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-rwxr-xr-xBuild/tools/tpm-ctan-check2
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/Changes24
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/README12
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib (renamed from Master/texmf-dist/doc/generic/pst-func/pstricks.bib)12
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdfbin225912 -> 2083694 bytes
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex646
-rw-r--r--Master/texmf-dist/dvips/pst-func/pst-func.pro221
-rw-r--r--Master/texmf-dist/tex/generic/pst-func/pst-func.tex382
-rw-r--r--Master/texmf-dist/tex/latex/pst-func/pst-func.sty3
-rw-r--r--Master/texmf-dist/tpm/pst-func.tpm8
-rw-r--r--Master/texmf/lists/pst-func2
11 files changed, 1176 insertions, 136 deletions
diff --git a/Build/tools/tpm-ctan-check b/Build/tools/tpm-ctan-check
index 7d1a5568641..bd4b0c52183 100755
--- a/Build/tools/tpm-ctan-check
+++ b/Build/tools/tpm-ctan-check
@@ -76,7 +76,7 @@ sub main
#"plnfss", # only a zip file on CTAN
"poemscol", "powerdot", "powerdot-doc-vn",
"ppr-prv", "preview", "proof", "pstricks", "pstricks-add",
- "pst-3d", "pst-barcode", "pst-blur", "pst-eucl",
+ "pst-3d", "pst-barcode", "pst-blur", "pst-eucl", "pst-func",
"pst-labo", "pst-lens", "pst-osci", "pst-pdgr", "pst-slpe",
"sciposter", "sectionbox", "sectsty", "seminar", "semioneside",
"setspace", "sf298", "sides", "skaknew", "sort-by-letters",
diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes
index d74ea98c5e8..32a3c0e4b09 100644
--- a/Master/texmf-dist/doc/generic/pst-func/Changes
+++ b/Master/texmf-dist/doc/generic/pst-func/Changes
@@ -1,4 +1,20 @@
..... pst-func.tex
+0.45 2006-04-22 make polarplot and algebraic option work
+ added \psplotImp for plotting implicit
+ defined functions (experimental)
+ accept plotstyle curve for \psBinomialN
+ new option barwidth for \psBinomial
+ new macro \psBinomial and \psBinomialN
+0.44 2006-01-16 new macros \psCumIntegral, \psIntegral
+ \psConv
+0.43 2005-12-19 new macro psSi for the integral sin Si(x)
+ and si(x)=Si(x)-pi/2
+ and Ci(x), the integral cosin
+0.42 2005-12-09 new macro psGaussI for the integral of Gauss
+ use mue as option name instead of xShift (\psGauss}
+0.41 2005-09-23 new macro pstPrintValue
+0.40 2005-04-09 new option xShift instaed of x0 for psPolynomial and Gauss
+0.39 2005-04-09 new option x0 for Gauss
0.38 2004-11-08 change the option Abbreviation to the right one
Derivation
0.37 2004-11-08 changes pstricks object type from closed to open
@@ -10,7 +26,15 @@
..... pst-func.sty
2004-10-18 first version
+ 2006-04-22 add pst-func.pro to the filelist
+
..... pst-func.pro
+0.06 2006-04-16 new subroutine MoverN (binomial coefficient)
+0.05 2005-12-19 new subroutine Si and si for the integral sin
+ new subroutine for the integral cosin
+ new subroutine factorial (recursive)
+0.04 2005-12-05 new subroutine Simpson for the integral of Gaussian curve
+0.03 2005-07-28 add the complex part
0.02 2004-11-08 change Abbreviation to the right name Derivation
0.01 2004-11-04 first version
diff --git a/Master/texmf-dist/doc/generic/pst-func/README b/Master/texmf-dist/doc/generic/pst-func/README
index 9d4d289a60f..0c204bf50f0 100644
--- a/Master/texmf-dist/doc/generic/pst-func/README
+++ b/Master/texmf-dist/doc/generic/pst-func/README
@@ -2,13 +2,13 @@ Save the files pst-func.sty|pro|tex in a directory, which is part of your
local TeX tree. The pro file should go into $TEXMF/dvips/pstricks/
Then do not forget to run texhash to update this tree.
For more information see the documentation of your LATEX distribution
-on installing packages into your LATEX distribution or the
+on installing packages into your local TeX system or read the
TeX Frequently Asked Questions:
(http://www.tex.ac.uk/cgi-bin/texfaq2html?label=instpackages).
-pst-func needs pst-plot and pstricks, which should be part of your
-local TeX installation, otherwise get it from a CTAN server, f.ex.
-ftp://ftp.ctan.org
+pst-func needs pst-plot (pstricks-add) and pstricks, which should
+be part of your local TeX installation, otherwise get it from a
+CTAN server, f.ex. ftp://ftp.ctan.org
-The documentation also needs pstricks-add, which is also available from
-CTAN or any mirror.
+PSTricks is PostScript Tricks, the documentation cannot be run
+with pdftex, use the sequence latex->dvips->ps2pdf. \ No newline at end of file
diff --git a/Master/texmf-dist/doc/generic/pst-func/pstricks.bib b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib
index 820a2401c7e..34f2b8aa705 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pstricks.bib
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib
@@ -68,7 +68,8 @@
@Book{voss:chaos,
author = {Herbert Vo{\ss}},
- title = {Chaos und {F}raktale selbst programmieren: von {M}andelbrotmengen {\"u}ber {F}arbmanipulationen zur perfekten Darstellung},
+ title = {Chaos und {F}raktale selbst programmieren: von {M}andelbrotmengen
+ {\"u}ber {F}arbmanipulationen zur perfekten Darstellung},
publisher = {{Franzis Verlag}},
year = {1994},
address = {Poing}
@@ -130,3 +131,12 @@
year = 1997
}
+@Book{PSTricks2,
+ author = {Herbert Vo\ss},
+ title = {\texttt{PSTricks} -- {G}rafik f\"ur \TeX{} und \LaTeX},
+ edition = {third},
+ publisher = {DANTE -- Lehmanns},
+ year = {2006},
+ address = {Heidelberg/Hamburg}
+}
+
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
index 3e66c6bbad3..2ec213a7d03 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
index 70fd42cc000..4e3ed6c7a00 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
@@ -1,7 +1,7 @@
\documentclass[a4paper,12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
-\usepackage{geometry}
+\usepackage{pamathx}
\usepackage{url}
\usepackage{amsmath}
\usepackage{tabularx}
@@ -9,25 +9,31 @@
\usepackage{pstricks}
\usepackage{pst-func}
\let\pstFuncFV\fileversion
-\usepackage{pstricks-add}
-\usepackage{pst-example}
+\usepackage{pst-math}
+\usepackage{pstricks-add}% for the alg parser
+\usepackage{showexpl}
+\lstset{pos=t,wide=true}
%
\usepackage{xspace}
\def\PS{PostScript\xspace}
+\def\CMD#1{{\ttfamily\textbackslash #1}}
+\def\dt{\ensuremath{\,\mathrm{d}t}}
%
-\psset{xyLabel=\footnotesize}
+\def\pshlabel{\footnotesize}
+\def\psvlabel{\footnotesize}
\usepackage[colorlinks,linktocpage]{hyperref}
%
\begin{document}
-\title{\texttt{pst-func}\\plotting special mathematical functions\thanks{%
- This document was written with \texttt{Kile: 1.6a (Qt: 3.1.1; KDE: 3.1.1;}
- \protect\url{http://sourceforge.net/projects/kile/}) and the PDF output
- was build with VTeX/Free (\protect\url{http://www.micropress-inc.com/linux})}\\
+\title{\texttt{pst-func}\\plotting special mathematical functions\\
\small v.\pstFuncFV}
-\author{Herbert Voß\thanks{%
+%\thanks{%
+% This document was written with \texttt{Kile: 1.6a (Qt: 3.1.1; KDE: 3.1.1;}
+% \protect\url{http://sourceforge.net/projects/kile/}) and the PDF output
+% was build with VTeX/Free (\protect\url{http://www.micropress-inc.com/linux})}\\
+\author{Herbert Vo\ss\thanks{%
%%JF
%Thanks to: Attila Gati and to John Frampton.
-Thanks to: Attila Gati, John Frampton and Lars Kotthoff.
+Thanks to: Attila Gati, John Frampton and Lars Kotthoff, Jose-Emilio Vila-Forcen.
}}
\date{\today}
@@ -37,7 +43,7 @@ Thanks to: Attila Gati, John Frampton and Lars Kotthoff.
\clearpage
-\section{\texttt{psPolynomial}}
+\section{\CMD{psPolynomial}}
The polynomial function is defined as
\begin{align}
f(x) &= a_0 + a_1x + a_2x^2 + a_3x^3 + \ldots +a_{n-1}x^{n-1} + a_nx^n\\
@@ -51,16 +57,72 @@ polynomial to calculate the function. The syntax is
\psPolynomial[<options>]{xStart}{xEnd}
\end{verbatim}
+With the option \verb+xShift+ one can do a horizontal shift to the graph of the function. With another
+than the predefined value the macro replaces $x$ by $x-x\mathrm{Shift}$; \verb+xShift=1+
+moves the graph of the polynomial function one unit to the right.
+
+
+\begin{center}
+\bgroup
+\psset{yunit=0.5cm,xunit=1cm}
+\begin{pspicture*}(-3,-5)(5,10)
+ \psaxes[Dy=2]{->}(0,0)(-3,-5)(5,10)
+ \psset{linewidth=1.5pt}
+ \psPolynomial[coeff=6 3 -1,linecolor=red]{-3}{5}
+ \psPolynomial[coeff=2 -1 -1 .5 -.1 .025,linecolor=blue]{-2}{4}
+ \psPolynomial[coeff=-2 1 -1 .5 .1 .025 .2 ,linecolor=magenta]{-2}{4}
+ \psPolynomial[coeff=-2 1 -1 .5 .1 .025 .2 ,linecolor=magenta,xShift=1,linestyle=dashed]{-2}{4}
+ \rput[lb](4,4){\textcolor{red}{$f(x)$}}
+ \rput[lb](4,8){\textcolor{blue}{$g(x)$}}
+ \rput[lb](2,4){\textcolor{magenta}{$h(x)$}}
+\end{pspicture*}
+\egroup
+\end{center}
+
+
+\begin{lstlisting}
+\psset{yunit=0.5cm,xunit=1cm}
+\begin{pspicture*}(-3,-5)(5,10)
+ \psaxes[Dy=2]{->}(0,0)(-3,-5)(5,10)
+ \psset{linewidth=1.5pt}
+ \psPolynomial[coeff=6 3 -1,linecolor=red]{-3}{5}
+ \psPolynomial[coeff=2 -1 -1 .5 -.1 .025,linecolor=blue]{-2}{4}
+ \psPolynomial[coeff=-2 1 -1 .5 .1 .025 .2 ,linecolor=magenta]{-2}{4}
+ \psPolynomial[coeff=-2 1 -1 .5 .1 .025 .2 ,linecolor=magenta,xShift=1,linestyle=dashed]{-2}{4}
+ \rput[lb](4,4){\textcolor{red}{$f(x)$}}
+ \rput[lb](4,8){\textcolor{blue}{$g(x)$}}
+ \rput[lb](2,4){\textcolor{magenta}{$h(x)$}}
+\end{pspicture*}
+\end{lstlisting}
+
+
+The plot is easily clipped using the star version of the
+\verb+pspicture+ environment, so that points whose coordinates
+are outside of the desired range are not plotted.
+The plotted polynomials are:
+\begin{align}
+f(x) & = 6 + 3x -x^2 \\
+g(x) & = 2 -x -x^2 +0.5x^3 -0.1x^4 +0.025x^5\\
+h(x) & = -2 +x -x^2 +0.5x^3 +0.1x^4 +0.025x^5+0.2x^6\\
+h^*(x) & = -2 +(x-1) -(x-1)^2 +0.5(x-1)^3 +\nonumber\\
+ & \phantom{ = }+0.1(x-1)^4 +0.025(x-1)^5+0.2(x-1)^6
+\end{align}
+
+
+
+
There are the following new options:
\noindent\medskip
-\begin{tabularx}{\linewidth}{>{\ttfamily}l|>{\ttfamily}l>{\ttfamily}lX@{}}
+{\tabcolsep=2pt
+\begin{tabularx}{\linewidth}{@{}>{\ttfamily}l>{\ttfamily}l>{\ttfamily}lX@{}}
\textrm{Name} & \textrm{Value} & \textrm{Default}\\\hline
coeff & a0 a1 a2 ... & 0 0 1 & The coefficients must have the order $a_0\ a_1\ a_2 \ldots$ and
be separated by \textbf{spaces}. The number of coefficients
is limited only by the memory of the computer ... The default
value of the parameter \verb+coeff+ is \verb+0 0 1+, which gives
the parabola $y=a_0+a_1x+a_2x^2=x^2$.\\
+xShift & <number> & 0 & $(x-xShift)$ for the horizontal shift of the polynomial\\
Derivation & <number> & 0 & the default is the function itself\\
markZeros & false|true & false & dotstyle can be changed\\
epsZero & <value> & 0.1 & The distance between two zeros, important for
@@ -70,51 +132,31 @@ dZero & <value> & 0.1 & When searching for all zero values, the function i
with this step\\
zeroLineTo & <number> & false & plots a line from the zero point to the value of the
zeroLineTo's Derivation of the polynomial function\\
+\end{tabularx}
+}
+
+\noindent
+{\tabcolsep=2pt
+\begin{tabularx}{\linewidth}{@{}>{\ttfamily}l>{\ttfamily}l>{\ttfamily}lX@{}}
+\textrm{Name} & \textrm{Value} & \textrm{Default}\\\hline
zeroLineStyle & <line style> & dashed & the style is one of the for PSTricks valid styles.\\
zeroLineColor & <color> & black & any valid xolor is possible\\
-zeroLineWidth & <width> & 0.5\textbackslash pslinewidth & \\
+zeroLineWidth & <width> & \rlap{0.5\textbackslash pslinewidth} & \\
\end{tabularx}
-
+}
\bigskip
The above parameter are only
valid for the \verb+\psPolynomial+
-macro, but can also be set in the usual way with \verb+\psset+.
-
-
-
-
-\begin{Beispiel}
-{\psset{yunit=0.5cm,xunit=1cm}
-\begin{pspicture*}(-3,-5)(5,10)
- \psaxes[Dy=2]{->}(0,0)(-3,-5)(5,10)
- \psset{linewidth=1.5pt}
- \psPolynomial[coeff=6 3 -1,linecolor=red]{-3}{5}
- \psPolynomial[coeff=2 -1 -1 .5 -.1 .025,linecolor=blue]{-2}{4}
- \psPolynomial[coeff=-2 1 -1 .5 .1 .025 .2 ,linecolor=magenta]{-2}{4}
- \rput[lb](4,4){\textcolor{red}{$f(x)$}}
- \rput[lb](4,8){\textcolor{blue}{$g(x)$}}
- \rput[lb](2,4){\textcolor{magenta}{$h(x)$}}
-\end{pspicture*}
-}
-\end{Beispiel}
-
-The plot is easily clipped using the star version of the
-\verb+pspicture+ environment, so that points whose coordinates
-are outside of the desired range are not plotted.
-The plotted polynomials are:
-\begin{align}
-f(x) & = 6 + 3x -x^2 \\
-g(x) & = 2 -x -x^2 +0.5x^3 -0.1x^4 +0.025x^5\\
-h(x) & = -2 +x -x^2 +0.5x^3 +0.1x^4 +0.025x^5+0.2x^6
-\end{align}
+macro, except \verb+x0+, which can also be used for the Gauss function. All
+options can be set in the usual way with \verb+\psset+.
\bigskip
-\begin{Beispiel}
+\begin{LTXexample}
\psset{yunit=0.5cm,xunit=2cm}
\begin{pspicture*}(-3,-5)(3,10)
\psaxes[Dy=2]{->}(0,0)(-3,-5)(3,10)
@@ -128,10 +170,10 @@ h(x) & = -2 +x -x^2 +0.5x^3 +0.1x^4 +0.025x^5+0.2x^6
\rput[lb](1,1){\textcolor{red}{$h^{\prime}(x)$}}
\rput[lb](-1,6){\textcolor{blue}{$h^{\prime\prime}(x)$}}
\end{pspicture*}
-\end{Beispiel}
-
+\end{LTXexample}
+%$
-\begin{Beispiel}
+\begin{LTXexample}
\psset{yunit=0.5cm,xunit=2cm}
\begin{pspicture*}(-3,-5)(3,10)
\psaxes[Dy=2]{->}(0,0)(-3,-5)(3,10)
@@ -142,13 +184,13 @@ h(x) & = -2 +x -x^2 +0.5x^3 +0.1x^4 +0.025x^5+0.2x^6
\psPolynomial[coeff=0 0 0 1,linecolor=cyan,%
linestyle=dotted,Derivation=3]{-2}{4}
\rput[lb](1.8,4){\textcolor{blue}{$f(x)=x^3$}}
- \rput[lb](0.2,8){\textcolor{red}{$f^{\prime}(x)=6x$}}
- \rput[lb](-2,5.5){\textcolor{magenta}{$f^{\prime\prime}(x)=6$}}
+ \rput[lb](0.2,8){\textcolor{red}{$f^{\prime\prime}(x)=6x$}}
+ \rput[lb](-2,5.5){\textcolor{magenta}{$f^{\prime\prime\prime}(x)=6$}}
\end{pspicture*}
-\end{Beispiel}
-
+\end{LTXexample}
+%$
-\begin{Beispiel}
+\begin{LTXexample}
\begin{pspicture*}(-5,-5)(5,5)
\psaxes{->}(0,0)(-5,-5)(5,5)%
\psset{dotscale=2}
@@ -160,9 +202,9 @@ h(x) & = -2 +x -x^2 +0.5x^3 +0.1x^4 +0.025x^5+0.2x^6
\psPolynomial[markZeros,linecolor=magenta,linewidth=1pt,linestyle=dotted,%
coeff=-1 1 -1 0 0.15,Derivation=2,zeroLineTo=1]{-4}{3}%
\end{pspicture*}
-\end{Beispiel}
+\end{LTXexample}
-\begin{Beispiel}
+\begin{LTXexample}
\psset{xunit=1.5}
\begin{pspicture*}(-5,-5)(5,5)
\psaxes{->}(0,0)(-5,-5)(5,5)%
@@ -175,11 +217,11 @@ h(x) & = -2 +x -x^2 +0.5x^3 +0.1x^4 +0.025x^5+0.2x^6
\psPolynomial[markZeros,linecolor=magenta,linewidth=1pt,linestyle=dotted,%
coeff=-1 1 -1 0 0.15,Derivation=2,zeroLineTo=1]{-4}{3}%
\end{pspicture*}
-\end{Beispiel}
+\end{LTXexample}
-
-\section{\texttt{psFourier}}
+\clearpage
+\section{\CMD{psFourier}}
A Fourier sum has the form:
\begin{align}
@@ -206,7 +248,7 @@ which gives the standard \verb+sin+ function. Note that
%the constant value can only be set with \verb+cosCoeff=<a0>+.
the constant value can only be set with \verb+cosCoeff=a0+.
-\begin{Beispiel}
+\begin{LTXexample}
\begin{pspicture}(-5,-3)(5,5.5)
\psaxes{->}(0,0)(-5,-2)(5,4.5)
\psset{plotpoints=500,linewidth=1pt}
@@ -214,9 +256,9 @@ the constant value can only be set with \verb+cosCoeff=a0+.
\psFourier[cosCoeff=0 0 2, linecolor=magenta]{-4.5}{4.5}
\psFourier[cosCoeff=2 0 2, linecolor=red]{-4.5}{4.5}
\end{pspicture}
-\end{Beispiel}
+\end{LTXexample}
-\begin{Beispiel}
+\begin{LTXexample}
\psset{yunit=0.75}
\begin{pspicture}(-5,-6)(5,7)
\psaxes{->}(0,0)(-5,-6)(5,7)
@@ -225,27 +267,28 @@ the constant value can only be set with \verb+cosCoeff=a0+.
\psFourier[sinCoeff= -1 1 -1 1 -1 1 -1 1,%
linecolor=blue,linewidth=1.5pt]{-4.5}{4.5}
\end{pspicture}
-\end{Beispiel}
+\end{LTXexample}
-\begin{Beispiel}
+\begin{LTXexample}
\begin{pspicture}(-5,-5)(5,5.5)
\psaxes{->}(0,0)(-5,-5)(5,5)
\psset{plotpoints=500,linewidth=1.5pt}
-\psFourier[sinCoeff=-.5 1 1 1 1 ,sinCoeff=-.5 1 1 1 1 1,%
+\psFourier[sinCoeff=-.5 1 1 1 1 ,cosCoeff=-.5 1 1 1 1 1,%
linecolor=blue]{-4.5}{4.5}
\end{pspicture}
-\end{Beispiel}
+\end{LTXexample}
-\section{\texttt{psBessel}}
-The Bessel function of order $n$ is defined as
+\clearpage
+\section{\CMD{psBessel}}
+The Bessel function of order $n$ is defined as
\begin{align}
-J_n(x) &=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\mathrm{d}t\\
+J_n(x) &=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\dt\\
&=\sum_{k=0}^{\infty}\frac{(-1)^k \left(\frac{x}{2}\right)^{n+2k}}{k!\Gamma(n+k+1)}
\end{align}
\noindent The syntax of the macro is
\begin{verbatim}
-\psBessel[options]{order}{xStart}{xEnd}
+\psBessel[options]{order}{xStart}{xEnd}
\end{verbatim}
There are two special parameters for the Bessel function, and also the
@@ -283,14 +326,14 @@ In particular, note that the default for
time consuming at this setting, it can be decreased in the usual
way, at the cost of some reduction in graphics resolution.
-\begin{Beispiel}
+\begin{LTXexample}
{
\psset{xunit=0.25,yunit=5}
\begin{pspicture}(-13,-.85)(13,1.25)
\rput(13,0.8){%
- $\displaystyle J_n(x)=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\mathrm{d}t$%
+ $\displaystyle J_n(x)=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\dt$%
}
-\psaxes[Dy=0.2,Dx=4,xyLabel=\footnotesize]{->}(0,0)(-30,-.8)(30,1.2)
+\psaxes[Dy=0.2,Dx=4]{->}(0,0)(-30,-.8)(30,1.2)
\psset{linewidth=1pt}
\psBessel[linecolor=red]{0}{-28}{28}%
\psBessel[linecolor=blue]{1}{-28}{28}%
@@ -298,33 +341,34 @@ way, at the cost of some reduction in graphics resolution.
\psBessel[linecolor=magenta]{3}{-28}{28}%
\end{pspicture}
}
-\end{Beispiel}
+\end{LTXexample}
-\begin{Beispiel}
+\begin{LTXexample}
{
\psset{xunit=0.25,yunit=2.5}
-\begin{pspicture}(-13,-.85)(13,2)
+\begin{pspicture}(-13,-1.5)(13,3)
\rput(13,0.8){%
$\displaystyle f(t) = 2.3 \cdot J_0 + 1.2\cdot \sin t + 0.37$%
}
-\psaxes[Dy=0.2,Dx=4,xyLabel=\footnotesize]{->}(0,0)(-30,-.8)(30,1.2)
+\psaxes[Dy=0.8,dy=2cm,Dx=4]{->}(0,0)(-30,-1.5)(30,3)
\psset{linewidth=1pt}
\psBessel[linecolor=red,constI=2.3,constII={t k sin 1.2 mul 0.37 add}]{0}{-28}{28}%
\end{pspicture}
}
-\end{Beispiel}
+\end{LTXexample}
-
-\section{\texttt{psGauss}}
-The Gauss function is defined as
+\clearpage
+\section{\CMD{psGauss} and \CMD{psGaussI}}
+The Gauss function is defined as
\begin{align}
-f(x) &= \dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\dfrac{x^2}{2\sigma{}^2}}
+f(x) &= \dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\dfrac{\left(x-\mu\right)^2}{2\sigma{}^2}}
\end{align}
-\noindent The syntax of the macro is
+\noindent The syntax of the macros is
\begin{verbatim}
\psGauss[options]{xStart}{xEnd}
+\psGaussI[options]{xStart}{xEnd}
\end{verbatim}
%%JF
@@ -334,33 +378,453 @@ f(x) &= \dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\dfrac{x^2}{2\sigma{}^2}}
%\noindent where the only new parameter is \verb+sigma=<value>+, with
%the default of \verb+0.5+ and can also be set in the usual way with
%\verb+\psset+. It is only valid for the \verb+psGauss+-macro.
-\noindent where the only new parameter is \verb+sigma=<value>+,
+\noindent where the only new parameter are \verb+sigma=<value>+ and \verb+mue=<value>+ for the
+horizontal shift,
which can also be set in the usual way with \verb+\psset+. It is
-significant only for the \verb+psGauss+-macro. The default is
-\verb+0.5+.
+significant only for the \verb+psGauss+- and \verb+\psGaussI+-macro. The default is
+\verb+sigma=0.5+ and \verb+mue=0+. The integral is caclulated wuth the Simson algorithm
+and has one special option, called \verb+Simpson+, which defines the number of intervalls per step
+and is predefined with 5.
-\begin{Beispiel}
+\bgroup
\psset{yunit=4cm,xunit=3}
-\begin{pspicture}(-2,0)(2,1)
+\begin{pspicture}(-2,-0.2)(2,1.4)
% \psgrid[griddots=10,gridlabels=0pt, subgriddiv=0]
- \psaxes[xyLabel=\footnotesize,Dy=0.25]{->}(0,0)(-2,0)(2,1)
+ \psaxes[Dy=0.25]{->}(0,0)(-2,0)(2,1.25)
\uput[-90](6,0){x}\uput[0](0,1){y}
\rput[lb](1,0.75){\textcolor{red}{$\sigma =0.5$}}
\rput[lb](1,0.5){\textcolor{blue}{$\sigma =1$}}
- \rput[lb](-2,0.5){$f(x)=\dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\dfrac{x^2}{2\sigma{}^2}}$}
+ \rput[lb](-2,0.5){$f(x)=\dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\dfrac{(x-\mu)^2}{2\sigma{}^2}}$}
\psGauss[linecolor=red, linewidth=2pt]{-1.75}{1.75}%
+ \psGaussI[linewidth=1pt,yunit=0.75]{-2}{2}%
+ \psGauss[linecolor=cyan, mue=0.5, linewidth=2pt]{-1.75}{1.75}%
\psGauss[sigma=1, linecolor=blue, linewidth=2pt]{-1.75}{1.75}
\end{pspicture}
-\end{Beispiel}
+\egroup
+
+
+\begin{lstlisting}[xrightmargin=-1cm]
+\psset{yunit=4cm,xunit=3}
+\begin{pspicture}(-2,-0.5)(2,1.25)
+% \psgrid[griddots=10,gridlabels=0pt, subgriddiv=0]
+ \psaxes[Dy=0.25]{->}(0,0)(-2,0)(2,1.25)
+ \uput[-90](6,0){x}\uput[0](0,1){y}
+ \rput[lb](1,0.75){\textcolor{red}{$\sigma =0.5$}}
+ \rput[lb](1,0.5){\textcolor{blue}{$\sigma =1$}}
+ \rput[lb](-2,0.5){$f(x)=\dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\dfrac{(x-x_0)^2}{2\sigma{}^2}}$}
+ \psGauss[linecolor=red, linewidth=2pt]{-1.75}{1.75}%
+ \psGaussI[linewidth=1pt,yunit=0.75cm]{-2}{2}%
+ \psGauss[linecolor=cyan, mue=0.5, linewidth=2pt]{-1.75}{1.75}%
+ \psGauss[sigma=1, linecolor=blue, linewidth=2pt]{-1.75}{1.75}
+\end{pspicture}
+\end{lstlisting}
+
+
+\clearpage
+\section{\CMD{psSi}, \CMD{pssi} and \CMD{psCi}}
+The integral sin and cosin are defined as
+\begin{align}
+\mathrm{Si}(x) &= \int_0^x\dfrac{\sin t}{t}\dt\\
+\mathrm{si}(x) &= - \int_x^{\infty}\dfrac{\sin t}{t}\dt=\mathrm{Si}(x)-\frac{\pi}{2}\\
+\mathrm{Ci}(x) &= -\int_x^{\infty}\dfrac{\cos t}{t}\dt=\gamma+\ln x +\int_0^{x}\dfrac{\cos t -1}{t}\dt
+\end{align}
+%
+\noindent The syntax of the macros is
+\begin{verbatim}
+\psSi[options]{xStart}{xEnd}
+\pssi[options]{xStart}{xEnd}
+\psCi[options]{xStart}{xEnd}
+\end{verbatim}
+
+
+\begin{LTXexample}[pos=t]
+\def\pshlabel#1{\footnotesize#1} \def\psvlabel#1{\footnotesize#1}
+\psset{xunit=0.5}
+\begin{pspicture}(-15,-4.5)(15,2)
+ \psaxes[dx=1cm,Dx=2]{->}(0,0)(-15.1,-4)(15,2)
+ \psplot[plotpoints=1000]{-14.5}{14.5}{ x RadtoDeg sin x div }
+ \psSi[plotpoints=1500,linecolor=red,linewidth=1pt]{-14.5}{14.5}
+ \pssi[plotpoints=1500,linecolor=blue,linewidth=1pt]{-14.5}{14.5}
+ \rput(-5,1.5){\color{red}$Si(x)=\int\limits_{0}^x \frac{\sin(t)}{t}\dt$}
+ \rput(8,-1.5){\color{blue}$si(x)=-\int\limits_{x}^{\infty} \frac{\sin(t)}{t}\dt=Si(x)-\frac{\pi}{2}$}
+ \rput(8,.5){$f(x)= \frac{\sin(t)}{t}$}
+\end{pspicture}
+\end{LTXexample}
+
+
+
+\begin{LTXexample}[pos=t]
+\def\pshlabel#1{\footnotesize#1} \def\psvlabel#1{\footnotesize#1}
+\psset{xunit=0.5}
+\begin{pspicture*}(-15,-4.2)(15,4.2)
+ \psaxes[dx=1cm,Dx=2]{->}(0,0)(-15.1,-4)(15,4)
+ \psplot[plotpoints=1000]{-14.5}{14.5}{ x RadtoDeg cos x Div }
+ \psCi[plotpoints=500,linecolor=red,linewidth=1pt]{-11.5}{11.5}
+ \psci[plotpoints=500,linecolor=blue,linewidth=1pt]{-11.5}{11.5}
+ \rput(-8,1.5){\color{red}$Ci(x)=-\int\limits_{x}^{\infty} \frac{\cos(t)}{t}\dt$}
+ \rput(8,1.5){\color{blue}$ci(x)=-Ci(x)+\ln(x)+\gamma$}
+\end{pspicture*}
+\end{LTXexample}
+
+
+\clearpage
+\section{\CMD{psIntegral}, \CMD{psCumIntegral} and \CMD{psConv}}
+These new macros\footnote{Created by Jose-Emilio Vila-Forcen}
+allows to plot the result of an integral using the Simpson numerical integration rule.
+The first one is the result of the integral of a function with two variables, and
+the integral is performed over one of them. The second one is the cumulative
+integral of a function (similar to \verb+\psGaussI+ but valid for all functions). The third
+one is the result of a convolution. They are defined as:
+\begin{align}
+\text{psIntegral}(x) &= \int_a^b f(x,t)dt \\
+\text{psCumIntegral}(x) &= \int_{\text{xStart}}^{x} f(t)dt \\
+\text{psConv}(x) & = \int_a^b f(t)g(x-t)dt
+\end{align}
+In the first one, the integral is performed from $a$ to $b$ and the function $f$ depends
+on two parameters. In the second one, the function $f$ depends on only one parameter, and the
+integral is performed from the minimum value specified for $x$ (\verb|xStart|) and the current
+value of $x$ in the plot. The third one uses the \CMD{psIntegral} macro to perform an approximation
+to the convolution, where the integration is performed from $a$ to $b$.
+
+The syntax of these macros is:
+\begin{verbatim}
+\psIntegral[<options>]{xStart}{xEnd}(a,b){ function }
+\psCumIngegral[<options>]{xStart}{xEnd}{ function }
+\psConv[<options>]{xStart}{xEnd}(a,b){ function f }{ function g }
+\end{verbatim}
+
+In the first macro, the function should be created such that it accepts two values: \verb|<x t function>|
+should be a value. For the second and the third functions, they only need to accept one
+parameter: \verb|<x function>| should be a value.
+
+There are no new parameters for these functions. The two most important ones are \verb-plotpoints-,
+which controls the number of points of the plot (number of divisions on $x$ for the plot) and
+\verb-Simpson-, which controls the precision of the integration (a larger number means a smallest
+step). The precision and the smoothness of the plot depend strongly on these two parameters.
+
+\bigskip
+\begin{LTXexample}
+%\usepackage{pst-math}
+\psset{xunit=0.5cm,yunit=2cm}
+\begin{pspicture}[linewidth=1pt](-10,-.5)(10,2)
+ \psaxes[dx=1cm,Dx=2]{->}(0,0)(-10,0)(10,2)
+ \psCumIntegral[plotpoints=200,Simpson=10]{-10}{10}{0 1 GAUSS}
+ \psIntegral[plotpoints=200,Simpson=10,linecolor=red]{-10}{10}(-4,6){1 GAUSS}
+ \psIntegral[plotpoints=200,Simpson=100,linecolor=green]{.1}{10}(-3,3){0 exch GAUSS}
+\end{pspicture}
+\end{LTXexample}
+
+In the example, the cumulative integral of a Gaussian is presented in black. In red, a
+Gaussian is varying its mean from -10 to 10, and the result is the integral from -4 to 6.
+Finally, in green it is presented the integral of a Gaussian from -3 to 3, where the
+variance is varying from .1 to 10.
+
+\begin{LTXexample}
+\psset{xunit=1cm,yunit=4cm}
+\begin{pspicture}[linewidth=1pt](-5,-.2)(5,1.1)
+ \psaxes[dx=1cm,Dx=1,Dy=0.5]{->}(0,0)(-5,0)(5,1.1)
+ \psplot[linecolor=blue,plotpoints=200]{-5}{5}{x abs 2 le {0.25}{0} ifelse}
+ \psplot[linecolor=green,plotpoints=200]{-5}{5}{x abs 1 le {.5}{0} ifelse}
+ \psConv[plotpoints=100,Simpson=1000,linecolor=red]{-5}{5}(-10,10)%
+ {abs 2 le {0.25}{0} ifelse}{abs 1 le {.5} {0} ifelse}
+\end{pspicture}
+\end{LTXexample}
+
+In the second example, a convolution is performed using two rectangle functions.
+The result (in red) is a trapezoid function.
+
+\clearpage
+
+\section{\CMD{psBinomial} and \CMD{psBinomialN}}
+
+These two macros plot binomial distribution, \CMD{psBinomialN} the normalized one. It is always
+done in the $x$-Intervall $[0;1]$.
+Rescaling to another one can be done by setting the \verb+xunit+ option
+to any other value.
+
+The binomial distribution gives the discrete probability distribution $P_p(n|N)$ of obtaining
+exactly $n$ successes out of $N$ Bernoulli trials (where the result of each
+Bernoulli trial is true with probability $p$ and false with probability
+$q=1-p$. The binomial distribution is therefore given by
+
+\begin{align}
+P_p(n|N) &= \binom{N}{n}p^nq^{N-n} \\
+ &= \frac{N!}{n!(N-n)!}p^n(1-p)^{N-n},
+\end{align}
+where $(N; n)$ is a binomial coefficient and $P$ the probability.
+
+The syntax is quite easy:
+\begin{verbatim}
+\psBinomial[<options>]{N}{probability p}
+\psBinomialN[<options>]{N}{probability p}
+\end{verbatim}
+
+There is a restriction in using the value for N. It depends to the probability, but in general
+one should expect problems with $N>100$. PostScript cannot handle such small values and there will
+be no graph printed. This happens on PostScript side, so \TeX\ doesn't report any problem in
+the log file. The valid options for the macros are \verb+markZeros+ to draw rectangles instead
+of a continous line and \verb+printValue+ for printing the $y$-values on top of the lines,
+rotated by 90\textdegree. For this option all other options from section~\ref{sec:printValue}
+for the macro \verb+\psPrintValue+ are valid, too. The only special option is \verb+barwidth+,
+which is a factor (no dimension) and set by default to 1. This option is only valid for
+the macro \CMD{psBinomial} and not for the normalized one!
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=1cm,yunit=5cm}%
+\begin{pspicture}(-1,-0.15)(7,0.55)%
+\psaxes[Dy=0.2,dy=0.2\psyunit]{->}(0,0)(-1,0)(7,0.5)
+\uput[-90](7,0){$k$} \uput[90](0,0.5){$P(X=k)$}
+\psBinomial[markZeros,printValue,fillstyle=vlines]{6}{0.4}
+\end{pspicture}
+\end{LTXexample}
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=1cm,yunit=10cm}%
+\begin{pspicture}(-1,-0.1)(8,0.6)%
+\psaxes[Dy=0.2,dy=0.2\psyunit]{->}(0,0)(-1,0)(8,0.5)
+\uput[-90](8,0){$k$} \uput[90](0,0.5){$P(X=k)$}
+\psBinomial[linecolor=red,markZeros,printValue,fillstyle=solid,
+ fillcolor=blue,barwidth=0.2]{7}{0.6}
+\end{pspicture}
+\end{LTXexample}
+
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=0.25cm,yunit=10cm}
+\begin{pspicture*}(-1,-0.1)(61,0.52)
+\psaxes[Dx=5,dx=5\psxunit,Dy=0.2,dy=0.2\psyunit]{->}(60,0.5)
+\uput[-90](60,0){$k$} \uput[0](0,0.5){$P(X=k)$}
+\psBinomial[markZeros,linecolor=red]{4}{.5}
+\psset{linewidth=1pt}
+\psBinomial[linecolor=green]{5}{.5}
+\psBinomial[linecolor=blue]{10}{.5}
+\psBinomial[linecolor=red]{20}{.5}
+\psBinomial[linecolor=magenta]{50}{.5}
+\psBinomial[linecolor=cyan]{75}{.5}
+\end{pspicture*}
+\end{LTXexample}
+
+The default binomial distribution has the mean of $\mu=E(X)=N\cdot p$ and a variant of $\sigma^2=\mu\cdot(1-p)$.
+The normalized distribution has a mean of $0$. Instead of $P(X=k)$ we use $P(Z=z)$ with $Z=\dfrac{X-E(X)}{\sigma(X)}$
+and $P\leftarrow P\cdot\sigma$.
+The macros use the rekursive definition of the binomial distribution:
+%
+\begin{align}
+P(k) &= P(k-1)\cdot\frac{N-k+1}{k}\cdot\frac{p}{1-p}
+\end{align}
+
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=1cm,yunit=5cm}%
+\begin{pspicture}(-3,-0.15)(4,0.55)%
+\psaxes[Dy=0.2,dy=0.2\psyunit]{->}(0,0)(-3,0)(4,0.5)
+\uput[-90](4,0){$z$} \uput[0](0,0.5){$P(Z=z)$}
+\psBinomialN[markZeros,fillstyle=vlines]{6}{0.4}
+\end{pspicture}
+\end{LTXexample}
+
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{yunit=10}
+\begin{pspicture*}(-8,-0.07)(8.1,0.55)
+\psaxes[Dy=0.2,dy=0.2\psyunit]{->}(0,0)(-8,0)(8,0.5)
+\uput[-90](8,0){$z$} \uput[0](0,0.5){$P(Z=z)$}
+\psBinomialN{125}{.5}
+\psBinomialN[markZeros,linewidth=1pt,linecolor=red]{4}{.5}
+\end{pspicture*}
+\end{LTXexample}
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{yunit=10}
+\begin{pspicture*}(-8,-0.07)(8.1,0.52)
+\psaxes[Dy=0.2,dy=0.2\psyunit]{->}(0,0)(-8,0)(8,0.5)
+\uput[-90](8,0){$z$} \uput[0](0,0.5){$P(Z=z)$}
+\psBinomialN[markZeros,linecolor=red]{4}{.5}
+\psset{linewidth=1pt}
+\psBinomialN[linecolor=green]{5}{.5}\psBinomialN[linecolor=blue]{10}{.5}
+\psBinomialN[linecolor=red]{20}{.5} \psBinomialN[linecolor=gray]{50}{.5}
+\end{pspicture*}
+\end{LTXexample}
+
+For the normalized distribution the plotstyle can be set to \verb+curve+ (\verb+plotstyle=curve+),
+then the binomial distribution looks like a normal distribution. This option is only
+valid vor \CMD{psBinomialN}. The option \verb+showpoints+ is valid if \verb+curve+ was chosen.
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=1cm,yunit=10cm}%
+\begin{pspicture*}(-4,-0.06)(4.1,0.57)%
+\psaxes[Dy=0.2,dy=0.2\psyunit]{->}(0,0)(-4,0)(4,0.5)%
+\uput[-90](4,0){$z$} \uput[90](0,0.5){$P(Z=z)$}%
+\psBinomialN[linecolor=red,fillstyle=vlines,showpoints=true,markZeros]{36}{0.5}%
+\psBinomialN[linecolor=blue,showpoints=true,plotstyle=curve]{36}{0.5}%
+\end{pspicture*}
+\end{LTXexample}
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=1cm,yunit=10cm}%
+\begin{pspicture*}(-4,-0.06)(4.2,0.57)%
+\psaxes[Dy=0.2,dy=0.2\psyunit]{->}(0,0)(-4,0)(4,0.5)%
+\uput[-90](4,0){$z$} \uput[90](0,0.5){$P(Z=z)$}%
+\psBinomialN[linecolor=red]{10}{0.6}%
+\psBinomialN[linecolor=blue,showpoints=true,plotstyle=curve]{10}{0.6}%
+\end{pspicture*}
+\end{LTXexample}
+
+
+\clearpage
+\section{\CMD{psplotImp} -- plotting implicit defined functions}
+This macro is still experimental! For a given area, the macro calculates in a
+first step row by row for every pixel (1pt) the function $f(x,y)$ and checks for an
+changing of the value from $f(x,y)<0$ to $f(x,y)>0$ or vice versa. If this happens,
+then the pixel must be a part of the curve of the function $f(x,y)=0$. In a second step the same is
+done column by column. This will take some time because an area of $400\times 300$
+pixel needs $120$ thousand calculations of the function value. The user still defines
+this area in his own coordinates, the translation into pixel (pt) is done internally by the
+macro.
+
+\begin{verbatim}
+\psplotImp[<options>](xMin,yMin)(xMax,yMax){<function f(x,y)>}
+\end{verbatim}
+
+The function must be of $f(x,y)=0$ and described in PostScript code, or alternatively with
+the option \verb+algebraic+ (\verb+pstricks-add+) in an algebraic form. No other value names than $x$ and $y$
+are possible. In general a starred \verb+pspicture+ environment maybe a good choice here.
+The given area for \verb+\psplotImp+ should be \textbf{greater} than the given \verb+pspicture+ area.
+
+\begin{LTXexample}[preset=\centering]
+\begin{pspicture*}(-3,-3.2)(3.5,3.5)
+\psaxes{->}(0,0)(-3,-3)(3.2,3)%
+\psplotImp[linewidth=2pt,linecolor=red](-5,-2.1)(5,2.1){%
+ x dup mul y dup mul add 4 sub }% circle r=2
+\uput[45](0,2){$x^2+y^2-4=0$}
+\psplotImp[linewidth=2pt,linecolor=blue,algebraic]%
+ (-5,-3)(4,2.4){ (x+1)^2+y^2-4 }% circle r=2
+\end{pspicture*}
+\end{LTXexample}
+
+\begin{LTXexample}[preset=\centering]
+\begin{pspicture*}(-3,-2.2)(3.5,2.5)
+\psaxes{->}(0,0)(-3,-2)(3.2,2)%
+\psplotImp[linewidth=2pt,linecolor=blue](-5,-2.2)(5,2.4){%
+ /xqu x dup mul def
+ /yqu y dup mul def
+ xqu yqu add dup mul 2 dup add 2 mul xqu yqu sub mul sub }
+\uput*[0](-3,2){$\left(x^2+y^2\right)^2-8(x^2-y^2)=0$}
+\psplotImp[linewidth=1pt,linecolor=red,algebraic](-5,-2.2)(5,2.4){% Lemniskate a =2
+ (x^2+y^2)^2-4*(x^2-y^2) }
+\end{pspicture*}
+\end{LTXexample}
+
+\begin{LTXexample}[preset=\centering]
+\begin{pspicture*}(-3,-3.2)(3.5,3.5)
+\psaxes{->}(0,0)(-3,-3)(3.2,3)%
+\psplotImp[linewidth=2pt,linecolor=green](-6,-6)(4,2.4){%
+ x 3 exp y 3 exp add 4 x y mul mul sub }
+\uput*[45](-2.5,2){$\left(x^3+y^3\right)-4xy=0$}
+\end{pspicture*}
+\end{LTXexample}
+
+
+\begin{LTXexample}[preset=\centering]
+\begin{pspicture*}(-5,-3.2)(5.5,4.5)
+\psaxes{->}(0,0)(-5,-3)(5.2,4)%
+\psplotImp[algebraic,linecolor=red](-6,-4)(5,4){ y*cos(x*y)-0.2 }
+\psplotImp[algebraic,linecolor=blue](-6,-4)(5,4){ y*cos(x*y)-1.2 }
+\end{pspicture*}
+\end{LTXexample}
+
+
+
+Using the \verb+polarplot+ option implies using the variables $r$ and $phi$ for describing
+the function, $y$ and $x$ are not respected in this case. Using the \verb+algebraic+ option
+for polar plots are also possible (see next example).
+
+\begin{LTXexample}[preset=\centering]
+\begin{pspicture*}(-3,-2.5)(3.75,2.75)\psaxes{->}(0,0)(-3,-2.5)(3.2,2.5)%
+\psplotImp[linewidth=2pt,linecolor=cyan,polarplot](-6,-3)(4,2.4){ r 2 sub }% circle r=2
+\uput*[45](0.25,2){$f(r,\phi)=r-2=0$}
+\psplotImp[polarplot,algebraic](-6,-3)(4,2.4){ r-1 }% circle r=1
+\end{pspicture*}
+\end{LTXexample}
+
+\begin{LTXexample}[preset=\centering]
+\begin{pspicture*}(-5,-2.2)(5.5,3.5)
+\pscircle(0,0){1}%
+\psaxes{->}(0,0)(-5,-2)(5.2,3)%
+\multido{\rA=0.01+0.2}{5}{%
+\psplotImp[linewidth=1pt,linecolor=blue,polarplot](-6,-6)(5,2.4){%
+ r dup mul 1.0 r div sub phi sin dup mul mul \rA\space sub }}%
+\uput*[45](0,2){$f(r,\phi)=\left(r^2-\frac{1}{r}\right)\cdot\sin^2\phi=0$}
+\end{pspicture*}
+\end{LTXexample}
+
+\begin{LTXexample}[preset=\centering]
+\begin{pspicture*}(-4,-3.2)(4.5,4.5)
+\psaxes{->}(0,0)(-4,-3)(4.2,4)%
+\psplotImp[algebraic,polarplot,linecolor=red](-5,-4)(5,4){ r+cos(phi/r)-2 }
+\end{pspicture*}
+\end{LTXexample}
+
+\clearpage
+
+\section{\CMD{psPrintValue}}\label{sec:printValue}
+This new macro allows to print single values of a math function. It has the syntax
+\begin{verbatim}
+\psPrintValue[<options>]{<PostScript code>}
+\end{verbatim}
+
+Important is the fact, that \CMD{psPrintValue} works on \PS\ side. For \TeX\ it is only a box of
+zero dimension. This is the reason why you have to put it into a box, which reserves horizontal
+space.
+
+There are the following new options:
+
+\noindent\medskip
+\begin{tabularx}{\linewidth}{>{\ttfamily}l|>{\ttfamily}l>{\ttfamily}lX@{}}
+\textrm{Name} & \textrm{Value} & \textrm{Default}\\\hline
+PSfont & PS font name & Times & only valid \PS font names are possible, e.g. \texttt{Times-Roman}, \texttt{Helvetica}, \texttt{Courier}, \texttt{AvantGard}, \texttt{Bookman}\\
+fontscale & <number> & 10 & the font scale in pt\\
+valuewidth & <number> & 10 & the width of the string for the converted
+ real number; if it is too small, no value is printed\\
+\end{tabularx}
+
+\begin{center}
+\psset{fontscale=12}
+\makebox[2em]{x(deg)} \makebox[5em]{$\sin x$} \makebox[5em]{$\cos x$}
+\makebox[5em]{$\sqrt x$}\makebox[7em]{$\sin x+\cos x$}\makebox[6em]{$\sin^2 x+\cos^2 x$}\\[3pt]
+\multido{\iA=0+10}{18}{
+ \makebox[1em]{\iA}
+ \makebox[5em]{\psPrintValue[PSfont=Helvetica]{\iA\space sin}}
+ \makebox[5em]{\psPrintValue[PSfont=Courier,fontscale=10]{\iA\space cos}}
+ \makebox[5em]{\psPrintValue[valuewidth=15,linecolor=blue,PSfont=AvantGarde]{\iA\space sqrt}}
+ \makebox[7em]{\psPrintValue[PSfont=Times-Italic]{\iA\space dup sin exch cos add}}
+ \makebox[6em]{\psPrintValue[PSfont=Palatino-Roman]{\iA\space dup sin dup mul exch cos dup mul add}}\\}
+\end{center}
+
+\bigskip
+
+\begin{lstlisting}
+\psset{fontscale=12}
+\makebox[2em]{x(deg)} \makebox[5em]{$\sin x$} \makebox[5em]{$\cos x$}
+\makebox[5em]{$\sqrt x$}\makebox[7em]{$\sin x+\cos x$}\makebox[6em]{$\sin^2 x+\cos^2 x$}\\[3pt]
+\multido{\iA=0+10}{18}{
+ \makebox[1em]{\iA}
+ \makebox[5em]{\psPrintValue[PSfont=Helvetica]{\iA\space sin}}
+ \makebox[5em]{\psPrintValue[PSfont=Courier,fontscale=10]{\iA\space cos}}
+ \makebox[5em]{\psPrintValue[valuewidth=15,linecolor=blue,PSfont=AvantGarde]{\iA\space sqrt}}
+ \makebox[7em]{\psPrintValue[PSfont=Times-Italic]{\iA\space dup sin exch cos add}}
+ \makebox[6em]{\psPrintValue[PSfont=Palatino-Roman]{\iA\space dup sin dup mul exch cos dup mul add}}\\}
+\end{lstlisting}
+
\section{Credits}
-Denis Girou | Manuel Luque | Timothy Van Zandt
+Denis Girou | Manuel Luque | Timothy Van Zandt
\nocite{*}
\bibliographystyle{plain}
-\bibliography{pstricks}
+\bibliography{pst-func-doc}
\end{document}
diff --git a/Master/texmf-dist/dvips/pst-func/pst-func.pro b/Master/texmf-dist/dvips/pst-func/pst-func.pro
index 580e702c837..56b43d8c605 100644
--- a/Master/texmf-dist/dvips/pst-func/pst-func.pro
+++ b/Master/texmf-dist/dvips/pst-func/pst-func.pro
@@ -3,9 +3,9 @@
%%
%% IMPORTANT NOTICE:
%%
-%% Package `pst-func.tex'
+%% Package `pst-func'
%%
-%% Herbert Voss <voss _at_ perce.de>
+%% Herbert Voss <voss _at_ pstricks.de>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
@@ -15,13 +15,70 @@
%% `pst-func' is a PSTricks package to plot special math functions
%%
%%
-%% version 0.02 / 2004-11-08 Herbert Voss <voss _at_ pstricks.de>
+%% version 0.06 / 2006-04-16 Herbert Voss <voss _at_ pstricks.de>
%
-/tx@FuncDict 40 dict def
+/tx@FuncDict 100 dict def
tx@FuncDict begin
%
/eps1 1.0e-05 def
/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
/MaxIter 255 def
/func { coeff Derivation FuncValue } def
/func' { coeff Derivation 1 add FuncValue } def
@@ -54,7 +111,7 @@ tx@FuncDict begin
y0 F sub /Phi exch def
Phi func /F2 exch def
F2 abs eps2 le { exit }{
- Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add div /Diff exch def
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
y0 Diff sub /y0 exch def
Diff abs eps1 le { exit } if
} ifelse
@@ -113,5 +170,159 @@ tx@FuncDict begin
} for
} def
%
+/Simpson { % on stack must be a b M
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
end
diff --git a/Master/texmf-dist/tex/generic/pst-func/pst-func.tex b/Master/texmf-dist/tex/generic/pst-func/pst-func.tex
index 122dfc0353a..efb3b102086 100644
--- a/Master/texmf-dist/tex/generic/pst-func/pst-func.tex
+++ b/Master/texmf-dist/tex/generic/pst-func/pst-func.tex
@@ -18,7 +18,7 @@
%%
\csname PSTfuncLoaded\endcsname
\let\PSTfuncLoaded\endinput
-% Requires PSTricks, pst-node
+% Requires PSTricks, pst-node, pst-xkey
\ifx\PSTricksLoaded\endinput\else\input pstricks.tex\fi
\ifx\PSTnodesLoaded\endinput\else\input pst-plot.tex\fi
\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey.tex \fi
@@ -27,17 +27,21 @@
% interface to the `xkeyval' package
\pst@addfams{pst-func}
-\def\fileversion{0.38}
-\def\filedate{2004/11/08}
-\message{`PST-func' v\fileversion, \filedate\space (Herbert Voss)}
+\def\fileversion{0.45}
+\def\filedate{2006/04/22}
+\message{`PST-func' v\fileversion, \filedate\space (hv)}
%
\pstheader{pst-func.pro}
+%\pstheader{pstricks-add.pro}
%\def\pst@funcdict{tx@FuncDict begin }
%\def\tx@saveCoor{\pst@3ddict saveCoor end }
%\def\tx@ConvertTo2D{\pst@3ddict ConvertTo2D end }
-
-\define@key[psset]{pst-func}{cosCoeff}{\edef\psk@cosCoeff{#1}}
-\define@key[psset]{pst-func}{sinCoeff}{\edef\psk@sinCoeff{#1}}
+%
+\define@key[psset]{pst-func}{xShift}{\def\psk@xShift{#1}}
+\psset[pst-func]{xShift=0}
+%
+\define@key[psset]{pst-func}{cosCoeff}{\def\psk@cosCoeff{#1}}
+\define@key[psset]{pst-func}{sinCoeff}{\def\psk@sinCoeff{#1}}
\psset[pst-func]{cosCoeff=0,sinCoeff=1} % coeff=a0 a1 a2 a3 ...
%
\def\psFourier{\@ifnextchar[{\psFourier@i}{\psFourier@i[]}}
@@ -63,14 +67,14 @@
}%
}\ignorespaces}
%
-\define@key[psset]{pst-func}{coeff}{\edef\psk@coeff{#1}}
-\define@key[psset]{pst-func}{Abbreviation}{\edef\psk@Deriviation{#1}}% compatibility
-\define@key[psset]{pst-func}{Derivation}{\edef\psk@Derivation{#1}}
+\define@key[psset]{pst-func}{coeff}{\def\psk@coeff{#1}}
+\define@key[psset]{pst-func}{Abbreviation}{\def\psk@Deriviation{#1}}% compatibility
+\define@key[psset]{pst-func}{Derivation}{\def\psk@Derivation{#1}}
\newif\ifPst@markZeros%
\define@key[psset]{pst-func}{markZeros}[true]{\@nameuse{Pst@markZeros#1}}
-\define@key[psset]{pst-func}{epsZero}{\edef\psk@epsZero{#1}}
-\define@key[psset]{pst-func}{dZero}{\edef\psk@dZero{#1}}
-\define@key[psset]{pst-func}{zeroLineTo}{\edef\psk@zeroLineTo{#1}}
+\define@key[psset]{pst-func}{epsZero}{\def\psk@epsZero{#1}}
+\define@key[psset]{pst-func}{dZero}{\def\psk@dZero{#1}}
+\define@key[psset]{pst-func}{zeroLineTo}{\def\psk@zeroLineTo{#1}}
\define@key[psset]{pst-func}{zeroLineColor}{\pst@getcolor{#1}\psk@zeroLineColor}
\newdimen\psk@zeroLineWidth
\define@key[psset]{pst-func}{zeroLineWidth}{\pssetlength\psk@zeroLineWidth{#1}}
@@ -124,7 +128,7 @@
\fi
/x x0 def
/xy {
- x coeff Derivation FuncValue \pst@number\psyunit mul
+ x \psk@xShift\space sub coeff Derivation FuncValue \pst@number\psyunit mul
x \pst@number\psxunit mul exch
} def
xy moveto
@@ -154,7 +158,7 @@
mark
/n 2 def
\psk@plotpoints {
- xy
+ xy
n 2 roll
/n n 2 add def
/x x dx add def
@@ -171,8 +175,8 @@
% Manuel Luque, Herbert Voss
% Look at the end for some more documentation about the algorithm
%
-\define@key[psset]{pst-func}{constI}{\edef\psk@constI{#1}}
-\define@key[psset]{pst-func}{constII}{\edef\psk@constII{#1}}
+\define@key[psset]{pst-func}{constI}{\def\psk@constI{#1 }}
+\define@key[psset]{pst-func}{constII}{\def\psk@constII{#1 }}
\psset{constI=1,constII=0}
%
\def\psBessel{\@ifnextchar[{\psBessel@i}{\psBessel@i[]}}
@@ -189,29 +193,355 @@
/J1 J1 0.1 xBessel
tB sin mul tB #2\space mul sub cos mul add def
} for
- t J1 180 div \psk@constI\space mul \psk@constII\space add
+ t J1 180 div \psk@constI mul \psk@constII add
}%
}\ignorespaces}
%
-\define@key[psset]{pst-func}{sigma}{\edef\psk@sigma{#1}}
-\psset{sigma=0.5}
+\define@key[psset]{pst-func}{sigma}{\def\psk@sigma{#1 }}
+\define@key[psset]{pst-func}{mue}{\def\psk@mue{#1 }}
+\psset[pst-func]{sigma=0.5,mue=0}
%
\def\psGauss{\@ifnextchar[{\psGauss@i}{\psGauss@i[]}}
\def\psGauss@i[#1]#2#3{{%
\pst@killglue%
\psset{plotpoints=200}%
\psset{#1}%
- \pstVerb{%
- /euler 2.718282 def
- /Const 1 \psk@sigma\space div 6.2831 sqrt div def
- }%
\psplot{#2}{#3}{%
- euler x dup mul 2 div \psk@sigma\space dup mul div neg exp Const mul%
+ Euler x \psk@mue sub dup mul 2 div \psk@sigma dup mul div neg exp
+ 1.0 \psk@sigma div TwoPi sqrt div mul%
}%
}\ignorespaces}
%
+\define@key[psset]{pst-func}{Simpson}{\def\psk@Simpson{#1 }}
+\psset[pst-func]{Simpson=5}
+%
+\def\psGaussI{\pst@object{psGaussI}}
+\def\psGaussI@i#1#2{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /a #1 def
+ /dx #2 #1 sub \psk@plotpoints\space div def
+ /b a dx add def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ tx@FuncDict begin
+ /Sigma 1 \psk@sigma div TwoPi sqrt div def
+ /SFunc {% x on Stack
+ Euler exch \psk@xShift\space sub dup mul 2 div Sigma dup mul div neg exp Sigma mul
+ } def
+ end
+ a scx 0 moveto
+ \psk@plotpoints 1 sub {
+ a b \psk@Simpson % a b M on Styack
+ tx@FuncDict begin Simpson I end % y value on stack
+ scy b scx exch lineto
+ /b b dx add def
+ } repeat
+ stroke
+ }%
+ \end@SpecialObj%
+}
+%
+\def\psSi{\pst@object{psSi}}
+\def\psSi@i#1#2{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /x #1 def
+ /dx #2 #1 sub \psk@plotpoints\space div def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ x scx x tx@FuncDict begin Si end scy moveto
+ \psk@plotpoints 1 sub {
+ x dup scx exch tx@FuncDict begin Si end scy lineto
+ /x x dx add def
+ } repeat
+ stroke
+ }%
+ \end@SpecialObj%
+}
+\def\pssi{\pst@object{pssi}}
+\def\pssi@i#1#2{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /x #1 def
+ /dx #2 #1 sub \psk@plotpoints\space div def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ x scx x tx@FuncDict begin si end scy moveto
+ \psk@plotpoints 1 sub {
+ x dup scx exch tx@FuncDict begin si end scy lineto
+ /x x dx add def
+ } repeat
+ stroke
+ }%
+ \end@SpecialObj%
+}
+%
+\def\psCi{\pst@object{psCi}}
+\def\psCi@i#1#2{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /x #1 def
+ /dx #2 #1 sub \psk@plotpoints\space div def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ x scx x tx@FuncDict begin Ci end scy moveto
+ \psk@plotpoints 1 sub {
+ x dup scx exch tx@FuncDict begin Ci end scy lineto
+ /x x dx add def
+ } repeat
+ stroke
+ }%
+ \end@SpecialObj%
+}
+\def\psci{\pst@object{psci}}
+\def\psci@i#1#2{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /x #1 def
+ /dx #2 #1 sub \psk@plotpoints\space div def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ x scx x tx@FuncDict begin ci end scy moveto
+ \psk@plotpoints 1 sub {
+ x dup scx exch tx@FuncDict begin ci end scy lineto
+ /x x dx add def
+ } repeat
+ stroke
+ }%
+ \end@SpecialObj%
+}
+%
+\define@key[psset]{pst-func}{PSfont}{\def\psk@PSfont{/#1 }}
+\define@key[psset]{pst-func}{valuewidth}{\def\psk@valuewidth{#1 }}
+\define@key[psset]{pst-func}{fontscale}{\def\psk@fontscale{#1 }}
+\psset[pst-func]{PSfont=Times-Roman,fontscale=10,valuewidth=10}
+%
+\def\psPrintValue{\pst@object{psPrintValue}}
+\def\psPrintValue@i#1{%
+ \begin@ClosedObj
+ \addto@pscode{
+ gsave \psk@PSfont findfont \psk@fontscale scalefont setfont
+ #1 \psk@valuewidth string cvs 0 0 moveto show grestore
+ }%
+ \end@ClosedObj%
+}
+%
+% Integrals 2006-01-16
+% Jose-Emilio Vila-Forcen, Herbert Voss
+%
+\def\psCumIntegral{\pst@object{psCumIntegral}}
+\def\psCumIntegral@i#1#2#3{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /a #1 def
+ /dx #2 #1 sub \psk@plotpoints\space div def
+ /b a dx add def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ tx@FuncDict begin /SFunc { #3 } def end
+ a scx 0 moveto
+ \psk@plotpoints 1 sub {
+ a b \psk@Simpson % a b M on Styack
+ tx@FuncDict begin Simpson I end % y value on stack
+ scy b scx exch lineto
+ /b b dx add def
+ } repeat
+ stroke
+ }%
+ \end@SpecialObj%
+}
+%
+\def\psIntegral{\pst@object{psIntegral}}
+\def\psIntegral@i#1#2(#3,#4)#5{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /a #3 def
+ /dx #4 #3 sub \psk@plotpoints\space div def
+ /b #4 def
+ /aa #1 def
+ /dd #2 #1 sub \psk@plotpoints\space div def
+ /t aa dd add def
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ tx@FuncDict begin /SFunc { t #5 } def end
+ a b \psk@Simpson % a b M on Stack
+ tx@FuncDict begin Simpson I end % y value on stack
+ scy t scx exch moveto
+ /t t dd add def
+ \psk@plotpoints 1 sub {
+ a b \psk@Simpson % a b M on Stack
+ tx@FuncDict begin Simpson I end % y value on stack
+ scy t scx exch lineto
+ /t t dd add def
+ } repeat
+ stroke
+ }%
+ \end@SpecialObj%
+}
+%
+\def\psConv{\@ifnextchar[{\psConv@i}{\psConv@i[]}}
+\def\psConv@i[#1]#2#3(#4,#5)#6#7{%
+ \psIntegral[#1]{#2}{#3}(#4,#5){pop pop x #6\space x t neg add #7\space mul}%
+}%
+%
+\newif\ifPst@printValue%
+\define@key[psset]{pst-func}{printValue}[true]{\@nameuse{Pst@printValue#1}}
+\define@key[psset]{pst-func}{barwidth}{\def\psFunc@barwidth{#1 }}% a factor, not a dimen
+\psset[pst-func]{printValue=false,barwidth=1}
+%
+\def\psBinomial{\pst@object{psBinomial}}
+\def\psBinomial@i#1#2{%
+ \begin@SpecialObj%
+ \addto@pscode{
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ /N #1 def
+ /p #2 def
+ /dx \psFunc@barwidth 2 div def
+ /q 1 p sub def
+ /kOld dx neg def
+ kOld scx 0 moveto % starting point
+% /Y 1 def % start value
+ 0 1 N { % N times
+ /k exch def % save loop variable
+ k 0 eq
+ { /Y q N exp def }
+ { /Y Y N k sub 1 add mul k div p mul q div def }
+ ifelse % recursive definition
+ kOld scx 0 L kOld scx Y scy L k dx add scx Y scy L
+ \ifPst@markZeros k dx add scx 0 L \fi
+ \ifPst@printValue
+ gsave \psk@PSfont findfont \psk@fontscale scalefont setfont
+ Y \psk@valuewidth string cvs
+ k scx \psk@fontscale 2 div add
+ Y scy \pst@number\pslabelsep add moveto
+ 90 rotate show grestore
+ \fi
+ /kOld kOld 1 add def
+ } for
+ }%
+ \psk@fillstyle
+ \pst@stroke
+ \end@SpecialObj%
+}
+%
+\def\psBinomialN{\pst@object{psBinomialN}}
+\def\psBinomialN@i#1#2{%
+ \pst@killglue
+ \begin@SpecialObj%
+ \def\cplotstyle{curve}%
+ \ifx\psplotstyle\cplotstyle \@nameuse{beginplot@\psplotstyle}\fi%
+ \addto@pscode{
+ \ifx\psplotstyle\cplotstyle /Curve true def \else /Curve false def \fi
+ /scx { \pst@number\psxunit mul } def
+ /scy { \pst@number\psyunit mul } def
+ /N #1 def
+ /p #2 def % probability
+ /q 1 p sub def
+ /E N p mul def
+ /sigma E q mul sqrt def % variant
+ /dx 1.0 sigma div 2 div def
+ /xOld dx neg E sub sigma div def
+ /xEnd xOld neg dx add scx def
+ Curve
+ { /Coors [xOld dx sub scx 0] def }% saves the coordinates for curve
+ { xOld scx 0 moveto } % starting point
+ ifelse
+ 0 1 N { % N times
+ /k exch def % save loop variable
+ k 0 eq
+ { /Y q N exp def }
+ { /Y Y N k sub 1 add mul k div p mul q div def }
+ ifelse % recursive definition
+ /x k E sub sigma div dx add def
+ /y Y sigma mul def % normalize
+ Curve
+ { x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def}
+ { xOld scx y scy L x scx y scy L
+ \ifPst@markZeros x scx 0 L \fi %
+ } ifelse
+ \ifPst@printValue
+ gsave \psk@PSfont findfont \psk@fontscale scalefont setfont
+ y \psk@valuewidth string cvs
+ x dx sub scx \psk@fontscale 2 div add
+ y scy \pst@number\pslabelsep add moveto
+ 90 rotate show grestore
+ \fi
+ /xOld x def
+ } for
+ Curve { [ xEnd 0 Coors aload pop} if % showpoints on top of the stack
+ }%
+ \ifx\psplotstyle\cplotstyle \@nameuse{endplot@\psplotstyle} \else%
+ \psk@fillstyle%
+ \pst@stroke%
+ \fi%
+ \end@SpecialObj%
+ \ignorespaces%
+}
+%
+% For polar plots
+\newif\ifpolarplot
+\define@key[psset]{pst-func}{polarplot}[true]{\@nameuse{polarplot#1}}
+\newif\ifPst@algebraic%
+\define@key[psset]{pst-func}{algebraic}[true]{\@nameuse{Pst@algebraic#1}}%
+\psset[pst-func]{polarplot=false,algebraic=false}
+%
+\def\psplotImp{\pst@object{psplotImp}}% 20060420
+\def\psplotImp@i(#1,#2)(#3,#4)#5{%
+ \pst@killglue
+ \begingroup
+ \begin@SpecialObj%
+ \addto@pscode{
+ /xMin #1 def
+ /xMax #3 def
+ /yMin #2 def
+ /yMax #4 def
+ \ifpolarplot
+ /@PolarAlgPlot (#5) tx@addDict begin AlgParser end cvx def
+ /Func {
+ /phi y x atan def
+ /r x y Pyth def
+ \ifPst@algebraic @PolarAlgPlot \else #5 \fi } def
+ \else
+ /Func \ifPst@algebraic (#5) tx@addDict begin AlgParser end cvx \else { #5 } \fi def
+ \fi
+ /xPixel xMax xMin sub \pst@number\psxunit mul round cvi def
+ /yPixel yMax yMin sub \pst@number\psxunit mul round cvi def
+ /dx xMax xMin sub xPixel div def
+ /dy yMax yMin sub yPixel div def
+ /setpixel { dy div exch dx div exch \pst@number\pslinewidth 2 div 0 360 arc fill } bind def
+%
+ /VZ true def % suppose that F(x,y)>=0
+ /x xMin def /y yMin def Func 0.0 lt { /VZ false def } if % erster Wert
+ xMin dx 1.5 div xMax {
+ /x exch def
+ yMin dy 1.5 div yMax {
+ /y exch def
+ Func 0 lt
+ { VZ { x y setpixel /VZ false def} if }
+ { VZ {}{ x y setpixel /VZ true def } ifelse } ifelse
+ } for
+ } for
+%
+ /x xMin def /y yMin def Func 0.0 lt { /VZ false def } if % erster Wert
+ yMin dy 1.5 div yMax {
+ /y exch def
+ xMin dx 1.5 div xMax {
+ /x exch def
+ Func 0 lt
+ { VZ { x y setpixel /VZ false def} if }
+ { VZ {}{ x y setpixel /VZ true def } ifelse } ifelse
+ } for
+ } for
+ }%
+ \end@SpecialObj%
+ \endgroup
+ \ignorespaces
+}
+%
\catcode`\@=\PstAtCode\relax
%
-%% END: pst-abspos.tex
+%% END: pst-func.tex
\endinput
%
diff --git a/Master/texmf-dist/tex/latex/pst-func/pst-func.sty b/Master/texmf-dist/tex/latex/pst-func/pst-func.sty
index 01da72601df..0c975dd68db 100644
--- a/Master/texmf-dist/tex/latex/pst-func/pst-func.sty
+++ b/Master/texmf-dist/tex/latex/pst-func/pst-func.sty
@@ -1,7 +1,8 @@
\RequirePackage{pstricks}
-\ProvidesPackage{pst-func}[2004/10/18 package wrapper for
+\ProvidesPackage{pst-func}[2006/04/22 package wrapper for
pst-func.tex (hv)]
\input{pst-func.tex}
\ProvidesFile{pst-func.tex}
[\filedate\space v\fileversion\space `PST-func' (hv)]
+\IfFileExists{pst-func.pro}{\@addtofilelist{pst-func.pro}}{}%
\endinput
diff --git a/Master/texmf-dist/tpm/pst-func.tpm b/Master/texmf-dist/tpm/pst-func.tpm
index f7307a17f03..87010f7b881 100644
--- a/Master/texmf-dist/tpm/pst-func.tpm
+++ b/Master/texmf-dist/tpm/pst-func.tpm
@@ -3,7 +3,7 @@
<rdf:Description about="http://texlive.dante.de/texlive/Package/pst-func.zip">
<TPM:Name>pst-func</TPM:Name>
<TPM:Type>Package</TPM:Type>
- <TPM:Date>2006/01/09 00:56:57</TPM:Date>
+ <TPM:Date>2006/04/22 08:16:24</TPM:Date>
<TPM:Version>1.0</TPM:Version>
<TPM:Creator>rahtz</TPM:Creator>
<TPM:Title>
@@ -24,18 +24,18 @@ defined by sigma
<TPM:Author>unknown</TPM:Author>
<TPM:Size>254837</TPM:Size>
<TPM:Build/>
- <TPM:RunFiles size="11448">
+ <TPM:RunFiles size="26094">
texmf-dist/dvips/pst-func/pst-func.pro
texmf-dist/tex/generic/pst-func/pst-func.tex
texmf-dist/tex/latex/pst-func/pst-func.sty
texmf-dist/tpm/pst-func.tpm
</TPM:RunFiles>
- <TPM:DocFiles size="243389">
+ <TPM:DocFiles size="2122108">
texmf-dist/doc/generic/pst-func/Changes
texmf-dist/doc/generic/pst-func/README
+texmf-dist/doc/generic/pst-func/pst-func-doc.bib
texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
texmf-dist/doc/generic/pst-func/pst-func-doc.tex
-texmf-dist/doc/generic/pst-func/pstricks.bib
</TPM:DocFiles>
<TPM:Provides>Package/pst-func</TPM:Provides>
</rdf:Description>
diff --git a/Master/texmf/lists/pst-func b/Master/texmf/lists/pst-func
index d071490519e..2a0c9b3d161 100644
--- a/Master/texmf/lists/pst-func
+++ b/Master/texmf/lists/pst-func
@@ -1,8 +1,8 @@
texmf-dist/doc/generic/pst-func/Changes
texmf-dist/doc/generic/pst-func/README
+texmf-dist/doc/generic/pst-func/pst-func-doc.bib
texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
texmf-dist/doc/generic/pst-func/pst-func-doc.tex
-texmf-dist/doc/generic/pst-func/pstricks.bib
texmf-dist/dvips/pst-func/pst-func.pro
texmf-dist/tex/generic/pst-func/pst-func.tex
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-26 12:22:43 +0000