mul \dspCircle{} add}% \rput[b]{0}(\r,\tickTxtX){\dspCircleLabel}\relax\fi % % draw ticks selectively according to user options % but here skip zero and intersections with the circle (if any) \FPupn\r{\tlimX{} 1 sub 2 div clip}% \def\xt{% \multido{\n=\stX+\incX}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickX{\n}\fi}% \multido{\n=\incX+\incX}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickX{\n}\fi}% \multido{\n=\stX+\incX}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickLabelX{\n}{$\n$}\fi}% \multido{\n=\incX+\incX}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickLabelX{\n}{$\n$}\fi}}% \def\yt{% \multido{\n=\stY+\incY}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickY{\n}\fi}% \multido{\n=\incY+\incY}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickY{\n}\fi}% \multido{\n=\stY+\incY}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickLabelY{\n}{$\n$}\fi}% \multido{\n=\incY+\incY}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickLabelY{\n}{$\n$}\fi}}% \ifDoXTicks\xt\fi \ifDoYTicks\yt\fi \ifComplexLabels% \rput[mr]{0}(\dspMaxX,1em){Re~}% \FPupn\r{\dspMaxY{} 0.6 \dspTSY{} mul sub}% \rput[t]{0}(-1.2em,\r){Im~}\relax\fi }{% \end{pspicture}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Keyvals for poles and zeros % \newif\ifPZPole \define@choicekey*[psset]{dspPZP}{type}[\ll\ln]{zero,pole}[zero]{% \ifcase\ln\relax \PZPolefalse \or \PZPoletrue \fi} \newif\ifPZLabel \define@choicekey*+[psset]{dspPZP}{label}[\ll\ln]{auto,none}[auto]{% \def\PZLabel{}\relax% \ifcase\ln\relax \PZLabeltrue \or \PZLabelfalse \fi}{% \PZLabeltrue \def\PZLabel{#1}} \define@key[psset]{dspPZP}{lpos}{\def\PZLP{#1}} \pst@addfams{dspPZP} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Plot pole-zero point % % \dspPZPoint[OPTIONS]{RE,IM} % % RE, IM coordinates % % Options: % % type = ["pole" | "zero"] circle or cross (default: pole) % label=["false" | TEXT ] the point's label (default: false) % lpos = ANGLE label position (default: 45) % \newcommand{\dspPZ}[2][]{% \presetkeys[psset]{dspPZP}{type=pole,label=auto}{}% \setkeys*[psset]{dspPZP}{#1}% \ifPZPole \psdot[dotstyle=+,dotsize=1.4ex,dotscale=1.5,dotangle=45, #1](\twoArgSplit#2) \else \psdot[dotstyle=*,dotsize=1.4ex,#1](\twoArgSplit#2) \fi \ifx\@empty\PZLabel \def\PZLabel{$(\twoArgSplit#2)$} \fi % tricky bug in pstricks so we can't use presetkeys for angle... Could not understand \ifdefined\PZLP \relax \else \def\PZLP{45} \fi \ifPZLabel \uput[\PZLP]{0}(\twoArgSplit#2){\PZLabel} \fi} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \define@key{dspCP}{width}{\setlength{\dspCPW}{#1}\setlength{\dspCPH}{#1}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % dspCP environment % % \begin{dspCP}[OPTIONS]{MAX} % % \newlength{\dspCPW}\newlength{\dspCPH} \newenvironment{dspCP}[3][]{% %% scale dimensions so that axes have equal units \setlength{\dspCPW}{0.37\textwidth}\setlength{\dspCPH}{\dspCPW} \setlength{\dspW}{\dspCPW}\setlength{\dspH}{\dspCPH} \setkeys*{dspCP}{#1}% \dspSetDims#2,#3,0\relax% \FPupn\g{\dspRngY{} {\strip@pt\dspCPW} / \dspRngX{} * 0 trunc}% \setlength{\dspCPH}{1pt*\g}% %% \begin{dspPlot}[#1,sidegap=0,inticks=true,width=\dspCPW,height=\dspCPH]{#2}{#3}% \ifYAxisExp\psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](0,\dspMinY)(0,\dspMaxY)\fi }{% %% redo ticks and axes since images may overlap a little \dspPlotFrame \ifDoXTicks\multido{\n=\stX+\incX}{\tlimX}{\dspTickX{\n}}\fi \ifDoYTicks\multido{\n=\stY+\incY}{\tlimY}{\dspTickY{\n}}\fi \end{dspPlot}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Plot Dirac deltas % % \dspPoints[OPTIONS]{x1 y1 x2 y2 ...} % \newcommand{\dspPoints}[2][]{% \listplot[plotstyle=dots,% showpoints=true, dotstyle=*,% dotsize=\dspDotSize, #1]{\m@keList#2 \relax}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Plot Dirac delta with value % % \dspDiracs[OPTIONS]{x, y}{text} % \newcommand{\dspPointValue}[3][]{% \psdot[dotstyle=*, dotsize=\dspDotSize, #1](\twoArgSplit#2)% \uput[45]{0}(\twoArgSplit#2){#3}} \newcommand{\dspPointValueSC}[3][]{% \SpecialCoor \psdot[dotstyle=*, dotsize=\dspDotSize, #1](#2)% \uput[45]{0}(\twoArgSplit#2){#3} \NormalCoor} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Plot image from file \newcommand{\dspImageFile}[1]{% \FPupn\u{2 \dspRngX{} 1.01 * / \dspMinX{} + }\FPupn\v{2 \dspRngY{} 1.01 * / \dspMinY{} + }% \setlength{\dspCPW}{1.01\dspW}\setlength{\dspCPH}{1.01\dspH}% \rput(\u,\v){\includegraphics[width=\dspCPW,height=\dspCPH]{#1}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Quick image plot, with frame but no additional space around it \newcommand{\dspShowImage}[2][0.37\textwidth]{% \psset{xunit=#1,yunit=#1}% \begin{pspicture}(0,0)(0,1)% \includegraphics[width=#1,height=#1]{#2}% \psframe[dimen=middle,linewidth=1.1pt](-0.01,0)(-.99,.99) \end{pspicture}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% Some geometrical primitives % \newif\ifPointToOrg \define@choicekey*[psset]{dspPZP}{toorg}[\ll\ln]{true,false}[false]{% \ifcase\ln\relax \PointToOrgtrue \or \PointToOrgfalse \fi} % [opts]{x,y}{label} \newcommand{\dspCPPoint}[3][]{% \setkeys*[psset]{dspPZP}{#1}% \psdot[dotstyle=*, dotsize=\dspDotSize, #1](#2)% \uput[45]{0}(#2){#3}% \ifPointToOrg\psline[linewidth=\dspTickLineWidth, #1](0,0)(#2)\fi} % [opts]{x,y in special coor}{label} \newcommand{\dspCPPointSC}[3][]{% \setkeys*[psset]{dspPZP}{#1}% \SpecialCoor% \psdot[dotstyle=*, dotsize=\dspDotSize, #1](#2)% \uput[45]{0}(#2){#3}% \ifPointToOrg\psline[linewidth=\dspTickLineWidth, #1](! 0 0 )(#2)\fi% \NormalCoor} % [opts]{x,y}{r} \newcommand{\dspCPCircle}[3][]{% \pscircle[#1](#2){#3\dspUnitX}} % [opts]{r}{a}{label} \newcommand{\dspCPCirclePoint}[4][]{% \setkeys*[psset]{dspPZP}{#1}% \SpecialCoor% \def\pcorps{! #3 cos #2 mul #3 sin #2 mul}% \FPupn\q{#2 1.1 * 2 trunc}% \uput*{\q\dspUnitX}[#3]{0}(0,0){#4}% \psdot[dotstyle=*, dotsize=\dspDotSize, #1](\pcorps)% \ifPointToOrg\psline[linewidth=\dspTickLineWidth, #1](! 0 0 )(\pcorps)\fi% \NormalCoor} % [opts] {r}{a}{b}{label} \newcommand{\dspCPArc}[5][]{% \FPupn\p{#3 #4 + 0.5 * 2 trunc}% \FPupn\q{#2 1.1 * 2 trunc}% \uput*{\q\dspUnitX}[\p]{0}(0,0){#5}% \psarc[linewidth=2\dspTickLineWidth, #1]{->}{#2\dspUnitX}{#3}{#4}} \newcommand{\dspCPArcn}[5][]{% \FPupn\p{#3 #4 + 0.5 * 2 trunc}% \FPupn\q{#2 1.1 * 2 trunc}% \uput*{\q\dspUnitX}[\p]{0}(0,0){#5}% \psarcn[linewidth=2\dspTickLineWidth, #1]{->}{#2\dspUnitX}{#3}{#4}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Helpers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% This is called at each plot setup with xmin, xmax, ymin, ymax and sidegap %% and sets all lengths \def\dspSetDims#1,#2,#3,#4,#5\relax{% \def\sideGap{#5}% % default sidegap: 5% of range \FPifneg\sideGap\FPupn\sideGap{#1 #2 - 0.05 * 0.5 + 2 trunc}\fi% \FPifgt\sideGap{1}\FPtrunc\sideGap\sideGap{0}\fi% %% %% active range for the independent variable \def\dspMinActX{#1}% \def\dspMaxActX{#2}% %% axes range (including sidegap) \FPupn\dspMinX{\sideGap{} #1 - clip}% \FPupn\dspMaxX{\sideGap{} #2 + clip}% \FPupn\dspRngX{#1 #2 - \sideGap{} 2 * + clip}% \FPupn\dspMinY{#3 0 + clip}% \FPupn\dspMaxY{#4 0 + clip}% \FPupn\dspRngY{#3 #4 - clip}% %% % if y-range is across zero we'll need to draw the x-axis \FPmul\u\dspMinY\dspMaxY% \FPifneg\u\XAxisExptrue\else\XAxisExpfalse\fi% %% same for x (but usually we never draw the y axis) \FPmul\u\dspMinX\dspMaxX% \FPifneg\u\YAxisExptrue\else\YAxisExpfalse\fi% %% %% pstricks units: we scale the units so that coordinates are "real" coords on the axes \FPupn\tmp{\dspRngX{} {\strip@pt\dspW} / } \setlength{\dspUnitX}{\tmp pt}% \FPupn\tmp{\dspRngY{} {\strip@pt\dspH} / }% \setlength{\dspUnitY}{\tmp pt}% %% %% basic unit based on the size of the image: ~1pt for a 10x5 cm box \FPupn\g{2 {\strip@pt\dspW} {\strip@pt\dspH} * root 0.005 * 0 round 1 max}% \setlength{\dspBU}{1pt*\g}% %% derived sizes: lines and fonts \setlength{\dspLineWidth}{1.8\dspBU}% \setlength{\dspDotSize}{5\dspBU}% \setlength{\dspStemWidth}{1.4\dspBU}% \fontsize{9\dspBU}{10\dspBU}\selectfont% % %% ticks on axes \setlength{\dspTickLen}{4\dspBU}% \setlength{\dspTickLineWidth}{0.4\dspBU}% \setlength{\dspXTickGap}{6\dspBU}\addtolength{\dspXTickGap}{2ex}% \setlength{\dspYTickGap}{2\dspBU}% \setlength{\dspFrameLineWidth}{2.2\dspTickLineWidth}% %% %% height of a line of text in psticks units \setlength{\dspTmpLen}{1em}% \FPupn\dspTSX{{\strip@pt\dspUnitX} {\strip@pt\dspTmpLen} / }% \FPupn\dspTSY{{\strip@pt\dspUnitY} {\strip@pt\dspTmpLen} / }% %% %% find the coordinates of the plot's bounding box, including labels \ifYLabel% \FPupn\LX{\dspTSX{} 4 * \dspMinX{} -}% \FPupn\RX{\dspTSX{} 4 * \dspMaxX{} +}% \else% \FPupn\LX{\dspTSX{} 2 * \dspMinX{} -}% \FPupn\RX{\dspTSX{} 2 * \dspMaxX{} +}% \fi \FPupn\TY{\dspTSY{} \dspMaxY{} +}% \def\outTicks{% \ifXTicks\FPupn\BY{\dspTSY{} 2.5 * \dspMinY{} -}\else\FPupn\BY{\dspTSY{} \dspMinY{} -}\fi% \ifXLabel\FPupn\BY{\dspTSY{} 1.5 * \BY{} -}\else\relax\fi }% \ifXAxisExp % ticks are inside \ifXLabel\FPupn\BY{\dspTSY{} 2.5 * \dspMinY{} -}\else\FPupn\BY{\dspTSY{} \dspMinY{} -}\fi% \else% ticks are outside \outTicks \fi% % did we select explicit outside ticks? \ifXTicksOut\outTicks \fi% %% %% x-axis resolution for plotting functions: ~60 values/cm \FPupn\dspPSPoints{{\strip@pt\dspW} 2 * 0 trunc}% %% \psset{xunit=\dspUnitX, yunit=\dspUnitY}% \psset{linewidth=\dspLineWidth}%www } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Draw axis labels (if required) under x axis and to left and right of y axes %% \def\dspLabels{% % horizontal label \ifXTicksOut\XAxisExpfalse\fi% \ifXLabel% \FPupn\mid{\dspMinX{} \dspMaxX{} + 0.5 mul}% \ifXAxisExp% \FPupn\pos{\dspTSY{} 2 * \dspMinY{} -}% \else% \ifXTicks% \FPupn\pos{\dspTSY{} 3 * \dspMinY{} -}% \else% \FPupn\pos{\dspTSY{} 2 * \dspMinY{} -}% \fi% \fi% \rput[b]{0}(\mid,\pos){\dspXLabel}% \fi% % \FPupn\mid{\dspMinY{} \dspMaxY{} + 0.5 mul}% \ifYTicks% \FPupn\pos{\dspTSX{} 3.4 * \dspMinX{} -}% \else% \FPupn\pos{\dspTSX{} 1 * \dspMinX{} -}% \fi% \rput[b]{90}(\pos,\mid){\dspYLabel} %% \FPupn\pos{\dspTSX{} 3 * \dspMaxX{} +}% \rput[b]{-90}(\pos,\mid){\dspYLabelR}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% This sets axes ticks (spacing and number) and prepares macros %% for plotting ticks and tick labels \def\dspSetupAxes{% %% tick increments; if incX/Y is zero, compute suitable value \FPifgt\incX{0}\FPupn\incX{\incX{} 2 trunc}% \else\FPupn\incX{\dspMinActX{} \dspMaxActX{} - 1 + 6 swap / 0 trunc 1 max}\relax\fi% \FPifgt\incY{0}\FPupn\incY{\incY{} 2 trunc}% \else\FPupn\incY{\dspMinY{} \dspMaxY{} - 1 + 6 swap / 0 trunc 1 max}\relax\fi% %% %% now find starting point and increment for ticks (and number of ticks) %% start with y-axis: \ifXAxisExp% is y=0 explicit or does it coincide with the lower edge? \def\haY{0}% % make sure ticks hit zero; add small epsilons to avoid ticks at the limits \FPupn\stY{\incY{} \dspMinY{} / 0.001 + 0 trunc \incY{} * 2 trunc}% \FPupn\tlimY{\stY{} \dspMaxY{} - 0.001 - \incY{} swap / abs 1 + 0 trunc}% \else% \def\haY{\dspMinY}% \FPupn\tlimY{\incY{} \dspRngY{} / abs 1 + 0 trunc}% \FPupn\stY{\dspMinY{} 2 trunc}% \incY{} 1 \tlimY{} - * \dspRngY{} - 0.5 * \dspMinY{} + 2 trunc}% \fi% % x-ticks outside of the box anyway? \ifXTicksOut\def\haY{\dspMinY}\relax\fi% % round off to integer if possible: \FPupn\v{\stY{} 0 trunc \stY{} - abs \incY{} 0 trunc \incY{} - abs + clip}% \FPifeq\v{0}\FPtrunc\stY\stY{0}\FPtrunc\incY\incY{0}\relax\fi% % %% now x-axis: \ifYAxisExp% we almost never draw the y-axis but need to see if x-axis spans zero % make sure ticks hit zero; add small epsilons to avoid ticks at the limits \FPupn\stX{\incX{} \dspMinX{} / 0 trunc \incX{} * 2 trunc}% \FPupn\tlimX{\incX{} \stX{} \dspMaxX{} - / abs 1 + 0 trunc}% \else% \FPupn\tlimX{\incX{} \dspRngX{} / abs 1 + 0 trunc}% \FPupn\stX{\dspMinX{} 2 trunc}% \FPupn\stX{\incX{} 1 \tlimX{} - * \dspRngX{} - 0.5 * \dspMinX{} + 2 trunc}% \fi% \FPupn\v{\stX{} 0 trunc \stX{} - abs \incX{} 0 trunc \incX{} - abs +}% \FPifzero\v\FPtrunc\stX\stX{0}\FPtrunc\incX\incX{0}\relax\fi% %% %% macros for drawing x-ticks \ifXInside% \FPupn\tickEndX{{\strip@pt\dspUnitY} {\strip@pt\dspTickLen} /}% \FPupn\tickTxtX{{\strip@pt\dspUnitY} {\strip@pt\dspXTickGap} 0.9 * / \dspMinY{} -}% tick label pos in PS units \FPupn\tickXB{\tickEndX{} \dspMinY{} +}% \FPupn\tickXT{\tickEndX{} \dspMaxY{} -}% \gdef\dspTickX##1{% \psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,\dspMinY)(##1,\tickXB)% \psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,\dspMaxY)(##1,\tickXT)}% % \gdef\dspTickLabelX##1##2{\uput{{2\dspYTickGap}}[180]{{0}}(\dspMinX,##1){{##2}}}% \gdef\dspTickLabelX##1##2{\rput*[B]{{0}}(##1,\tickTxtX){{##2}}}% \else% \FPupn\tickEndX{{\strip@pt\dspUnitY} {\strip@pt\dspTickLen} / \haY{} -}% tick len in PS units \FPupn\tickTxtX{{\strip@pt\dspUnitY} {\strip@pt\dspXTickGap} / \haY{} -}% tick label pos in PS units \gdef\dspTickX##1{\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,\haY)(##1,\tickEndX)}% \gdef\dspTickLabelX##1##2{\rput*[B]{{0}}(##1,\tickTxtX){{##2}}}% \fi% %% macros for drawing y-ticks \FPupn\tickEndY{{\strip@pt\dspUnitX} {\strip@pt\dspTickLen} /}% \FPupn\tickXB{\tickEndY{} \dspMinX{} +}% \FPupn\tickXT{\tickEndY{} \dspMaxX{} -}% \gdef\dspTickY##1{% \psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](\dspMinX,##1)(\tickXB,##1)% \psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](\dspMaxX,##1)(\tickXT,##1)}% \gdef\dspTickLabelY##1##2{\uput{{2\dspYTickGap}}[180]{{0}}(\dspMinX,##1){{##2}}}% \gdef\dspTickLabelYR##1##2{\uput{{2\dspYTickGap}}[0]{{0}}(\dspMaxX,##1){{##2}}}% } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % simplify fractions of pi \newcount\dspNum \newcount\dspDen \def\simplifyPiFrac#1#2{% \ifnum#1=0 $0$\else % zero is zero \dspNum=#1 \dspDen=#2 % \divide\dspNum by\dspDen \multiply\dspNum by\dspDen % see if frac is simply an integer \ifnum\dspNum=#1 \divide\dspNum by\dspDen \ifnum\dspNum=1 $\pi$\else \ifnum\dspNum=-1 $-\pi$\else $\number\dspNum\pi$\fi\fi\else% \dspNum=#1 % \ifnum\dspNum<0 \multiply\dspNum by-1 \def\s{-}\else\def\s{}\fi % normalize sign \divide\dspDen by\dspNum \multiply\dspDen by\dspNum % see if frac is of type 1/x \ifnum\dspDen=#2 \divide\dspDen by\dspNum $\s\pi / \number\dspDen$\else % \dspNum=#1\dspDen=#2 % \removeFactor{10}\removeFactor{9}\removeFactor{8}% remove some common factors \removeFactor{7}\removeFactor{6}\removeFactor{5}% \removeFactor{4}\removeFactor{3}\removeFactor{2}% $\number\dspNum \pi / \number\dspDen$\fi% \fi % \fi} %% simplify a fraction (not the full Euclid, but it's ok for our purposes) \newcount\dspTerm \newcount\dspFact \def\removeFactor#1{\dspFact=#1 \dspTerm=\dspNum% \divide\dspTerm by\dspFact \multiply\dspTerm by\dspFact % \ifnum\dspTerm=\dspNum % \dspTerm=\dspDen % \divide\dspTerm by\dspFact \multiply\dspTerm by\dspFact % \ifnum\dspTerm=\dspDen % \divide\dspNum by\dspFact \divide\dspDen by\dspFact % \fi % \fi} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % space-separated lists must have at least two pairs of elements. % Duplicate singletons % \def\m@keList#1 #2 #3\relax{% \ifx& #1 #2 #1 #2 \else #1 #2 #3 \fi } \def\twoArgSplit#1,#2{#1, #2} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % prepend the ordinal index to each element of a space-separated list % \def\m@keIndexedList#1#2{% \count0=#1% \expandafter\m@kixl\trim #2 |} \def\m@kixl#1 {% \ifx#1|% \let\next=\relax% \else{\number\count0} \ #1\ \advance\count0 by1\let\next=\m@kixl\fi% \next} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % perform an action on all consecutive pairs in a space-separated list % \def\doOnPairs#1#2{% \def\action{#1}% \expandafter\p@rseB\trim #2 |} \def\p@rseB#1 #2 #3{% \csname \action\endcsname{#1}{#2}% \ifx#3|% \let\next=\@gobble% \else% \let\next=\p@rseB\fi% \next #3} \def\@gobble#1{} \def\trim#1{% \romannumeral-`\.\expandafter\noexpand#1% } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % PsTricks overrides % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Lollipop line style, by Denis.Girou at idris.fr %%%%%%%%%%%%%%%%%%%%%%%% %% \let\beginplot@LineToXAxis\beginplot@line \def\endplot@LineToXAxis{\psLineToXAxis@ii} \let\beginqp@LineToXAxis\beginqp@line \let\doqp@LineToXAxis\doqp@line \let\endqp@LineToXAxis\endqp@line \let\testqp@LineToXAxis\testqp@line % \def\psLineToXAxis@ii{% \addto@pscode{\pst@cp \psline@iii \tx@LineToXAxis}% \end@OpenObj} % \def\tx@LineToXAxis{LineToXAxis } % % Adapted from Line \pst@def{LineToXAxis}<{% NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def CP 2 copy moveto pop 0 Lineto n { 2 copy moveto pop 0 Lineto } repeat CP 4 2 roll ArrowB 2 copy moveto pop 0 L pop pop } if}> \makeatother \endinput