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-rw-r--r--graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex70
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},