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Diffstat (limited to 'graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex')
-rw-r--r-- | graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex | 70 |
1 files changed, 56 insertions, 14 deletions
diff --git a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex index cf3819048b..f47e587290 100644 --- a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex +++ b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex @@ -1,6 +1,8 @@ -%% $Id: pst-func-doc.tex 1184 2020-06-06 18:36:57Z herbert $ -\documentclass[fontsize=11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false, - headings=small, headinclude=false,footinclude=false,oneside]{pst-doc} +\RequirePackage{pdfmanagement-testphase} +\DeclareDocumentMetadata{} +%% $Id: pst-func-doc.tex 306 2021-10-29 14:48:08Z herbert $ +\documentclass[fontsize=11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,headings=small, + headinclude=false,footinclude=false,oneside]{pst-doc} \usepackage{pst-func} \let\pstFuncFV\fileversion \usepackage{pst-math} @@ -48,7 +50,7 @@ \author{Herbert Vo\ss} \docauthor{} \date{\today} -\maketitle +\settitle \tableofcontents \psset{unit=1cm} @@ -76,7 +78,9 @@ Thanks to \\ Jürgen Gilg, Christophe Jorssen, Lars Kotthoff, + Marcel Krüger, Buddy Ledger, + Pablo Gonzáles Luengo, Manuel Luque, Patrice Mégret, Svend Mortensen, @@ -609,7 +613,7 @@ which plots the envelope curve instead of the Bernstein polynomial. \clearpage -\subsection{Laguerre Polynomial} +\subsection{\Lcs{psLaguerre} -- Laguerre Polynomial} It is defined as \[ L_n(x)=\sum_{k=0}^n\frac{(-1)^k}{k!}\binom{n}{k}x^k @@ -634,10 +638,11 @@ L_n(x)=\sum_{k=0}^n\frac{(-1)^k}{k!}\binom{n}{k}x^k \clearpage -\subsection{Legendre Polynomial} -It is defined as an orthogonal system +\subsection{\Lcs{psLegendre} -- Legendre Polynomial} +It is defined by the contour integral: \[ -\int\limits_{-1}^{+1}P_m(x)(P_n(x)\mathrm dx=0, \text{ with } n\ne m +P_n(x)=\frac1{2\pi} \oint(1-2tx+t^2)^{-1/2}t^{-n-1}\mathrm dt +%\int\limits_{-1}^{+1}P_m(x)(P_n(x)\mathrm dx=0, \text{ with } n\ne m \] For the computatíon we use a recursive definition: @@ -1532,6 +1537,8 @@ labelangle=80,LabelColor=blue]{6}{0.4} \end{pspicture} \end{LTXexample} +%$ + \begin{LTXexample}[pos=t,preset=\centering] \psset{xunit=0.25cm,yunit=10cm} \begin{pspicture*}(-1,-0.05)(61,0.52) @@ -1821,7 +1828,7 @@ and has the syntax \end{LTXexample} \clearpage -\subsection{$\chi^2$-distribution} +%\subsection{$\chi^2$-distribution} The $\chi^2$-distribution is a continuous probability distribution. It usually arises when a $k$-dimensional vector's orthogonal components are independent and each follow a standard normal distribution. @@ -2108,7 +2115,7 @@ example. \end{LTXexample} \clearpage -\section{The Lorenz curve} +\section{\nxLcs{psLorenz}, Lorenz curve} The so-called \Index{Lorenz curve} is used in economics to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of \textit{ordered individuals} mapped onto the corresponding cumulative proportion @@ -2118,9 +2125,15 @@ then the sample Lorenz curve is the \textit{polygon} joining the points $(h/n,L_ where $h=0, 1, 2,\ldots n, L_0=0$ and $L_h=\sum_{i=1}^h x_i^{\prime}$. \begin{BDef} -\LcsStar{psLorenz}\OptArgs\Largb{data file} +\LcsStar{psLorenz}\OptArgs\OptArg*{<X data>}\Largb{Y data} \end{BDef} + +Without defining data for the x values the Y data will be sorted +and then printed over the relativ x values. For example: 5 y values +will be printed for $x\in[0, 0.2, 0.4, 0.6, 0.8, 1]$ + + \begin{LTXexample}[pos=t,preset=\centering] \psset{lly=-6mm,llx=-5mm} \psgraph[Dx=0.2,Dy=0.2,axesstyle=frame](0,0)(1,1){6cm}{6cm} @@ -2131,16 +2144,28 @@ where $h=0, 1, 2,\ldots n, L_0=0$ and $L_h=\sum_{i=1}^h x_i^{\prime}$. \endpsgraph \end{LTXexample} + + +\begin{LTXexample}[pos=t,preset=\centering] +\psset{lly=-6mm,llx=-5mm} +\psgraph[Dx=0.2,Dy=0.2,axesstyle=frame](0,0)(1,1){6cm}{6cm} +\psline[linestyle=dashed](1,1) +\psLorenz[linecolor=blue!30,linewidth=1.5pt,showpoints]{1 4 6 9 100} +\psLorenz[linecolor=red!60,linewidth=1.5pt,showpoints]<83 104 134 143 185>{460 343 406 501 1662} +\psLorenz[linecolor=green,linewidth=1.5pt]{0 0.577 0.934 0.947 0.969 0.986} +\endpsgraph +\end{LTXexample} + There exists an optional argument \Lkeyword{Gini} for the output of the \Index{Gini coefficient}. -It is by default set to \false. With \true the value is caculated and printed below the +It is by default set to \false. With \true\ the value is caculated and printed below the origin of the coordinate system. \begin{LTXexample}[pos=t,preset=\centering] \psset{lly=-13mm,llx=-5mm} \psgraph[Dx=0.2,Dy=0.2,axesstyle=frame](0,0)(1,1){6cm}{6cm} \psline[linestyle=dashed](1,1) -\psLorenz[linewidth=1.5pt,Gini]{0.025 0.275 0.2 0.270 0.230} -\psLorenz[plotstyle=dots,dotstyle=square,dotscale=1.5]{0.025 0.275 0.2 0.270 0.230} +\psLorenz[linewidth=1.5pt,Gini]<83 104 134 143 185>{460 343 406 501 1662} +\psLorenz[plotstyle=dots,dotstyle=square,dotscale=1.5]<83 104 134 143 185>{460 343 406 501 1662} \endpsgraph \end{LTXexample} @@ -2210,6 +2235,23 @@ and unit. \end{LTXexample} \egroup + + + +\bgroup +\begin{LTXexample}[pos=t,preset=\centering] +\definecolorseries{col}{rgb}{last}{red}{blue} +\resetcolorseries[41]{col} +\psset{unit=.5} +\pspicture(-9,-9)(9,9) + \psaxes[Dx=2,Dy=2,tickstyle=bottom,ticksize=2pt]{->}(0,0)(-9,-9)(9,9) + \multido{\rA=0.2+0.1,\iA=0+1}{40}{% + \psLame[radiusA=8,radiusB=7,startAngle=45,endAngle=315, + linecolor={col!![\iA]},linewidth=.5pt]{\rA}} +\endpspicture +\end{LTXexample} +\egroup + \clearpage \section{\nxLcs{psThomae} -- the popcorn function} \Index{Thomae's function}, also known as the \Index{popcorn function}, |