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| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/README | 2 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib | 4 | ||||
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| -rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex | 229 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/generic/pst-func/pst-func.tex | 7 |
6 files changed, 122 insertions, 122 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes index 49914efffed..3436a9d6a39 100644 --- a/Master/texmf-dist/doc/generic/pst-func/Changes +++ b/Master/texmf-dist/doc/generic/pst-func/Changes @@ -1,4 +1,6 @@ ..... pst-func.tex +0.56 2008-10-31 - fix bug with \psPoisson, thanks to Gerry Coombes + - index for the documentation 0.55 2008-06-12 added code for Thomae's function, aka popcorn function 0.54 2008-03-22 added Bernstein code for Bernstein polynomials with optional argument for the envolope curve diff --git a/Master/texmf-dist/doc/generic/pst-func/README b/Master/texmf-dist/doc/generic/pst-func/README index 3dbe4b5fed4..f5728262e61 100644 --- a/Master/texmf-dist/doc/generic/pst-func/README +++ b/Master/texmf-dist/doc/generic/pst-func/README @@ -1,6 +1,7 @@ pst-func: plotting special mathematical functions: -- psBezier -- psPolynomial (with derivations) +-- psBernstein (with envelope option) -- psFourier -- psBessel -- psSi and pssi (integral sin) @@ -19,6 +20,7 @@ pst-func: plotting special mathematical functions: -- psTDist for Student's t-distribution -- psBetaDist for Beta distribution -- psLame (Lam\`e\ Curve -- a superellipse) +-- psThomae (popcorn function) -- psplotImp (plotting implicit defined functions) -- psVolume (rotating f(x) around the x-axis) -- psPrintValue diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib index 03605872ec3..59752ab3c9a 100644 --- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib +++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib @@ -135,9 +135,9 @@ @Book{PSTricks2, author = {Herbert Vo\ss}, title = {\texttt{PSTricks} -- {G}rafik f\"ur \TeX{} und \LaTeX}, - edition = {4.}, + edition = {5.}, publisher = {DANTE -- Lehmanns}, - year = {2007}, + year = {2008}, 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 Binary files differindex fe3a82af098..588de4a7140 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 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 ddf50223156..08a64c173fa 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 @@ -1,37 +1,15 @@ \documentclass[dvips,a4paper,english]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} -%\usepackage{pamathx}% use this if you have the palatino math font -\usepackage{arev}% use this if you do not have the palatino math font -%\usepackage[scaled=0.9]{luximono}% use this if you do not have the palatino math font -\usepackage{url} -\usepackage{amsmath} -\usepackage{tabularx} -\usepackage{longtable} -%\usepackage{fancyhdr} -%\pagestyle{fancy} -\usepackage{xkvview} -\usepackage{pstricks} +\usepackage{pst-news} \usepackage{pst-func} \let\pstFuncFV\fileversion \usepackage{pst-math} -\usepackage{pstricks-add}% for the alg parser -\usepackage{babel} -\usepackage{showexpl} \lstset{pos=t,wide=true,language=PSTricks, - morekeywords={psGammaDist,psChiIIDist,psTDist,psFDist,psBetaDist,psPlotImpl},basicstyle=\small\ttfamily} -\lstdefinestyle{syntax}{backgroundcolor=\color{blue!20},numbers=none,xleftmargin=0pt,xrightmargin=0pt, - frame=single} -% -\usepackage{xspace} -\def\PS{PostScript\xspace} -\def\CMD#1{{\ttfamily\textbackslash #1}} -\def\dt{\ensuremath{\,\mathrm{d}t}} -\def\Index#1{\index{#1}#1} + morekeywords={psGammaDist,psChiIIDist,psTDist,psFDist,psBetaDist,psPlotImpl},basicstyle=\footnotesize\ttfamily} % \def\pshlabel#1{\footnotesize#1} \def\psvlabel#1{\footnotesize#1} -\usepackage[colorlinks,linktocpage]{hyperref} % \begin{document} \title{\texttt{pst-func}\\[1cm] @@ -62,7 +40,11 @@ Thanks to: \texttt{pst-func} loads by default the following packages: \texttt{pst-plot}, \texttt{pstricks-add}, \texttt{pst-math}, \texttt{pst-xkey}, and, of course \texttt{pstricks}. All should be already part of your local \TeX\ installation. If not, or in case -of having older versions, go to \url{http://www.CTAN.org/} and load the newest version.}} +of having older versions, go to \url{http://www.CTAN.org/} and load the newest version. + +{\itshape If \LPack{pstricks-add} is loaded together with the package \LPack{pst-func} then the \Lkeyword{InsideArrow} + of the \Lcs{psbezier} macro doesn't work!}}} + \end{center} \vfill \clearpage @@ -70,7 +52,7 @@ of having older versions, go to \url{http://www.CTAN.org/} and load the newest v \clearpage -\section{\CMD{psBezier\#}} +\section{\Lcs{psBezier\#}} This macro can plot a B\'ezier spline from order 1 up to 9 which needs (order+1) pairs of given coordinates. @@ -91,7 +73,7 @@ large numbers of control points, and the fact that moving a single control point changes the global shape of the curve. The former is sometimes avoided by smoothly patching together low-order Bézier curves. -The macro \CMD{psBezier} (note the upper case B) expects the number of the order +The macro \Lcs{psBezier} (note the upper case B) expects the number of the order and $n=order+1$ pairs of coordinates: \begin{lstlisting}[style=syntax] @@ -99,7 +81,7 @@ and $n=order+1$ pairs of coordinates: \end{lstlisting} The number of steps between the first and last control points is given -by the keyword \verb=plotpoints= and preset to 200. It can be +by the keyword \Lkeyword{plotpoints} and preset to 200. It can be changed in the usual way. @@ -188,7 +170,7 @@ changed in the usual way. \section{Polynomials} -\subsection{\CMD{psPolynomial}} +\subsection{\Lcs{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\\ @@ -197,15 +179,15 @@ f^{\prime\prime}(x) &= 2a_2 + 6a_3x + \ldots +(n-1)(n-2)a_{n-1}x^{n-3} + n(n-1)a \end{align} -\noindent so \verb+pst-func+ needs only the coefficients of the +\noindent so \LPack{pst-func} needs only the \Index{coefficients} of the polynomial to calculate the function. The syntax is \begin{lstlisting}[style=syntax] \psPolynomial[<options>]{xStart}{xEnd} \end{lstlisting} -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+ +With the option \Lkeyword{xShift} one can do a horizontal shift to the graph of the function. With another +than the predefined value the macro replaces $x$ by $x-x\mathrm{Shift}$; \Lkeyword{xShift}=1 moves the graph of the polynomial function one unit to the right. @@ -262,33 +244,33 @@ There are the following new options: \noindent\medskip {\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 +\begin{tabularx}{\linewidth}{@{}l>{\ttfamily}l>{\ttfamily}lX@{}} +Name & \textrm{Value} & \textrm{Default}\\\hline +\Lkeyword{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 +\Lkeyword{xShift} & <number> & 0 & $(x-xShift)$ for the horizontal shift of the polynomial\\ +\Lkeyword{Derivation} & <number> & 0 & the default is the function itself\\ +\Lkeyword{markZeros} & false|true & false & dotstyle can be changed\\ +\Lkeyword{epsZero} & <value> & 0.1 & The distance between two zeros, important for the iteration function to test, if the zero value still exists\\ -dZero & <value> & 0.1 & When searching for all zero values, the function is scanned +\Lkeyword{dZero} & <value> & 0.1 & When searching for all zero values, the function is scanned with this step\\ -zeroLineTo & <number> & false & plots a line from the zero point to the value of the +\Lkeyword{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> & \rlap{0.5\textbackslash pslinewidth} & \\ +\begin{tabularx}{\linewidth}{@{}l>{\ttfamily}l>{\ttfamily}lX@{}} +Name & \textrm{Value} & \textrm{Default}\\\hline +\Lkeyword{zeroLineStyle} & <line style> & dashed & the style is one of the for PSTricks valid styles.\\ +\Lkeyword{zeroLineColor} & <color> & black & any valid xolor is possible\\ +\Lkeyword{zeroLineWidth} & <width> & \rlap{0.5\textbackslash pslinewidth} & \\ \end{tabularx} } @@ -296,9 +278,8 @@ zeroLineWidth & <width> & \rlap{0.5\textbackslash pslinewidth} & \\ \bigskip The above parameter are only -valid for the \verb+\psPolynomial+ -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+. +valid for the \Lcs{psPolynomial} macro, except \verb+x0+, which can also be used for the Gauss function. All +options can be set in the usual way with \Lcs{psset}. @@ -367,7 +348,7 @@ options can be set in the usual way with \verb+\psset+. \end{LTXexample} \clearpage -\subsection{\CMD{psBernstein}} +\subsection{\Lcs{psBernstein}} The polynomials defined by % \[ B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} \] @@ -389,8 +370,8 @@ illustrated below for $n=20$. \psBernstein[<options>](tStart,tEnd)(i,n) \end{lstlisting} -The \verb=(tStart,tEnd)= are \emph{optional} and preset by \verb=(0,1)=. The only new optional -argument is the boolean key \texttt{envelope}, which plots the envelope curve instead +The (\Lkeyword{tStart}, \Lkeyword{tEnd}) are \emph{optional} and preset by \verb=(0,1)=. The only new optional +argument is the boolean key \Lkeyword{envelope}, which plots the envelope curve instead of the Bernstein polynomial. \begin{LTXexample}[width=5cm,pos=l] @@ -459,7 +440,7 @@ of the Bernstein polynomial. \psset{unit=1cm} \clearpage -\section{\CMD{psFourier}} +\section{\Lcs{psFourier}} A Fourier sum has the form: \begin{align} @@ -470,8 +451,8 @@ s(x) = \frac{a_0}{2} & + a_1\cos{\omega x} + a_2\cos{2\omega x} + \ldots + b_m\sin{m\omega x} \end{align} -\noindent The macro \verb+psFourier+ plots Fourier sums. The -syntax is similiar to \verb+psPolynomial+, except that there are +\noindent The macro \Lcs{psFourier} plots \Index{Fourier sums}. The +syntax is similiar to \Lcs{psPolynomial}, except that there are two kinds of coefficients: \begin{lstlisting}[style=syntax] @@ -479,13 +460,13 @@ two kinds of coefficients: \end{lstlisting} The coefficients must have the orders $a_0\ a_1\ a_2\ \ldots$ and $b_1\ b_2\ b_3\ \ldots$ and be separated by -\textbf{spaces}. The default is \verb+cosCoeff=0,sinCoeff=1+, +\textbf{spaces}. The default is \Lkeyword{cosCoeff}=0,\Lkeyword{sinCoeff}=1, which gives the standard \verb+sin+ function. Note that %%JF, I think it is better without the angle brackets, but %%you know the conventions used better than I do, so you %%may disagree. %the constant value can only be set with \verb+cosCoeff=<a0>+. -the constant value can only be set with \verb+cosCoeff=a0+. +the constant value can only be set with \Lkeyword{cosCoeff}=\verb+a0+. \begin{LTXexample} \begin{pspicture}(-5,-3)(5,5.5) @@ -518,7 +499,7 @@ the constant value can only be set with \verb+cosCoeff=a0+. \end{LTXexample} \clearpage -\section{\CMD{psBessel}} +\section{\Lcs{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)\dt\\ @@ -532,7 +513,7 @@ J_n(x) &=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\dt\\ \end{lstlisting} There are two special parameters for the Bessel function, and also the -settings of many \verb+pst-plot+ or \verb+pstricks+ parameters +settings of many \LPack{pst-plot} or \LPack{pstricks} parameters affect the plot. \begin{lstlisting}[style=syntax] @@ -541,13 +522,13 @@ affect the plot. \psset{constI=1,constII=0} \end{lstlisting} -These two "'constants"` have the following meaning: +These two ,,constants`` have the following meaning: \[ f(t) = constI \cdot J_n + constII \] \noindent -where $constI$ and $constII$ must be real PostScript expressions, e.g.: +where \Lkeyword{constI} and \Lkeyword{constII} must be real PostScript expressions, e.g.: \begin{lstlisting}[style=syntax] \psset{constI=2.3,constII=t k sin 1.2 mul 0.37 add} @@ -563,7 +544,7 @@ f(t) = 2.3 \cdot J_n + 1.2\cdot \sin t + 0.37 In particular, note that the default for -\verb+plotpoints+ is $500$. If the plotting computations are too +\Lkeyword{plotpoints} is $500$. If the plotting computations are too time consuming at this setting, it can be decreased in the usual way, at the cost of some reduction in graphics resolution. @@ -602,7 +583,7 @@ way, at the cost of some reduction in graphics resolution. \clearpage -\section{\CMD{psSi}, \CMD{pssi} and \CMD{psCi}} +\section{\Lcs{psSi}, \Lcs{pssi} and \Lcs{psCi}} The integral sin and cosin are defined as \begin{align} \mathrm{Si}(x) &= \int_0^x\dfrac{\sin t}{t}\dt\\ @@ -650,12 +631,12 @@ The integral sin and cosin are defined as \clearpage -\section{\CMD{psIntegral}, \CMD{psCumIntegral} and \CMD{psConv}} +\section{\Lcs{psIntegral}, \Lcs{psCumIntegral} and \Lcs{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 +integral of a function (similar to \Lcs{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)\mathrm{d}t \\ @@ -664,8 +645,8 @@ one is the result of a convolution. They are defined as: \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 +integral is performed from the minimum value specified for $x$ (\Lkeyword{xStart}) and the current +value of $x$ in the plot. The third one uses the \Lcs{psIntegral} macro to perform an approximation to the convolution, where the integration is performed from $a$ to $b$. The syntax of these macros is: @@ -680,9 +661,9 @@ In the first macro, the function should be created such that it accepts two valu 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-, +There are no new parameters for these functions. The two most important ones are \Lkeyword{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 +\Lkeyword{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 @@ -715,13 +696,13 @@ variance is varying from .1 to 10. \end{LTXexample} In the second example, a convolution is performed using two rectangle functions. -The result (in red) is a trapezoid function. +The result (in red) is a \Index{trapezoid function}. \clearpage \section{Distributions} -All distributions which use the $\Gamma$- or $\ln\Gamma$-function need the \verb+pst-math+ package, -it defines the PostScript functions \verb+GAMMA+ and \verb+GAMMALN+. \verb+\pst-func+ reads by default the PostScript -file \verb+pst-math.pro+. It is part of any \TeX\ distribution and should also be on +All distributions which use the $\Gamma$- or $\ln\Gamma$-function need the \LPack{pst-math} package, +it defines the PostScript functions \Lps{GAMMA} and \Lps{GAMMALN}. \LPack{pst-func} reads by default the PostScript +file \LFile{pst-math.pro}. It is part of any \TeX\ distribution and should also be on your system, otherwise install or update it from \textsc{CTAN}. It must the latest version. \begin{LTXexample}[pos=l,width=7cm] @@ -750,12 +731,12 @@ f(x) &= \dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\dfrac{\left(x-\mu\right)^2}{2\sigma{} \psGaussI[options]{xStart}{xEnd} \end{lstlisting} -\noindent where the only new parameter are \verb+sigma=<value>+ and \verb+mue=<value>+ for the +\noindent where the only new parameter are \Lkeyword{sigma}=<value>+ and \Lkeyword{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+- 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 +which can also be set in the usual way with \Lcs{psset}. It is +significant only for the \Lcs{psGauss}- and \Lcs{psGaussI}-macro. The default is +\Lkeyword{sigma}=0.5 and \Lkeyword{mue}=0. The integral is caclulated wuth the Simson algorithm +and has one special option, called \Lkeyword{Simpson}, which defines the number of intervalls per step and is predefined with 5. @@ -780,9 +761,9 @@ and is predefined with 5. \clearpage \subsection{Binomial distribution}\label{sec:bindistri} -These two macros plot binomial distribution, \CMD{psBinomialN} the normalized one. It is always +These two macros plot binomial distribution, \Lcs{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 +Rescaling to another one can be done by setting the \Lkeyword{xunit} option to any other value. The binomial distribution gives the discrete probability distribution $P_p(n|N)$ of obtaining @@ -816,12 +797,12 @@ The syntax is quite easy: 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, +the log file. The valid options for the macros are \Lkeyword{markZeros} to draw rectangles instead +of a continous line and \Lkeyword{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+, +for the macro \Lcs{psPrintValue} are valid, too. The only special option is \Lkeyword{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! +the macro \Lcs{psBinomial} and not for the normalized one! \psset[pst-func]{barwidth=1} \begin{LTXexample}[pos=t,preset=\centering] @@ -865,7 +846,7 @@ the macro \CMD{psBinomial} and not for the normalized one! \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} +\psBinomial[linecolor=cyan]{0,55,75}{.5} \end{pspicture*} \end{LTXexample} @@ -915,9 +896,9 @@ P(k) &= P(k-1)\cdot\frac{N-k+1}{k}\cdot\frac{p}{1-p} -For the normalized distribution the plotstyle can be set to \verb+curve+ (\verb+plotstyle=curve+), +For the normalized distribution the plotstyle can be set to \Lkeyval{curve} (\Lkeyword{plotstyle}=\Lkeyval{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. +valid vor \Lcs{psBinomialN}. The option \Lkeyword{showpoints} is valid if \Lkeyval{curve} was chosen. \begin{LTXexample}[pos=t,preset=\centering] @@ -1011,6 +992,17 @@ in which \texttt{M} is an optional argument with a default of 0. \psset{xunit=1cm,yunit=20cm}% \begin{pspicture}(-1,-0.05)(14,0.25)% \uput[-90](14,0){$k$} \uput[90](0,0.2){$P(X=k)$} +\psPoisson[linecolor=blue,markZeros,fillstyle=solid,barwidth=0.4, + fillcolor=blue!10,printValue,valuewidth=20]{10}{6} % N lambda +\psaxes[Dy=0.1,dy=0.1\psyunit]{->}(0,0)(-1,0)(11,0.2) +\end{pspicture} +\end{LTXexample} + + +\begin{LTXexample}[pos=t,preset=\centering] +\psset{xunit=1cm,yunit=20cm}% +\begin{pspicture}(-1,-0.05)(14,0.25)% +\uput[-90](14,0){$k$} \uput[90](0,0.2){$P(X=k)$} \psPoisson[printValue,valuewidth=20]{2,11}{6} % M,N lambda \psaxes[Dy=0.1,dy=0.1\psyunit]{->}(0,0)(-1,0)(14,0.2) \end{pspicture} @@ -1023,11 +1015,12 @@ in which \texttt{M} is an optional argument with a default of 0. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have -two free parameters, labeled alpha and beta. -The gamma distribution with parameters $\alpha$, $\beta$ is defined as +two free parameters, labeled $alpha$ and $beta$. It is defined as +% \[ f(x)=\frac{\beta(\beta x)^{\alpha-1}e^{-\beta x}}{\Gamma(\alpha)} \qquad -\text{for $x>0$ and $\alpha$, $\beta>0$}\] +\text{for $x>0$ and $\alpha$, $\beta>0$} +\] % and has the syntax @@ -1099,13 +1092,13 @@ D_r(\chi^2) &= int_0^{\chi^2}\frac{t^{r/2-1}e^{-t/2}\mathrm{d}t}{\Gamma(1/2r)2^{ \clearpage \subsection{Student's $t$-distribution} -A statistical distribution published by William Gosset in 1908 under his %. His employer, Guinness Breweries, +A \Index{statistical distribution} published by \Index{William Gosset} in 1908 under his %. His employer, Guinness Breweries, %required him to publish under a pseudonym %, so he chosed ,,Student``. %Given N independent measurements x_i, let %t=(x^_-mu)/(s/sqrt(N)), -The $t$-distribution with parameter $\nu$ has the density function +The $t$-distribution with parameter $\nu$ has the \Index{density function} \[ f(x)=\frac1{\sqrt{\nu\pi}}\cdot \frac{\Gamma[(\nu+1)/2]}{\Gamma(\nu/2)}\cdot\frac1{[1+(x^2/\nu)]^{(\nu+1)/2}} \qquad @@ -1172,7 +1165,7 @@ A general type of statistical distribution which is related to the gamma distrib Beta distributions have two free parameters, which are labeled according to one of two notational conventions. The usual definition calls these $\alpha$ and $\beta$, and the other uses $\beta^\prime=\beta-1$ and $\alpha^\prime=\alpha-1$. The beta distribution is -used as a prior distribution for binomial proportions in Bayesian analysis. +used as a prior distribution for binomial proportions in \Index{Bayesian analysis}. % %The plots are for various values of ($\alpha,\beta$) with $\alpha=1$ and $\beta$ ranging from 0.25 to 3.00. % @@ -1205,7 +1198,7 @@ and has the syntax (with a default setting of $\alpha=1$ and $\beta=1$): \iffalse \clearpage \subsection{Bose-Einstein distribution} -A distribution which arises in the study of integer spin particles in physics, +A distribution which arises in the study of integer \Index{spin particles} in physics, \[ P(x)=\frac{x^s}{e^{x-mu}-1}\qquad\text{with $s\in\mathbb{Z}$ and $\mu\in\mathbb{R}} \] @@ -1219,7 +1212,7 @@ and has the syntax (with a default setting of $s=1$ and $\mu=1$): \clearpage -\section{\CMD{psLame} -- Lam\'e Curve, a superellipse} +\section{\nxLcs{psLame} -- Lam\'e Curve, a superellipse} A superellipse is a curve with Cartesian equation % \begin{align} @@ -1237,9 +1230,9 @@ x = a\cdot\cos^{\frac{2}{r}} t\\ y = b\cdot\sin^{\frac{2}{r}} t \end{align} % -Superellipses with $a=b$ are also known as Lam\'e curves or Lam\'e ovals and +\Index{Superellipses} with $a=b$ are also known as \Index{Lam\'e} curves or Lam\'e ovals and the restriction to $r>2$ is sometimes also made. The following -table summarizes a few special cases. Piet Hein used $\frac{5}{2}$ with a number of different +table summarizes a few special cases. \Index{Piet Hein} used $\frac{5}{2}$ with a number of different $\frac{a}{b}$ ratios for various of his projects. For example, he used $\frac{a}{b}=\frac{6}{5}$ for Sergels Torg (Sergel's Square) in Stockholm, and $\frac{a}{b}=\frac{3}{2}$ for his table. @@ -1258,16 +1251,16 @@ $\frac{5}{2}$ & Piet Hein's ,,superellipse`` \end{tabular} \end{center} -If $r$ is a rational, then a superellipse is algebraic. However, for irrational $r$, +If $r$ is a rational, then a \Index{superellipse} is algebraic. However, for irrational $r$, it is transcendental. For even integers $r=n$, the curve becomes closer to a -rectangle as $n$ increases. The syntax of the \verb+\psLame+ macro is: +rectangle as $n$ increases. The syntax of the \Lcs{psLame} macro is: \begin{lstlisting}[style=syntax] \psLame[settings]{r} \end{lstlisting} -It is internally ploted as a parametric plot with $0\le\alpha\le360$. Available keywords -are \verb+radiusA+ and \verb+radiusB+, both are preset to 1, but can have any valid value +It is internally plotted as a \Index{parametric plot} with $0\le\alpha\le360$. Available keywords +are \Lkeyword{radiusA} and \Lkeyword{radiusB}, both are preset to 1, but can have any valid value and unit. \bgroup @@ -1285,12 +1278,12 @@ and unit. \clearpage -\section{\CMD{psThomae} -- the popcorn function} +\section{\Lcs{psThomae} -- the popcorn function} -Thomae's function, also known as the popcorn function, -the raindrop function, the ruler function or the -Riemann function, is a modification of the Dirichlet function. -This real-valued function f(x) is defined as follows: +\Index{Thomae's function}, also known as the \Index{popcorn function}, +the \Index{raindrop function}, the \Index{ruler function} or the +\Index{Riemann function}, is a modification of the \Index{Dirichlet} function. +This real-valued function $f(x)$ is defined as follows: \[ f(x)=\begin{cases} \frac{1}{q}\mbox{ if }x=\frac{p}{q}\mbox{ is a rational number}\\ @@ -1317,7 +1310,7 @@ The plotted number of points is the third parameter. \clearpage -\section{\CMD{psplotImp} -- plotting implicit defined functions} +\section{\Lcs{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, @@ -1331,10 +1324,10 @@ macro. \psplotImp[<options>](xMin,yMin)(xMax,yMax){<function f(x,y)>} \end{lstlisting} -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 $y$ +The function must be of $f(x,y)=0$ and described in \PS code, or alternatively with +the option \\Lkeyword{algebraic} (\LPack{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. +The given area for \Lcs{psplotImp} should be \textbf{greater} than the given \Lenv{pspicture} area. \begin{LTXexample}[preset=\centering] \begin{pspicture*}(-3,-3.2)(3.5,3.5) @@ -1380,8 +1373,8 @@ The given area for \verb+\psplotImp+ should be \textbf{greater} than the given \ -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 +Using the \Lkeyword{polarplot} option implies using the variables $r$ and $phi$ for describing +the function, $y$ and $x$ are not respected in this case. Using the \Lkeyword{algebraic} option for polar plots are also possible (see next example). \begin{LTXexample}[preset=\centering] @@ -1413,9 +1406,9 @@ for polar plots are also possible (see next example). \clearpage -\section{\CMD{psVolume} -- Rotating functions around the x-axis} +\section{\Lcs{psVolume} -- Rotating functions around the x-axis} -This macro shows the behaviour of a rotated function around the x-axis. +This macro shows the behaviour of a \Index{rotated function} around the x-axis. \begin{lstlisting}[style=syntax] \psVolume[<options>](xMin,xMax){<steps>}{<function f(x)>} @@ -1537,14 +1530,14 @@ $f(x)$ has to be described as usual for the macro psplot. \clearpage -\section{\CMD{psPrintValue}}\label{sec:printValue} -This new macro allows to print single values of a math function. It has the syntax +\section{\Lcs{psPrintValue}}\label{sec:printValue} +This new macro allows to \Index{print} single values of a math function. It has the syntax \begin{lstlisting}[style=syntax] \psPrintValue[<options>]{<PostScript code>} \end{lstlisting} -Important is the fact, that \CMD{psPrintValue} works on \PS\ side. For \TeX\ it is only a box of +Important is the fact, that \Lcs{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. @@ -1613,6 +1606,8 @@ decimals & <number> & -1 & the number of printed decimals, a negative v Rafal Bartczuk | Gerry Coombes | Denis Girou | Christophe Jorssen | Manuel Luque | Timothy Van Zandt and \url{http://mathworld.wolfram.com} +\printindex + \bgroup \raggedright \nocite{*} 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 b1a9af308f5..4b2e5a47beb 100644 --- a/Master/texmf-dist/tex/generic/pst-func/pst-func.tex +++ b/Master/texmf-dist/tex/generic/pst-func/pst-func.tex @@ -29,8 +29,8 @@ % interface to the `xkeyval' package \pst@addfams{pst-func} -\def\fileversion{0.55} -\def\filedate{2008/06/12} +\def\fileversion{0.56} +\def\filedate{2008/10/31} \message{`PST-func' v\fileversion, \filedate\space (hv)} % \pstheader{pst-func.pro} @@ -543,8 +543,9 @@ 90 rotate show grestore \fi /kOld kOld 1 add def + \ifPst@markZeros kOld scx 0 moveto \fi } for - \ifPst@markZeros\else k dx add scx 0 L \fi % last line down to x-axis + \ifPst@markZeros \else k dx add scx 0 L \fi % last line down to x-axis }% % \psk@fillstyle % \pst@stroke |