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| author | Karl Berry <karl@freefriends.org> | 2008-07-23 22:05:21 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2008-07-23 22:05:21 +0000 |
| commit | 903bcd69ed64192404fac218d3366dd3d35f9d0e (patch) | |
| tree | 51f518bdeb9a1334a35011c25d52fecf33f14dd3 /Master | |
| parent | 329ad4fd9e0e1e49d6493164695b4f9e08d855e5 (diff) | |
new chinese doc lnotes (19jul08)
git-svn-id: svn://tug.org/texlive/trunk@9732 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master')
57 files changed, 36734 insertions, 1 deletions
diff --git a/Master/texmf-doc/doc/chinese/lnotes/README b/Master/texmf-doc/doc/chinese/lnotes/README new file mode 100644 index 00000000000..ca6211e5471 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/README @@ -0,0 +1,20 @@ +LaTeX Notes + +This Chinese document is an introduction to TeX/LaTeX. It covers basic text typesetting, math, graphics, table, Chinese language & fonts, and some miscellaneous features (hyperlink, long document, bibliography, index, page layout). + +This package contains six files: +readme.txt +history.txt +license.txt +lnotes.dvi +lnotes.pdf +src.zip + +The source files are encoded in UTF-8. + +This readme is in English because CTAN websites support only ASCII readmes. + +Any comments are welcome. I could be accessed at TeX board of smth.org or by email. + +Alpha Huang +huang.xingang@gmail.com
\ No newline at end of file diff --git a/Master/texmf-doc/doc/chinese/lnotes/history.txt b/Master/texmf-doc/doc/chinese/lnotes/history.txt new file mode 100644 index 00000000000..7b07a3b3cb4 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/history.txt @@ -0,0 +1,28 @@ +原文链接：http://www.dralpha.com/chs/tech/lnotes.pdf + +感谢各位同学的帮助和支持，群众的眼睛是贼亮的:) + +无以为报，只好为每位同学的意见增加一个版本号。 + +v1.17 2008/06/02 +- 序中DreamWeaver更正为Dreamweaver，第4页RedHat更正为Red Hat，Unbuntu更正为Ubuntu；第2页和跋中的象字更正为像；33页Shakespear更正为Shakespeare；80页的编字更正为遍。感谢hkkhhk。 +- 第二章中对齐方式术语统一改为居左、居中、居右、居顶、居底；90页表8.1中的Times Roman更正为Times；跋中挥手改为挥衣袖，家里有本徐志摩诗集，基本没看过。感谢yakun@smth.org。 +- 跋加到了目录中，以前漏掉了一个\backmatter。 +- 43页MetaPost版本号更新为1.005。感谢Xubuntu@smth.org。 +- 去掉了58页多余的一个句号。感谢tex@smth.org。 +- 去掉了27页表3.3中重复的\ddot；28页两处分割改为分隔；补上了29页漏掉的对齐两字；42页gnulot更正为gnuplot。再次感谢IMB@smth.org。 +- 关于披阅和批阅，当代多用批阅，但是我手头的《红楼梦》庚辰本和程乙本用的都是披阅，故不更改。感谢yyzz11@smth.org。 +- 插图和字体两章中Bezier的翻译更正为贝塞尔。感谢careworn@smth.org。 +- 第二章和第六章中cross-reference的翻译改为交叉引用；20页小节标题和23页脚注中英文单词之间加入空格；43页MetaPost版本号更新为1.004；更正了80页图6.2的标题；跋中采用了XeTeX和LuaTeX的logo。感谢LittleLeo@smth.org。 +- 86页脚注中张林波的单位更正为计算数学所。感谢yli@smth.org。 +- 更正了78页图6.1的标题。感谢meteorrain@smth.org。 +- 去掉了94页多余的\verb。感谢snoopyzhao@smth.org。 +- 24页两个\sigma中后一个更正为\varsigma；87页一脚注加了句号。感谢primenumber@smth.org。 +- 更正了9页脚注中Fuchs的名字；11页去掉一个重复的“用”字。感谢IMB@smth.org。 +- 去掉了35页\latex的反斜杠。感谢PiscesGold@smth.org。 +- 去掉了c70usong.fd中utf8hei的\CJKbold，黑体原本不该再加粗。感谢PaladinHL@smth.org。 + +v1.0 2008/05/15 +- 大约花了两个半月。 +- 感谢jjgod@smth.org的“kpsewhich cid-x.map”。 +- 感谢Langpku@smth.org的“initexmf --edit-config-file=dvipdfmx”。
\ No newline at end of file diff --git a/Master/texmf-doc/doc/chinese/lnotes/license.txt b/Master/texmf-doc/doc/chinese/lnotes/license.txt new file mode 100644 index 00000000000..94c0329318c --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/license.txt @@ -0,0 +1,17 @@ +%% LaTeX Notes +%% Copyright 2008 Alpha Huang +% +% This work may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either version 1.3 +% of this license or (at your option) any later version. +% The latest version of this license is in +% http://www.latex-project.org/lppl.txt +% and version 1.3 or later is part of all distributions of LaTeX +% version 2005/12/01 or later. +% +% This work has the LPPL maintenance status `maintained'. +% +% The Current Maintainer of this work is Alpha Huang. +% +% This work consists of the files readme.txt, lnotes.dvi, lnotes.pdf, +% history.txt, license.txt, src.zip. diff --git a/Master/texmf-doc/doc/chinese/lnotes/lnotes.pdf b/Master/texmf-doc/doc/chinese/lnotes/lnotes.pdf Binary files differnew file mode 100644 index 00000000000..3becdbfd495 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/lnotes.pdf diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/basics.tex b/Master/texmf-doc/doc/chinese/lnotes/src/basics.tex new file mode 100644 index 00000000000..a95baf212e9 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/basics.tex @@ -0,0 +1,490 @@ +\chapter{入门} + +\section{Hello, World!} +\label{sec:hello_world} +把下面例子用编辑器保存为~\verb|hello_world.tex|，这就是一个最简单的~\LaTeX~源文件。 + +\begin{code} +%hello_world.tex +\documentclass{article} +\begin{document} + Hello, World! +\end{document} +\end{code} + +有了源文件，我们可以在命令行把它编译成~DVI~文件（DVI~格式见\ref{sec:dvi}小节）。此命令知道输入的是~\LaTeX~源文件，所以这里的~\verb|.tex|~后缀可以省略。以后的示例中可以省略的后缀都用~\verb|()|~标出，不再特别声明。 +\begin{code} +latex hello_world(.tex) +\end{code} + +如果系统显示类似下面的错误信息，请检查源文件是否有拼写错误。\verb|.log|~文件里有更详细的编译信息。 +\begin{code} +! LaTeX Error: +... +! Emergency stop. +... +No pages of output. +Transcript written on hello_world.log. +\end{code} + +如果编译成功，系统会报出类似下面的信息： +\begin{code} +Output written on hello_world.dvi (1 page, 232 bytes). +Transcript written on hello_world.log. +\end{code} + +每种~\LaTeX~发行包附带不同的~DVI~浏览器，比如~MiKTeX~的是~yap。 +\begin{code} +yap hello_world(.dvi) +\end{code} + +\section{格式及其转换} +\subsection{页面描述语言} +\label{sec:pdl} +页面描述语言（Page Description Language，PDL）是一种在较高层次上描述实际输出结果的语言。本文只讨论其中三种与~\LaTeX~紧密相关的格式：DVI、PostScript、PDF。 + +\subsubsection{PostScript} +最早的打印机只用于打印字符，它使用的硬字符与打字机类似。后来出现的点阵（dot matrix）打字机用一系列的点来“画”出字符，当然它也可以画出图形。当时矢量图的打印只能由绘图仪（plotter）来完成。 + +1976~年，施乐（Xerox）推出了首台激光打印机，它结合了点阵打印机和绘图仪的优点，可以同时打印高质量的图形和文字。 + +同一时期，John Warnock~也在酝酿一种类似于~Forth~的图形设计语言，也就是后来的~PostScript（PS），当时他正在旧金山一家电脑图形公司~Evans \& Sutherland~工作。1978~年老板想让~Warnock~搬到位于犹他州的总部，他不想搬家就跳槽到了施乐。 + +Warnock~和~Martin Newell~开发了新的图形系统~JaM（John and Martin），它后来被合并到施乐的打印机驱动程序~InterPress~中去。这两位还开发过另一个系统~MaJ。 + +1982~年，Warnock~和施乐研究中心图形实验室主任~Chuck Geschke~一起离开施乐，成立了~Adobe~公司。Newell~后来也加入了~Adobe。 + +1984~年~Adobe~发布~PS~后不久，Steve Jobs~跑来参观，并建议用它来驱动激光打印机。次年，武装着~PS~驱动的~Apple LaserWriter~横空出世，打响了~80~年代中期桌面出版革命的第一枪。 + +90~年代中后期，廉价喷墨打印机的流行使得~PS~逐渐式微，因为~PS~驱动对它们毕竟是一个成本负担。 + +\subsubsection{PDF} +1993~年，Adobe~推出了一种开放的格式：Portable Document Format（PDF），它于~2007~年成为~ISO 32000~标准。除了开放，PDF~比起~PS~还有一些其它优势： +\begin{itemize} + \item PDF~基本上是~PS~的一个子集，因此更轻便。 + \item PDF~可以嵌入更先进的字体，具体见\ref{sec:font}节。 + \item PDF~支持嵌入乱七八糟的东东，比如动画。 + \item PDF~支持透明图形。 +\end{itemize} + +PDF~虽然拥有上述优势，起初它的推广却并不顺利，因为其读写工具~Acrobat~太贵。Adobe~很快推出了免费的~Acrobat Reader（后更名为~Adobe Reader），并不断改进~PDF，终于使它超越了曾经的事实标准~PS，成为网络时代电子文档的新标准。 + +\subsubsection{DVI} +\label{sec:dvi} +Knuth~最初设计的~\TeX~只能用于~XGP~打印机，这台打印机本身还需要一台~PDP-6~主机为它服务。1979~年，David Fuchs\footnote{Fuchs~本科毕业于普林斯顿，1978~年进入斯坦福攻读博士学位。他不是~Knuth~的学生，但是完成过一些~\TeX~的开发任务。他在~Adobe~工作过一段时间，现在混入了娱乐圈，担任过电影《Red Diaper Baby》和《Haiku Tunnel》的制片人。}提出把~\TeX~的输出改为设备无关的格式，也就是~Device Independent format（DVI）。 + +DVI~只是一种中间格式，用户还需要另外的处理程序（driver）把它转换为其它格式，比如~PS~或~PDF~，甚至~PNG、SVG~等。DVI~不能嵌入字体和图形，PS~和~PDF~可以选择是否嵌入字体。 + +\subsubsection{Ghostscript} +\label{sec:ghostscript} +PS~输出时需要一个解释器（Raster Image Processor，RIP）来把它转换为点阵图形。RIP~可以是软件，也可以是固件（firmware）或硬件\footnote{固件~RIP~在打印机内置处理器上运行，硬件~RIP~常见于高端打印设备。}。 + +Ghostscript~是一个基于~RIP~的软件包，除了~RIP~它还有一些其它功能，比如处理~EPS，把~PS~转换为~PDF~等。Ghostscript~已经被移植到~Windows、Unix/Linux、Mac OS~等多种操作系统，和它匹配的前端图形用户界面（GUI）有\href{http://pages.cs.wisc.edu/~ghost/}{GSview、Ghostview、gv}等。 + +\subsection{格式转换} +\label{sec:convert_format} +DVI、PS、PDF~等格式的的转换关系如\Fref{fig:convert_format}所示。 + +\begin{figure}[htbp] +\centering +\begin{tikzpicture} + \node[box] (tex) {.tex}; + \node[box] (dvi) [right=5 of tex] {.dvi}; + \node[box] (pdf) [right=6 of dvi] {.pdf}; + \node[box] (ps) [above=3 of pdf] {.ps}; + \path (tex) edge [arrow] node[auto] {latex} (dvi) + (dvi) edge [arrow] node[auto] {dvipdfm} (pdf) + (dvi.north) [arrow,draw] to node[above,sloped] {dvips} (ps.west) + (ps) edge [arrow] node[right] {ps2pdf} (pdf) + (tex) edge [arrow,bloop] (pdf); + \node [below=.7 of dvi] {pdflatex}; +\end{tikzpicture} +\caption{格式转换} +\label{fig:convert_format} +\end{figure} + +最早的~driver~是~\verb|dvips|，它把~DVI~转换为~PS。\verb|dvipdf|~把~DVI~转为~PDF，它后来被~\verb|dvipdfm|~所取代；\verb|dvipdfm|~主要用于处理单字节字符，1999~年之后停止开发；在~\verb|dvipdfm|~基础上发展来的~\verb|dvipdfmx|~可以处理多字节编码（字符编码详见\ref{sec:encoding}节）。 + +pdf\TeX~是一种特殊的driver，它跳过~DVI，直接用~\TeX~源文件生成~PDF。基于~pdf\TeX~的~pdf\LaTeX~则把\LaTeX~源文件转为~PDF。 + +包老师倾向于~\verb|dvipdfmx|，因为它对图形格式的兼容性较好，而且擅长处理中文。 + +得到~DVI~后，我们可以在控制台用以下命令把它转为~PDF。 +\begin{code} +dvipdfm hello_world(.dvi) +\end{code} + +我们也可以把它转为~PS，接着用~Ghostscript~的一个命令行程序把它转换为~PDF，注意第二个命令需要~\verb|.ps|~后缀。一般情况下不推荐这种方法，因为它多了个步骤。 +\begin{code} +dvips hello_world(.dvi) +ps2pdf hello_world.ps +\end{code} + +pdf\LaTeX~用法如下。 +\begin{code} +pdflatex hello_world(.tex) +\end{code} + +\section{\LaTeX~语句} +\LaTeX~源文件的每一行称作一条语句（statement），语句可以分三种：命令（command）、数据（data）和注释（comment）。 + +命令分为两种：普通命令和环境（environment）。普通命令以\verb|\|~起始，大多只有一行；而环境包含一对起始声明和结尾声明，用于多行的场合。命令和环境可以互相嵌套。 + +数据就是普通内容。注释语句以~\verb|%|~起始，它在编译过程中被忽略。 + +例如在\ref{sec:hello_world}节例1中，第一行是注释，第二行是普通命令；第三、五行是环境的起始和结尾声明；第四行是数据。 + +\section{文档结构} +\subsection{文档类、序言、正文} +\LaTeX~源文件的结构分三大部分，依次为：文档类声明、序言（可选）、正文。 + +文档类声明用来指定文档的类型；序言（preamble）用来完成一些特殊任务，比如引入宏包，定义命令，设置环境等；文档的实际内容则放在正文部分。这里的正文指得是\verb|\begin{document}|和\verb|\end|~\verb|{document}|之间的部分，和通常人们心目中的“正文”概念有所出入。 + +这三部分的基本语法如下： +\begin{code} +\documentclass[options]{class} %文档类声明 +\usepackage[options]{package} %引入宏包 +... +\begin{document} %正文 +... +\end{document} +\end{code} + +常用的文档类（documentclass）有三种：\verb|article、report、book|，它们的常用选项见\fref{tab:class_options}。 + +\begin{table}[htbp] +\centering +\caption{文档类常用选项} +\label{tab:class_options} +\begin{tabularx}{350pt}{lX} + \toprule + 10pt, 11pt, 12pt & 正文字号，缺省10pt。\LaTeX~会根据正文字号选择标题、上下标等的字号。\\ + letterpaper, a4paper & 纸张尺寸，缺省是~letter。\\ + notitlepage, titlepage & 标题后是否另起新页。article~缺省~notitlepage，report~和~book~缺省有~titlepage。\\ + onecolumn, twocolumn & 栏数，缺省单栏。\\ + oneside, twoside & 单面双面。article~和~report~缺省单面，book~缺省双面。\\ + landscape & 打印方向横向，缺省纵向。\\ + openany, openright & 此选项只用于~report~和~book。report~缺省~openany~，book~缺省~openright。\\ + draft & 草稿模式。有时某些行排得过满，draft~模式可以在它们右边标上粗黑线提醒用户。\\ + \bottomrule +\end{tabularx} +\end{table} + +\LaTeX~的核心只提供基本的功能，系统以宏包（package）的形式提供附加功能或增强原有功能。其它一些编程语言也有类似的模块化机制，比如~C/C++~的~\verb|#include|，Java~的~\verb|import|。 + +\subsection{标题、摘要、章节} + + +一份文档正文部分的开头通常有标题、作者、摘要等信息，之后是章节等层次结构，内容则散布于层次结构之间。 + +标题、作者、日期等命令如下，注意\verb|\maketitle|~命令要放在最后。 +\begin{code} +\title{标题} +\author{作者} +\today +\maketitle +\end{code} + +摘要环境用法如下： +\begin{code} +\begin{abstract} +... +\end{abstract} +\end{code} + +常用的层次结构命令如下， +\begin{code} +\chapter{...} +\section{...} +\subsection{...} +\subsubsection{...} +\end{code} + +每个高级层次可以包含若干低级层次。\verb|article|~中没有~\verb|chapter|，而~\verb|report|~和~\verb|book|~则支持上面所有层次。 + +\subsection{目录} + +我们可以用~\verb|\tableofcontents|~命令来生成整个文档的目录，\LaTeX~会自动设定目录包含的章节层次，也可以用~\verb|\setcounter|~命令来指定目录层次深度。 +\begin{code} +\tableofcontents +\setcounter{tocdepth}{2} +\end{code} + +如果不想让某个章节标题出现在目录中，可以使用以下带~\verb|*|~的命令来声明章节。 +\begin{code} +\chapter*{...} +\section*{...} +\subsection*{...} +\end{code} + +类似地，我们也可以用以下命令生成插图和表格的目录，插图和表格功能将在后面章节中介绍。 + +\begin{code} +\listoffigures +\listoftables +\end{code} + +当章节或图表等结构发生变化时，我们需要执行两遍编译命令以获得正确结果。\LaTeX~之所以设计成这样可能是因为当时的电脑内存容量有限。 + +\section{文字排版} +\subsection{字符输入} +文档中可以输入的内容大致可以分为：普通字符、控制符、特殊符号、注音符号、预定义字符串等。而这些内容有两种输入模式：文本模式（缺省）和数学模式，普通的行间（inline）数学模式用\verb|\$...\$|来表示。 + +\LaTeX~中有些字符（例如~\verb|# $ % ^ & _ { } ~ \|~等）被用作特殊的控制符，所以不能直接输入，多数需要在前面加个~\verb|\|。而~\verb|\|~本身则要用~\verb|\textbackslash|~命令来输入，因为~\verb|\\|~被用作了换行指令。很奇怪为什么不用~C~语言的~\verb|\n|，也许是因为~\TeX~的编程语言是~Pascal。 + +\begin{code} +\# \$ \% \^{} \& \_ \{ \} \~{} \textbackslash +\end{code} + +\Fref{tab:symbol}~提供了一些符号的输入方法示例，完整的符号列表见~Scott Pakin的《The Comprehensive \LaTeX~ Symbol List》\citep{Pakin_2008}。 + +\begin{table}[htbp] +\centering +\caption{一些符号和预定义字符串} +\label{tab:symbol} +\begin{tabular}{llllll} + \toprule + \multicolumn{2}{c}{特殊符号} & \multicolumn{2}{c}{注音符号} & + \multicolumn{2}{c}{预定义字符串} \\ + \cmidrule(lr){1-2} \cmidrule(lr){3-4} \cmidrule(lr){5-6} + \textcopyright & \verb|\textcopyright| & \aa & \verb|\aa| & + \today & \verb|\today| \\ + \textregistered & \verb|\textregistered| & \AA & \verb|\AA| & + \TeX & \verb|\TeX| \\ + $^\circ$C & \verb|$^\circ$C| & \ae & \verb|\ae| & + \LaTeX & \verb|\LaTeX| \\ + \textyen & \verb|\textyen| & \o & \verb|\o| & + \LaTeXe & \verb|\LaTeXe| \\ + \pounds & \verb|\pounds| & \"o & \verb|\"o| & + \MF & \verb|\MF| \\ + \texteuro & \verb|\texteuro| & \^o & \verb|\^o| & + \MP & \verb|\MP| \\ + \dots & \verb|\dots| & \~o & \verb|\~o| & \\ + \bottomrule +\end{tabular} +\end{table} + +\subsection{换行、换页、断字} +通常~\LaTeX~会自动换行、换页。用户也可以用~\verb|\\|~或~\verb|\newline|~来强制换行；用~\verb|\newpage|~来强制换页。 + +一般情况下~\LaTeX~会尽量均匀地断字（Hyphenate），使得每一行的字间距分布整齐。但有时我们也需要显式指明断字位置，比如下例就指明~BASIC~这个词不能断开，而~blar-blar-blar~可以在-处断开。 +\begin{code} +\hyphenation{BASIC blar-blar-blar} +\end{code} + +\subsection{字样、字号} + +\LaTeX~会自动调整正文、标题、章节、上下标、脚注等的字样\footnote{关于字样详见\ref{sec:typeface}节}、字号。我们也可以用\fref{tab:typeface_command}中的命令来设置字样；用\fref{tab:fontsize_command}中的命令来设置相对字号，比如正文字号是~10pt、11pt、12pt~时，tiny的字号就分别是~5pt、6pt、6pt。 + +\LaTeX~有一个特别的字样强调命令：\verb|\emph|，它在不同字样和装饰环境下有不同效果。比如周围文字是正体，它就是斜体；反之它就是正体。 + +\begin{table}[hbtp] +\centering +\caption{字样命令} +\label{tab:typeface_command} +\begin{tabular}{llll} + \toprule + \verb|\textrm{...}| & \textrm{roman} & + \verb|\textbf{...}| & \textbf{bold face} \\ + \verb|\textsf{...}| & \textsf{sans serif} & + \verb|\textit{...}| & \textit{italic} \\ + \verb|\texttt{...}| & \texttt{typewriter} & + \verb|\textsl{...}| & \textsl{slanted} \\ + \\ + \verb|\emph{...}| & \emph{emphasized} & + \verb|\underline{...}| & \underline{underline} \\ + \verb|\textsc{...}| & \textsc{Small Caps} & & \\ + \bottomrule +\end{tabular} +\end{table} + +\begin{table}[htbp] +\centering +\caption{字号命令} +\label{tab:fontsize_command} +\begin{tabular}{llll} + \toprule + & \multicolumn{3}{c}{正文字号} \\ + \cmidrule(lr){2-4} + 命令 & 10pt & 11pt & 12pt \\ + \midrule + \verb|\tiny| & 5pt & 6pt & 6pt \\ + \verb|\scriptsize| & 7pt & 8pt & 8pt \\ + \verb|\footnotesize| & 8pt & 9pt & 10pt \\ + \verb|\small| & 9pt & 10pt & 11pt \\ + \verb|\normalsize| & 10pt & 11pt & 12pt \\ + \verb|\large| & 12pt & 12pt & 14pt \\ + \verb|\Large| & 14pt & 14pt & 17pt \\ + \verb|\LARGE| & 17pt & 17pt & 20pt \\ + \verb|\huge| & 20pt & 20pt & 25pt \\ + \verb|\Huge| & 25pt & 25pt & 25pt \\ + \bottomrule +\end{tabular} +\end{table} + +\section{常用命令环境} +\subsection{列表} + +\LaTeX~中有三种列表环境：\verb|itemize、enumerate、description|，它们的一般用法如下： + +\begin{demo} +\begin{itemize} + \item C++ + \item Java + \item HTML +\end{itemize} +\end{demo} + +\begin{demo} +\begin{enumerate} + \item C++ + \item Java + \item HTML +\end{enumerate} +\end{demo} + +\begin{demo} +\begin{description} + \item{C++} 一种编程语言 + \item{Java} 另一种编程语言 + \item{HTML} 一种标记语言 +\end{description} +\end{demo} + +\subsection{对齐} +\LaTeX~中的段落缺省两端对齐（fully justified），我们也可以让段落居左、居右或居中对齐。 + +\begin{demo} +\begin{flushleft} +本段落\\ +居左 +\end{flushleft} +\end{demo} + +\begin{demo} +\begin{flushright} +本段落\\ +居右 +\end{flushright} +\end{demo} + +\begin{demo} +\begin{center} +本段落\\ +居中 +\end{center} +\end{demo} + +\subsection{摘录} +\LaTeX~中有三种摘录环境：\verb|quote、quotation、verse|。\verb|quote|~两端都缩进，\verb|quotation|~在~\verb|quote|~的基础上增加了首行缩进，\verb|verse|~比~\verb|quote|~多了第二行起的缩进。 + +\begin{demo} +正文 +\begin{quote} +引文两端都缩进。 +\end{quote} +正文 +\end{demo} + +\begin{demo} +正文 +\begin{quotation} +引文两端缩进，首行缩进。 +\end{quotation} +正文 +\end{demo} + +\begin{demo} +正文 +\begin{verse} +引文两端缩进，第二行起缩进。 +\end{verse} +正文 +\end{demo} + +\subsection{原文照排} +一般文档中，命令和源代码通常使用等宽字样来表示，也就是原文照排。对此~\LaTeX~提供了~\verb|\verb|~命令（一般用于在正文中插入较短的命令）和~\verb|verbatim|~环境。后者有带~\verb|*|~的版本用来标明空格。 + +\begin{demo} +正文中插入\verb|command| +\begin{verbatim} +printf("Hello, world!"); +\end{verbatim} +\begin{verbatim*} +printf("Hello, world!"); +\end{verbatim*} +\end{demo} + +\subsection{交叉引用} +我们常常需要引用文档中~\verb|section、subsection、figure、table|~等对象的编号，这种功能叫作交叉引用（cross referencing）。 + +\LaTeX~中可以用~\verb|\label{marker}|~命令来定义一个标记，标记名可以是任意字符串，但是在全文中须保持唯一。之后可以用~\verb|\ref{marker}|~命令来引用标记处章节或图表的编号，用~\verb|\pageref{marker}|~来引用标记处的页码。 + +\begin{demo} +被引用处\label{sec}\\ +...\\ +第\pageref{sec}页\ref{sec}节 +\end{demo} + +文档中新增交叉引用后，第一次执行~\verb|latex|~或~\verb|pdflatex|~编译命令时会得到类似下面的警告信息。因为第一次编译只会扫描出有交叉引用的地方，第二次编译才能得到正确结果。 + +\begin{code} +LaTeX Warning: There were undefined references. +... +LaTeX Warning: Label(s) may have changed. Rerun to get cross- +references right. +\end{code} + +\subsection{脚注} +脚注（footnote）的一般用法如下: +\begin{demo} +这里是一段正文。\footnote{这里是一段脚注。} +\end{demo} + +\section{长度单位} +\LaTeX~中的常用长度单位如\Fref{tab:unit}~所示。point~是个传统印刷业采用的单位，而~big point~是~Adobe~推出~PS~时新定义的单位。em~是个相对单位，比如当前字体是~11pt~时，1em~就是~11pt。 +\begin{table}[htbp] +\caption{常用长度单位} +\label{tab:unit} +\centering +\begin{tabular}{llllll} + \toprule + in & 英寸 & pt & point, 1/72.27 in & em & 当前字体中字母M的宽度 \\ + cm & 厘米 & bp & big point, 1/72 in & ex & 当前字体中字母X的高度 \\ + mm & 毫米 & pc & pica, 12 pt & mu & math unit，1/18 em \\ + \bottomrule +\end{tabular} +\end{table} + +\section{盒子} +\LaTeX~在排版时把每个对象（小到一个字母，大到一个段落）都视为一个矩形盒子（box），我们在~HTML~和~CSS~中也可以见到类似的模型。 + +\subsection{mbox~和~fbox} + +\LaTeX~中最简单的盒子是~\verb|\mbox|~和~\verb|\fbox|。前者把一组对象组合起来，后者在此基础上加了个边框。 +\begin{demo} +\mbox{010 6278 5001} +\fbox{010 6278 5001} +\end{demo} + +\subsection{makebox~和~framebox} +稍复杂的~\verb|\makebox|~和~\verb|\framebox|~提供了宽度和对齐方式控制选项。这里用~l、r、s~分别代表居左、居右和分散对齐。 +\begin{demo} +%语法：[宽度][对齐方式]{内容} +\makebox[100pt][l]{居左} +\framebox[100pt][r]{居右} +\end{demo} + +\subsection{parbox~和~minipage} +大一些的对象比如整个段落可以用~\verb|\parbox|~命令和~\verb|\minipage|~环境，两者语法类似，也提供了对齐方式和宽度的选项。但是这里的对齐方式是指与周围内容的纵向关系，用~t、c、b~分别代表居顶、居中和居底对齐。 + +\begin{demo} +%语法：[对齐方式]{宽度}{内容} +\parbox[c]{90pt}{锦瑟无端五十弦，\\一弦一柱思华年。}李商隐 +\end{demo} + +细心的读者会发现~\verb|\parbox|~和~\verb|\minipage|~的选项排列顺序和~\verb|\makebox|~和~\verb~\framebox|~的不一致，可能出自不同的作者。 + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/dscf4684.jpg b/Master/texmf-doc/doc/chinese/lnotes/src/dscf4684.jpg Binary files differnew file mode 100644 index 00000000000..93eb1089555 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/dscf4684.jpg diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/examples/arrow.mps b/Master/texmf-doc/doc/chinese/lnotes/src/examples/arrow.mps new file mode 100644 index 00000000000..7aa8b8630ea --- /dev/null +++ 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y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + 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grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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stroke +grestore end + +@endspecial 1 TeXcolorgray +0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_color.eps b/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_color.eps new file mode 100644 index 00000000000..831316a4c5a --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_color.eps @@ -0,0 +1,1653 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software +%%Title: pst_color.dvi +%%CreationDate: Thu May 01 22:28:30 2008 +%%BoundingBox: 148 626 239 668 +%%EndComments +%DVIPSWebPage: (www.radicaleye.com) +%DVIPSCommandLine: dvips -E pst_color.dvi -o pst_color.eps +%DVIPSParameters: dpi=600 +%DVIPSSource: TeX output 2008.05.01:2228 +%%BeginProcSet: tex.pro 0 0 +%! +/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S +N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 +mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 +0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ +landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize +mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ +matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round +exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ +statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] +N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin +/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array +/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 +array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get +}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} +B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr +1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S +/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy +setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask +restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn +/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put +}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ +bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ +userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale 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+%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale 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itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + 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N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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{PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate 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+end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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TeXcolorgray 0 TeXcolorgray eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_grid.eps b/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_grid.eps new file mode 100644 index 00000000000..fe1316af047 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_grid.eps @@ -0,0 +1,1649 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software +%%Title: pst_grid.dvi +%%CreationDate: Thu May 01 22:28:31 2008 +%%BoundingBox: 148 596 339 668 +%%EndComments +%DVIPSWebPage: (www.radicaleye.com) +%DVIPSCommandLine: dvips -E pst_grid.dvi -o pst_grid.eps +%DVIPSParameters: dpi=600 +%DVIPSSource: TeX output 2008.05.01:2228 +%%BeginProcSet: tex.pro 0 0 +%! +/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S +N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 +mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 +0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ +landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize +mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ +matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round +exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ +statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] +N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin +/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array +/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 +array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get +}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} +B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype 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false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale 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/hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if 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rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale 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Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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+/Lineto { Arcto } def false 0 setlinejoin Line gsave 0.8 SLW 0 setgray +1. .setopacityalpha 0 setlinecap stroke grestore end + +@endspecial 1 TeXcolorgray +0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_linestyle.eps b/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_linestyle.eps new file mode 100644 index 00000000000..4d2597ccf33 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/examples/pst_linestyle.eps @@ -0,0 +1,1653 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software +%%Title: pst_linestyle.dvi +%%CreationDate: Thu May 01 22:28:31 2008 +%%BoundingBox: 148 626 239 668 +%%EndComments +%DVIPSWebPage: (www.radicaleye.com) +%DVIPSCommandLine: dvips -E pst_linestyle.dvi -o pst_linestyle.eps +%DVIPSParameters: dpi=600 +%DVIPSSource: TeX output 2008.05.01:2228 +%%BeginProcSet: tex.pro 0 0 +%! +/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S +N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 +mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 +0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ +landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize +mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ +matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round +exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ +statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] +N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin +/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array +/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 +array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N +df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A +definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get +}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} +B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr +1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S +/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy +setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask +restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn +/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put +}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ +bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ +userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale 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gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end 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for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } 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{ NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath {0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath} def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def + /AsteriskPath {20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath} def + /Asterisk {AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + fill} def + /Basterp {50 250 220 500 0 500 curveto + -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath {50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath} def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath {40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath} def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath} def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill + .775 .775 scale CrossPath fill} def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill + .775 .775 scale BoldCrossPath fill} def + /Otimes {CirclePath .9 .9 scale 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DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch/.notdef put} for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def + CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath {-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath} def + /SolidPentagon 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known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def 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def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p +delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} +B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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w}B/n{ +p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S +rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: pstricks.pro 0 0 +% $Id: pstricks.pro 10 2008-01-18 13:31:24Z herbert $ +% +% PostScript prologue for pstricks.tex. +% Version 1.03, 2008/01/01 +% For distribution and copyright, see pstricks.tex. +% +% +systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if +systemdict /.setblendmode known not {/.setblendmode { pop } def } if +systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +/PathLength { flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def + }{ /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { ADict begin + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } + ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +%-----------------------------------------------------------------------------% + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 7 2007-12-29 22:21:13Z herbert $ +% +% PostScript prologue for PSTricks algorithm parser +% Version 0.01, 2008/01/01 +% For distribution and copyright, see pstricks.tex. hv@pstricks.de +% +%-----------------------------------------------------------------------------% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->E<condition_operators>E +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval<func> +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 7 2007-12-29 22:21:13Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.00, 2006/12/19 +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt <tvz@Princeton.EDU> +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Herbert Voss (hv) - 2004/12/27 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +% +10 dict dup begin + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def +% See end of file in /BuildGlyph 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+%%EndProlog +%%Page: 1 1 + 0 0 0 setrgbcolor 0 0.5 dtransform truncate idtransform setlinewidth pop + [] 0 setdash 1 setlinecap 1 setlinejoin 10 setmiterlimit +newpath 0 0 moveto +100 50 lineto stroke +showpage +%%EOF diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/fonts.tex b/Master/texmf-doc/doc/chinese/lnotes/src/fonts.tex new file mode 100644 index 00000000000..af471ce458f --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/fonts.tex @@ -0,0 +1,183 @@ +\chapter{字体} + +关于字体有三个重要概念：glyph、typeface、font。glyph~通常被翻译为字形，也有翻译为字体的；typeface~是一个书法和印刷领域的概念，它通常被翻译为字体或书体；font~曾经和~typeface~混用，但现在一般用作电脑领域的概念，在中国大陆被翻译为字体，在台湾被翻译为字型。 + +上述翻译的混乱令人十分无奈，包老师决定在本文中把它们分别翻译为字形、字样、字体，以正视听。 + +字形是一个字符的具体图形表现形式，一个字符可以有多个字形，比如汉字中的“強／强”、“戶／户／戸”；字样是一组相同风格样式的字形的集合，比如中文字样有宋、仿、楷、黑、隶、篆等；一种字样可以对应电脑上的几种字体。 + +\section{字样} +\label{sec:typeface} +拉丁字母的字样主要有三大类：Serif（Roman）、Sans Serif~和~Mono-space~（Typewriter）。Serif~的笔画边缘部分有些装饰，类似于中文的宋体、仿宋、楷体、魏书等。Sans Serif~的笔画则是平滑的，类似于中文的黑体。Sans~这个词来源于法语，就是“没有”的意思。Monospace~则是等宽字样。 + +每一类字样都可以有加粗（bold）、斜体（italic）、倾斜（oblique）等修饰效果。Italic~通常对原字样进行过重新设计，它修饰精细，多用于~Serif；~Oblique~也称作~slanted，基本上是把正体倾斜，多用于~Sans Serif。通常~oblique~看起来比~italic~要宽一些。 + +\Fref{tab:typeface}列出了几种常见的字样。 + +\begin{table}[htbp] +\caption{常见字样} +\label{tab:typeface} +\centering +\begin{tabular}{llll} + \toprule + 操作系统 & Serif & Sans Serif & Monospace \\ + \midrule + Mac OS & Times & Helvetica & Courier \\ + Windows & Times New Roman & Arial & Courier New \\ + \bottomrule +\end{tabular} +\end{table} + +\section{字体格式} +\label{sec:font} + +\subsection{点阵字体和矢量字体} +电脑上用的字体（font）按数据格式可以分为三大类：点阵字体（bitmap）、轮廓（outline）字体和笔画（stroke-based）字体。 + +点阵字体通过点阵来描述字形。早期的电脑受到容量和绘图速度的限制，多采用点阵字体。点阵字体后来渐渐被轮廓字体所取代，但是很多小字号字体仍然使用它，因为这种情况下轮廓字体缩放太多会导致笔画不清晰。 + +轮廓字体又称作矢量字体，它通过一组直线段和曲线来描述字形。轮廓字体易于通过数学函数进行缩放等变换，形成平滑的轮廓。轮廓字体的主要缺陷在于它所采用的贝塞尔曲线（Bézier curves）在光栅（raster）设备（比如显示器和打印机）上不能精确渲染，因而需要额外的补偿处理比如字体微调（font hinting）。但是随着电脑硬件的发展，人们一般不在意它比点阵字体多出的处理时间。 + +笔画字体其实也是轮廓字体，不过它描述的不是完整的字形，而是笔画。它多用于东亚文字。 + +\subsection{常见字体} + +常见的轮廓字体技术有：Type 1~和~Type 3、TrueType、OpenType、~\MF~等。 + +Adobe~的~Type 1~和~Type 3~基于~PS，它们采用三次贝塞尔曲线。Type 1~支持微调，它使用一个简化的~PS~子集；Type 3~不支持微调，但它可以使用全部~PS~功能，因此既可以包含轮廓字体也可以包含点阵字体信息。 + +1991~年，Apple~发布了~TrueType，它采用二次贝塞尔曲线。二次曲线处理起来比三次曲线快，但是需要更多的点来描述。所以从~TrueType~到~Type 1的转换是无损的，反之是有损的。1994~年，Apple~着手研究~TrueType~的下一代技术：TrueType GX，它后来演变为Apple Advanced Typography（AAT）。 + +1996~年，微软和~Adobe~联合发布了~OpenType。它比起~AAT~的优势有：跨平台、开放和易于开发、支持更多的语言比如阿拉伯语。 + +早在~1984~年~Knuth~就发布了~\MF，它与~TrueType~和~OpenType的区别是，不直接描述字形轮廓，而描述生成轮廓的笔的轨迹。笔的形状可以是椭圆形或多边形，尺寸缩放自如，字形边缘也柔和一些。两种字体可以用同一个~\MF~文件，当然还有不同的参数。\MF~技术如此先进，却没有流行开来。对此~Knuth~解释道，要求一位设计字体的艺术家掌握~60~个参数太变态了，那是用来折磨数学家的。 + +Type 1~和~Type 3~把字体信息存储在两种文件里：metrics~和~glyph~文件。metrics~文件有~AFM（Adobe font metrics）和~PFM（printer font metrics），glyph~文件有~PFA（printer font ASCII）和~PFB（printer font binary）。~\LaTeX~使用的~metrics~格式是~TFM（TeX Font Metrics）。 + +TrueType~的文件后缀是~.ttf，OpenType~的是~.ttf~和~.otf。\MF~虽然用矢量图形来定义字形，实际输出的却是一种点阵格式：PK~（packed raster）。 + +上述字体按技术的先进性，从高到低的排序为：OpenType、~TrueType、Type 1、Type 3、PK，我们应优先选用~OpenType~和~TrueType。 + +\subsection{合纵连横} +Adobe~收取的~Type 1~专利许可费一度十分昂贵，穷人们只好用免费的~Type 3。为了打破这种垄断，Apple~开发了~TrueType。1991~年~TrueType~发布之后，Adobe随即公开了~Type 1~的规范，~Type 1~字体从贵族堕落为平民，因而流行开来。 + +1980~年代中后期，Adobe~的大部分盈利来自于~PS~解释器的许可费。面对这种垄断局面，微软和~Apple~联合了起来。微软把买来的~PS~解释器~TrueImage~授权给~Apple，Apple~则把~TrueType~授权给微软。 + +微软得隆望蜀，又企图获得~AAT~的许可证，未遂。为了打破~Apple~的垄断，微软联合~Adobe~在1996年发布了~OpenType。Adobe~在2002~年末将其字体库全面转向~OpenType。 + +上面这几出精彩好戏充分展示了商场上的勾心斗角、尔虞我诈，没有永恒的伙伴，只有永恒的利益。但它同时也告诉我们，市场竞争中受益的还是广大的消费者。 + +\section{字体应用} + +PS~支持~Type 1~和~Type 3，而~PDF~除了这两种还支持~TrueType~和~OpenType。\verb|latex|、DVI浏览器、各种~driver~分别采用不同的字体技术。 + +\subsection{DVI} +\verb|latex|~编译~\LaTeX~源文件生成~DVI~时只需要\verb|.tfm|~文件，因为~DVI~并不包含字形信息，而只包含对字体的引用。DVI~浏览器显示~DVI~时一般使用~PK，它在系统中查找相应的~\verb|.pk|~文件，若找不到就调用~\MF~在后台自动生成。 + +\subsection{dvips} +缺省情况下，\verb|dvips|~也会查找~\verb|.pk|~，或调用~\MF~自动生成；然后把~PK~转换成包含点阵字体的~Type 3，它的参数~\verb|-D|~可以用来控制该点阵字体的分辨率。用~\verb|ps2pdf|~处理含~Type 3~的~PS~时，输出的自然是含~Type 3~的~PDF。 + +GSview~在低分辨率下可以很好地渲染~Type 3，Adobe Reader~或~Acrobat~却不能，因为它们使用的~Adobe Type Manager~不支持包含完整~PS~的~Type 3。含~Type 3~的~PDF~看起来会有些模糊，所以应尽量避免使用。 + +\verb|dvips|~的另一个参数~\verb|-Ppdf|~把~Type 1~嵌入生成的~PS，这样再~\verb|ps2pdf|~就能生成含~Type 1~的~PDF。 + +\verb|dvips|~不支持真正的（native）TrueType，用户只能把~TrueType~先转成~PK~或~Type 1，这样绕了个弯效果总会打些折扣。 + +\verb|dvips|~的字体详细使用方法可查阅其手册\citep{Rokicki_2005}第~6~章，此处不赘述。 + +\subsection{dvipdfm(x)} +\verb|dvipdfm|~支持~PK~和~Type 1，它可以用一个~\verb|t1fonts.map|~文件建立~PK~文件和~Type 1~文件之间的映射，这样生成的~PDF~用的就是~Type 1。\verb|dvipdfm|~也不支持真正的~TrueType。 + +\verb|dvipdfmx|~通过正确的设置可以使用真正的~TrueType，它对中日韩等东亚文字的支持也较好，所以它对我们来说是~Driver~的首选。 + +\section{TrueType~字体安装配置} +CJK~自带的~UTF-8~编码字体~gbsn~和~gkai只包含~GB2312~字符集，而~CTeX~只提供~GBK~编码字体，因此中文用户通常需要自己安装配置~UTF-8~编码的~TrueType~字体。 + +在使用~TrueType~之前，用户通常需要作以下准备工作： +\begin{enumerate} + \item 用转换程序~\verb|ttf2tfm|~生成~TFM。 + \item 配置字体定义文件~\verb|.fd|。 + \item 配置~\verb|ttf2pk|~，因为~DVI~浏览器和~\verb|dvips|~都会自动调用~\verb|ttf2pk|~来生成~PK。 + \item 配置~\verb|dvipdfmx|。 +\end{enumerate} + +\subsection{目录和文件} +通常每个发行包都会参照~TDS~建立自己的目录系统，把各种文件发在固定的位置。比如~MiKTeX~顶层目录如下，在本节后面的示例中我们将使用这些目录的缩写。 +\begin{code} +Install: D:\edit\MiKTeX 2.7 +UserData: C:\Documents and Settings\Alpha\Local Settings\ + Application Data\MiKTeX\2.7 +UserConfig: C:\Documents and Settings\Alpha\ + Application Data\MiKTeX\2.7 +\end{code} + +目录多了有个缺点，文件不知道放在哪里好。MiKTeX~中有的配置文件居然在四个目录下各有一份，实在是令人发指。幸好我们可以用下面的命令检查配置文件的具体名字和路径。 + +\begin{code} +initexmf --edit-config-file=ttf2pk +\end{code} + +\subsection{ttf2tfm} +比如我们想把~\verb|SimSun18030.ttc|（18030~字符集的新宋体）转换为~UTF8~编码的字体文件，我们需要执行以下步骤。 + +\begin{enumerate} + \item 把需要的~\verb|.ttf|~文件复制到~\verb|UserData/fonts/truetype/chinese/|。 + \item 用下面的命令生成\verb|.tfm|~和~\verb|.enc|~文件。 + \item 把~\verb|*.tfm|~复制到~\verb|UserData/fonts/tfm/chinese/utf8song/|。 + \item 把~\verb|*.enc|~复制到~\verb|UserData/fonts/enc/chinese/utf8song/|。 +\end{enumerate} + +\begin{code} +ttf2tfm SimSun18030.ttc -q -w utf8song@Unicode@ +\end{code} + +\subsection{字体定义文件} +字体定义文件将字体引用名和实际的字体文件联系起来，比如我们在~\verb|CJK|~环境中引用~\verb|usong|~时，系统将会找到并使用~\verb|utf8song*.tfm|。 + +\begin{code} +%UserData\tex\latex\CJK\UTF8\C70usong.fd +\ProvidesFile{c70usong.fd} +%character set: GB18030 +%font encoding: Unicode +\DeclareFontFamily{C70}{usong}{\hyphenchar \font\m@ne} +\DeclareFontShape{C70}{usong}{m}{n}{<-> CJK * utf8song}{} +\DeclareFontShape{C70}{usong}{m}{it}{<-> CJK * utf8song}{} +\DeclareFontShape{C70}{usong}{bx}{n}{<-> CJKb * utf8song}{ + \CJKbold} +\endinput +\end{code} + +\subsection{配置~\texttt{ttf2pk}} +MiKTeX~中~\verb|ttf2pk|~的配置文件是~\verb|ttf2pk.ini|~，在其它的发行包中可能是~\verb|ttf2pk.cfg|。 + +\verb|ttf2pk.ini|~中有一个~\verb|.map|~文件列表，后者定义了~TrueType~应该按编码转为~PK~等信息。 + +比如下面这个文件列表会让~\verb|ttf2pk|~读取~\verb|foo.map|~和~\verb|bar.map|。 + +\begin{code} +map foo.map +map bar.map +\end{code} + +如果系统找不到~\verb|ttf2pk.ini|，它会缺省使用~\verb|ttfonts.map|。 +\begin{code} +%UserData\ttf2tfm\base\ttfonts.map +utf8song@Unicode@ SimSun18030.ttc +\end{code} + +\subsection{配置~\texttt{dvipdfmx}} +配置~\verb|dvipdfmx|~是为了让~PDF~正确地嵌入~TrueType，否则生成的文件中的内容不能复制、粘贴。 + +\begin{code} +%UserConfig\dvipdfm\config\dvipdfmx.cfg +f cid-x.map +\end{code} + +\begin{code} +%UserData\dvipdfm\config\cid-x.map +utf8song@Unicode@ unicode SimSun18030.ttc +\end{code} + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/graphics.tex b/Master/texmf-doc/doc/chinese/lnotes/src/graphics.tex new file mode 100644 index 00000000000..03256a1fb42 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/graphics.tex @@ -0,0 +1,1256 @@ +\chapter{插图} +\label{sec:graphics} + +\begin{quotation} +A picture says more than a thousand words. +\begin{flushright} +--- Shakespeare +\end{flushright} +\end{quotation} + +当年~Knuth~开发~\TeX~时，GIF、JPEG、PNG、EPS~等图形格式还没有问世，所以~DVI~不能直接支持这些格式。但是高手就是高手，Knuth~在~\TeX~上留了一个后门：\verb|\special|~命令，让后面的~Driver~决定怎样处理图形。 + +这和当年老毛把港澳台，老邓把钓鱼岛都“留给后人解决”有异曲同工之妙。曾经有位出版社的编辑看上了包老师写的一个程序，要包老师改改当作教学辅助软件出版，但是包老师手头没有~DOS~中断的资料没办法加鼠标操作。该编辑说：你把鼠标驱动打包在软件里，让用户自己琢磨是怎么回事。 + +下面我们会在~\ref{sec:graphics_format}~节介绍一下~\LaTeX~所用图形格式，\ref{sec:includegraphics}~节介绍怎样插入已有的图形，\ref{sec:mp}--\ref{sec:pgf}~节讨论怎样制作矢量图形。 + +\section{图形格式} +\label{sec:graphics_format} + +\LaTeX~支持点阵图形格式~JPEG~和~PNG，也支持矢量格式~EPS~和~PDF。对于示意图，我们应该首选矢量格式；包含大量自然色彩的图像（比如照片）应该选~JPEG，人工点阵图像应该选~PNG。 + +\subsection{EPS} +80~年代中后期，PS~风头之劲一时无两，人们自然会考虑把它作为文档中嵌入图形的标准格式。然而~PS~实在太强大，人们担心嵌入文档的~PS~会搞破坏，于是就产生了戴着手铐的~Encapsulated PostScript（EPS）。出于同样的原因，人们也担心嵌入~HTML~的~ActiveX、Java Applet、JavaScript~中混入恶意代码，所以才会对它们也有所限制。 + +早年间~DVI~经常被转换为~PS，所以~EPS~就成了~\LaTeX~的标准图形格式。 + +\subsection{Driver~们的口味} + +\subsubsection{dvips} +\verb|dvips|~喜欢~PS，所以就爱屋及乌只支持嵌入~EPS。MiKTeX~看不惯这种垄断行为，就把~\verb|dvips|~破解，添加了对~JPEG~和~PNG~的支持。如果你反对这种黑客破解行径，只好找软件把其它图形格式转换为~EPS。 + +\subsubsection{pdf\LaTeX} +pdf\LaTeX~支持~JPEG、PNG和PDF，不支持~EPS。传说pdf\LaTeX~不支持~EPS~的原因是~PS~解释器的版权问题。包老师认为这种说法不可信，因为~1997~年~Hàn The Thành~发布~pdf\TeX~时~PS~已经被~PDF~赶超，Adobe~与其保护~PS~还不如保护~PDF。 + +\LaTeX~有两个宏包~\verb|epstopdf|~和~\verb|pst-pdf|~可以实时地（on the fly）把~EPS~转换为~PDF\footnote{在这里on the fly是指在后台处理，用户不用操心。包老师不确定把它翻译为“实时”是否合适，因为~real time~通常被翻译为实时。对于用户无须干涉、知情的情况，有人说~user transparent，也有人说~black box，语言还真奇妙。}。然而前者有安全漏洞，后者用法繁琐，用户最好还是用其它软件事先把~EPS~转为~PDF。 + +\subsubsection{dvipdfm} +\verb|dvipdfm|~支持~JPEG、PNG、PDF，不支持~EPS，但是它可以实时地调用~Ghostscript~把~EPS~转为~PDF。所以从图形格式支持的角度来讲，\verb|dvipdfm|~比~\verb|dvips|~和~pdf\LaTeX~都好。 + +那位同学说了，你这么多废话作甚，直接告诉我们用~\verb|dvipdfm|~不就完了。然而你别忘了~\verb|dvipdfm|~需要~DVI~作为输入，不幸的是用来生成~DVI~的~\verb|latex|~对~JPEG~和~PNG~有意见。 + +综上所述，这些~driver~都不能把图形格式痛快地通吃，所以同学们别着急，且听包老师慢慢忽悠怎样转换和处理图形格式。 + +\subsection{图形格式转换} + +注意把点阵图形转换为矢量图形并不能提高图形本身的质量，正所谓“garbage in, garbage out”。 + +\subsubsection{JPEG~和~PNG~的范围框} + +作为中间格式的~DVI~不包含图形本身，它只记录图形的尺寸和文件名，因为具体的图形处理由后面的~driver~负责。DVI~中图形的尺寸来自它的范围框（bounding box），而~\verb|latex|~无法从点阵图形文件中提取这一信息，所以我们需要以某种方式把范围框信息告诉它。 + +一种方法是打开图形文件，记下尺寸，插入图形时加上相应的参数。 + +另一种方法用~\verb|ebb|~程序生成一个含范围框信息的文件。比如下例会生成~\verb|graph.bb|~文件，有了它插入图形时就不需要范围框参数。注意有时此程序算出的范围框不准，不知道是它的~bug~还是包老师的人品问题。 +\begin{code} +ebb graph.jpg +\end{code} + +\subsubsection{其它格式转为EPS} +有很多程序都可以把点阵图形转换为~EPS，比如~\href{http://www.imagemagick.org/}{ImageMagick}，以及~\href{http://www.tex.ac.uk/cgi-bin/texfaq2html?label=dvipsgraphics}{~a2ping/sam2p、bmeps、jpeg2ps、sam2p}~等。 + +PS~从~Level 2~开始才支持点阵图形压缩，所以在把其它格式转为~EPS~时应尽量使用~Level 2~或~3，否则输出的~EPS~会很大。 + +下面是一个~ImageMagick~中~\verb|convert|~程序的例子。 +\begin{code} +convert photo.jpg eps2:photo.eps +\end{code} + +另外还有一种~PS~虚拟打印机的方法，优点是可以把几乎所有文件“打印”成~EPS，缺点是输出的是~PS Level 1，即使驱动程序提供了其它~Level~的选项。 + +\begin{enumerate} +\item 找一个~PS~打印机驱动程序。Windows~安装盘附带很多打印机驱动，其中带~PS~字样的就是~PS~驱动。包老师选的是“HP Color LaserJet 8550-PS”，Adobe~提供的~PS~驱动效果不太好。其它驱动安装过程可能稍有不同。 +\item 安装时端口选“FILE”，或者后面打印时选择“Print to File”。高级选项里的~PS~选项选“Encapsulated PostScript (EPS)”。 +\item 打开点阵图形文件，打印到上面的虚拟打印机，输出的文件就是~EPS，但是它没有范围框。 +\item 用~GSview~打开上面生成的~EPS，不用理会没范围框的警告，Options~菜单里选上“EPS Clip”，用~File~菜单的“PS to EPS”生成含范围框的~EPS。 +\end{enumerate} + +\subsubsection{其它格式转为~PDF} + +\LaTeX~附带的~\verb|epstopdf|~程序\footnote{这个命令行程序和上面提到的~epstopdf~宏包是两样东西。}可以把~EPS~转为~PDF。类似地我们也可以安装一个~PDF~虚拟打印机，用它来把其它图形文件转为~PDF。 + +\section{插入图形} +\label{sec:includegraphics} + +\subsection{插入命令} +如今万事俱备，只欠插入。上回讲到哪儿来着？Yeah，~Knuth~的后门~\verb|\special|。 + +用低级命令~\verb|\special|~来插入图形很不爽，于是~\LaTeX~v2.09~增加了~\verb|epsf|~和~\verb|psfig|~宏包。之后~\LaTeXe~推出了更好的~\verb|graphics|~和~\verb|graphicx|~宏包，这两个宏包有个共同的命令：\verb|\includegraphics|。\verb|graphicx|~版本的语法更简单，功能更强大，所以一般推荐用它。 + +插入图形的具体命令如下，如果是点阵图形需要加范围框参数（左上角和右下角坐标）。 + +\begin{code} +\includegraphics[bb=0 0 410 307]{photo.jpg} +\end{code} + +若想省略文件后缀，可在插入图形前使用两个命令。前者指定一个后缀列表，让~\LaTeX~自行查找；后者告诉~\LaTeX~未知后缀的都是~EPS。 +\begin{code} +\DeclareGraphicsExtensions{.eps,.mps,.pdf,.jpg,.png} +\DeclareGraphicsRule{*}{eps}{*}{} +\end{code} + +\subsection{缩放、旋转} +\Fref{tab:scale_angle}~和\Fref{tab:clip}~的选项可以用来缩放、旋转和裁剪插图。 + +\begin{table}[htbp] +\caption{includegraphics~命令的缩放和旋转选项} +\label{tab:scale_angle} +\centering +\begin{tabularx}{350pt}{lX} + \toprule + scale & 缩放比例 \\ + width & 宽度 \\ + height & 高度 \\ + totalheight & 范围框高度，旋转时它不等于高度 \\ + keepaspectratio & 如果不使用它而同时指定插图的宽度、高度，长宽比可能会失调；使用它时长宽比不变，宽度、高度都不超过指定参数 \\ + angle & 旋转角度 \\ + origin & 旋转原点 \\ + \bottomrule +\end{tabularx} +\end{table} + +\begin{table}[htbp] +\caption{includegraphics~命令的裁剪选项} +\label{tab:clip} +\centering +\begin{tabularx}{350pt}{lX} + \toprule + viewport & 可视区域的左上角和右下角坐标。\\ + trim & 左、下、右、上四边裁剪的数值。\\ + clip & 是否真正裁剪。缺省为false，不执行裁剪，多出的部分就那样放着；设置为true时执行裁剪。似乎是多此一举。\\ + \bottomrule +\end{tabularx} +\end{table} + +若想深入了解~\LaTeX~插入图形的功能，请参考~Keith Reckdahl~的《Using Imported Graphics in \LaTeX~ and pdf\LaTeX》\citep{Reckdahl_2006}（简称epslatex）。 + +\subsection{figure环境} +插图通常需要占据大块空白，所以在文字处理软件中用户经常需要调整插图的位置。\LaTeX~有一个~\verb|figure|~环境可以自动完成这样的任务，这种自动调整位置的环境称作浮动环境。 + +\begin{code} +\begin{figure}[htbp]%位置选项 +\centering +\includegraphics[bb=0 0 410 307,scale=.8]{photo} +\caption{10个月大的Anna} +\label{fig:anna} +\end{figure} +\end{code} + +\begin{figure}[htbp] +\centering +\includegraphics[bb=0 0 410 307,scale=.8]{dscf4684} +\caption{10个月大的Anna} +\label{fig:anna} +\end{figure} + +上述代码中，\verb|[htbp]|~选项用来指定插图排版的理想位置，这几个字母分别代表~here、top、bottom、float page，也就是固定位置、页顶、页尾、单独的浮动页。我们可以使用这几个字母的任意组合，一般不推荐单独使用~\verb|[h]|，因为那个位置也许很不合适，\LaTeX~会很生气。 + +\verb|\centering|~用来使插图居中，\verb|\caption|~命令设置插图标题，\LaTeX~会自动给浮动环境的标题加上编号。注意~\verb|label|~应放在\verb|caption|~之后，否则引用时指向的是前一个插图。 + +\subsection{插入多幅图形} +\subsubsection{并排摆放，共享标题} +当我们需要两幅图片并排摆放，并共享标题时，可以在~\verb|figure|~环境中使用两个~\verb|\includegraphics|~命令。 + +\begin{fdemo}{ +\centering +\includegraphics[scale=2]{examples/subfig_left.mps} +\includegraphics[scale=2]{examples/subfig_right.mps} +\captionof{figure}{反清复明} +} +\begin{figure}[htbp] +\centering +\includegraphics{left} +\includegraphics{right} +\caption{反清复明} +\end{figure} +\end{fdemo} + +\subsubsection{并排摆放，各有标题} +如果想要两幅并排的图片各有自己的标题，可以在~\verb|figure|~环境中使用两个~\verb|minipage|~环境，每个环境里插入一个图。 +\begin{code} +\begin{figure}[htbp] +\centering +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics{left} + \caption{清明} +\end{minipage} +\end{code} +\begin{code} +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics{right} + \caption{反复} +\end{minipage} +\end{figure} +\end{code} + +\begin{figure}[htbp] +\centering +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics[scale=2]{examples/subfig_left.mps} + \caption{清明} +\end{minipage} +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics[scale=2]{examples/subfig_right.mps} + \caption{反复} +\end{minipage} +\end{figure} + +\subsubsection{并排摆放，共享标题，各有子标题} +如果想要两幅并排的图片共享一个标题，并各有自己的子标题，可以使用~\verb|subfig|~宏包提供的~\verb|\subfloat|~命令。 + +\verb|subfloat|~命令缺少宽度参数。虽然我们可以用~\verb|\hspace|~命令调整子图的距离，子标题却只能和子图本身一样宽，就会出现折行。 +\begin{code} +\usepackage{subfig} +\begin{figure}[htbp] +\centering +\subfloat[清明]{ + \label{fig:subfig_a} + \includegraphics{left} +} +\hspace{80pt} +\subfloat[反复]{ + \label{fig:subfig_b} + \includegraphics{right} +} +\caption{反清复明} +\end{figure} +\end{code} + +每个子图可以有各自的引用，就象这个样子：\Fref{fig:subfig_a}、\Fref{fig:subfig_b}。 +\begin{figure}[htbp] +\centering +\subfloat[清明]{ + \label{fig:subfig_a} + \includegraphics[scale=2]{examples/subfig_left.mps} +} +\hspace{80pt} +\subfloat[反复]{ + \label{fig:subfig_b} + \includegraphics[scale=2]{examples/subfig_right.mps} +} +\caption{反清复明} +\end{figure} + +\subsubsection{改进的子图方法} +为了避免子标题折行，我们可以在~\verb|\subfloat|~里再嵌套个~\verb|minipage|，因为后者是有宽度的。 +\begin{code} +\begin{figure}[htbp] +\centering +\subfloat[清明]{ +\label{fig:improved_subfig_a} +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics{left} +\end{minipage} +} +\subfloat[反复]{ +\label{fig:improved_subfig_b} +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics{right} +\end{minipage} +} +\caption{反清复明} +\end{figure} +\end{code} + +\begin{figure}[htbp] +\centering +\subfloat[清明]{ +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics[scale=2]{examples/subfig_left.mps} +\end{minipage} +} +\subfloat[反复]{ +\begin{minipage}[t]{0.3\textwidth} + \centering + \includegraphics[scale=2]{examples/subfig_right.mps} +\end{minipage} +} +\caption{反清复明} +\end{figure} + +\section{图形绘制工具比较} +与~\LaTeX~配套使用的绘图工具主要有三种：\MP、PSTricks~和~PGF，它们的特点如下。 + +\begin{itemize} +\item 工作方式。\MP~离线绘图，生成的~EPS~可以插入~\LaTeX~文档；PSTricks~和~PGF~都采用在线绘图的方式，也就是~\LaTeX~文档内直接使用绘图命令。 +\item 兼容性。\MP~生成的~MPS~需要先转为~PDF~才能被~pdf\LaTeX~使用；PSTricks~生成的~EPS和~pdf\LaTeX~不兼容；PGF~提供针对各种~driver~的接口，兼容性最好。 +\item 功能。PSTricks~有~PS~作后盾，功能最强；\MP~擅长处理数学内容；PGF~的流程图有独到之处。 +\end{itemize} + +限于篇幅，本文只对这三种工具进行简介。除了它们，用户也可以考虑一些面向~\LaTeX~的绘图前端，比如~Unix/Linux~下的~xfig~和~Windows~下的~TpX；或可以输出~EPS~的专用软件，比如~gnuplot~和~Matlab。 + +\section{\MP} +\label{sec:mp} + +1989~年~John D. Hobby\footnote{Hobby 1985年从斯坦福获博士学位，导师就是Knuth，现供职于贝尔实验室。}开始设计一种绘图语言及其编译器，也就是~\MP。\MP~从~\MF~那里获得了大量灵感和源代码，学生从导师那里顺点东西自然是手到擒来。\MP~和~\MF~语法类似，\MP~的主要优点在于是它输出的是~EPS，而且支持彩色；\MF~输出的是点阵格式，不支持彩色。Knuth~声称自己画图时只用~\MP。 + +从~Hobby~主页上~\MP~的更新记录看，它的最后版本是~0.63，年份是~1994。目前~Taco Hoekwater\footnote{他也是LuaTeX开发者之一。}继续~\MP~的开发工作，最新版本是~1.005。 + +本文只对~\MP~作简单介绍，若想深入了解请参阅~Hobby~的《A User's Manual for MetaPost》\citep{Hobby_2007}。 + +\subsection{准备工作} +用户一般需要把~\MP~源文件（.mp）用一个命令行程序~\verb|mpost|~编译为一种特殊的~EPS，也称作~MPS，然后再把~MPS~插入~\LaTeX~源文件中使用。 +\begin{figure}[htbp] +\centering +\begin{tikzpicture} + \node[box] (mp) {.mp}; + \node[box, right=5 of mp] (mps) {.mps}; + \path (mp) edge [arrow] node[auto] {mpost} (mps); +\end{tikzpicture} +\caption{MetaPost~的编译} +\label{fig:mp} +\end{figure} + +一个~\MP~源文件可以包含多个图形，一般形式如下。代码中每行语句以~\verb|;|~结尾，注释行以~\verb|%|~起始。每个图形的绘图命令包含在一对起始和结尾声明之间。文件结尾也要有一个结尾声明。 +\begin{code} +beginfig(1); %图形起始 +... %绘图命令 +endfig; %图形结尾 + +beginfig(2); +... +endfig; +... +end; %文件结尾 +\end{code} + +假如上面的源文件名字是~\verb|fig.mp|，我们可以执行以下编译命令。 +\begin{code} +mpost fig(.mp) +\end{code} + +编译后就会生成“fig.1、fig.2、$\cdots$”~等文件，每个文件的后缀就是相应的图形起始声明的编号。所以此编号在一个源文件中应保持唯一，否则后生成的文件就会覆盖前面的。 + +这样的文件名管理起来很麻烦，插入它们时也不能省略后缀，因为~\LaTeX~不能识别它们。用~\verb|\DeclareGraphicsExtensions|~来逐一声明后缀看起来很傻，自己改文件名更傻，\verb|\DeclareGraphicsRule|~也显得不够严谨。 + +然而~\MP~已经考虑到这个问题，为此提供了一个文件名模板命令。把下面的代码加到源文件头部，编译输出的文件名就会是“fig-01.mps、fig-02.mps、$\cdots$”。 +\begin{code} +filenametemplate "%j-%2c.mps"; %加在源文件头部 +\end{code} + +我们也可以把这个命令加在每个图形的起始声明之前，指定个性化的输出文件名，这样可能更便于记忆。 +\begin{code} +filenametemplate "flowchart.mps" %加在每个图形前面 +\end{code} + +MPS~可以用~GSview~查看，我们也可以用以下命令把它转为~PDF~再用~Adobe Reader~查看。 + +\begin{code} +epstopdf flowchart.mps +\end{code} + +\subsection{基本图形对象} +为了节省空间，本节后面的示例会略去图形起始声明和结尾声明等不重要的细节。 + +\subsubsection{直线} + +绘图命令~\verb|draw|~把几个点以直线段连接起来。\MP~中的缺省长度单位是~bp，用户也可以使用\Fref{tab:unit}~中的其它单位。我们还可以定义一个缩放系数，把坐标都转换成此系数的倍数，这样以后想缩放图形时只要改这个系数即可。 + +注意~\MP~中的变量赋值符号是~\verb|:=|，而~\verb|=|~用于方程式。变量在同一源文件中只须定义一次，其后的图形中都可以使用。 + +\begin{fdemo}{\includegraphics{examples/line.mps}} +draw (0,0)--(40,0)--(20,20)--(0,0); +u:=10pt; %缩放系数 +draw (5u,0)--(9u,0)--(7u,2u)--cycle; +\end{fdemo} + +几段直线或曲线可以构成一条路径（path），在路径末尾加个~\verb|cycle|~就能构成封闭路径（closed path）。上例中的两个三角形看起来都是封闭的，但是前面这个其实不是真正的封闭路径。 + +\subsection{点和线宽} +\verb|drawdot|~命令可以在指定坐标画一个点，为了使它醒目些我们可以换支粗一点的画笔。\MP~中的画笔缺省是直径~0.5pt~的圆形，拿它画出来的线宽就是~0.5pt。 + +\begin{fdemo}{\includegraphics{examples/dot.mps}} +draw (0,0)--(10u,4u); +pickup pencircle scaled 2pt; +drawdot (0,0); +drawdot (10u,4u); +\end{fdemo} + +上面的~\verb|pickup|~是一种全局操作，也就是说它会影响到之后所有的绘图命令，我们也可以用~\verb|withpen|~为单个绘图命令设置画笔。 + +\begin{code} +draw (0,0)--(10u,4u) withpen pencircle scaled 2pt; +\end{code} + +\subsubsection{曲线} +曲线和直线的命令相近，只是把连接两个点的~\verb|--|~换成了~\verb|..|。如果共用一些坐标，直线和曲线也可以混在一条语句里画。 + +\begin{fdemo}{\includegraphics{examples/curve.mps}} +draw (0,.5u)..(5u,3u)..(10u,1.5u).. + (7u,0)..(5u,1.5u)..(7u,1.5u); +\end{fdemo} + +\MP~的曲线用三次贝塞尔（Cubic B\'ezier）算法实现。用户可以在命令中增加~direction（方向）、Tension（张力）和~Curl（曲率）等控制，限于篇幅本文不赘述。 + +\subsubsection{预定义图形} +~\verb|fullcircle|~命令以原点为圆心画一个单位圆，类似的预定义图形还有~\verb|halfcircle、quartercircle、unitsquare|~等。注意单位正方形的参考点在左下而不在其中心。 + +通过不同的横向和纵向缩放系数，我们可以把圆形和正方形变成椭圆和长方形。 + +\begin{code} +draw fullcircle scaled 2u; +draw halfcircle scaled 2u shifted (3u,0); +draw quartercircle scaled 2u shifted (5u,0); +draw fullcircle xscaled 4u yscaled 2u shifted (9u,0); +draw unitsquare scaled 2u shifted (12u,-u); +draw unitsquare xscaled 4u yscaled 2u shifted (15u,-u); +\end{code} + +\begin{out} +\includegraphics{examples/predefined.mps} +\end{out} + +\subsection{图形控制} + +\subsubsection{线型和箭头} +在绘制图形时，我们不仅可以变换线宽，也可以使用多种线型。 +\begin{code} +draw (0,0)--(10u,0) dashed withdots; +draw (0,1u)--(10u,1u) dashed withdots scaled 2; +draw (0,2u)--(10u,2u) dashed evenly; +draw (0,3u)--(10u,3u) dashed evenly scaled 2; +\end{code} + +\begin{out} +\includegraphics{examples/dashed.mps} +\end{out} + +箭头和直线、曲线的语法相近，注意画反向箭头时需要把两个坐标用一对~\verb|()|~括起来。 + +\begin{fdemo}{\includegraphics{examples/arrow.mps}} +drawarrow (0,4u)--(9u,4u); +drawarrow reverse ((0,2u)--(9u,2u)); +drawdblarrow (0,0)--(9u,0); +\end{fdemo} + +\subsubsection{颜色和填充} +\MP~预定义的颜色有黑、白、红、绿、蓝，它们的~RGB~值分别为(0,0,0)、(1,1,1)、(1,0,0)、(0,1,0)、(0,0,1)，缺省色就是黑色。 + +绘图命令一般都可以通过~\verb|withcolor|~参数来使用各种颜色。封闭路径可以用~\verb|fill|~命令填充。 + +\begin{fdemo}{\includegraphics{examples/color.mps}} +draw (0,4u)--(9u,4u) withcolor red; +draw (0,2u)--(9u,2u) withcolor green; +draw (0,0)--(9u,0) withcolor blue; +\end{fdemo} + +\begin{code} +fill p scaled u; +fill p scaled u shifted (3u,0) withcolor red; +fill p scaled u shifted (6u,0) withcolor green; +fill p scaled u shifted (9u,0) withcolor blue; +\end{code} + +\begin{out} +\includegraphics{examples/fill.mps} +\end{out} + +另一个命令~\verb|filldraw|~可以看作是~\verb|fill+draw|，它除了填充外还会把路径用指定的画笔画一遍。然而不幸的是画边缘和填充内部只能用同一种颜色，所以它的用处不大。 + +除了为每个绘图命令单独指定颜色，我们也可以使用一个全局命令，使得其后的绘图命令都使用某种颜色。 +\begin{code} +drawoption(withcolor blue); +\end{code} + +下面的方法可以用来定义基本色以外的颜色，用基本色混色或直接用RGB值效果是一样的。 + +\begin{code} +color c[]; +c1 := .9red + .6green + .3blue; +c2 := (.9,.6,.3); +\end{code} + +\subsubsection{图形变换} +我们可以对路径进行缩放、平移、旋转等变换操作，横向和纵向缩放可以分开进行。由于旋转是围绕原点进行的，所以要注意平移和旋转的顺序。下例中定义了一个~\verb|path|~变量，以便后面重用。 + +\begin{code} +path p; +p := (0,0)--(2,0)--(1,1.732)--cycle; +draw p scaled u; +draw p xscaled 2u yscaled u shifted (3u,0); +draw p scaled u rotated 60 shifted (8u,0); +\end{code} + +\begin{out} +\includegraphics{examples/transform.mps} +\end{out} + +\subsubsection{标注} +\verb|\label|~命令可以在指定的点附近加文字标注。\MP~也可以用一对~\verb|btex|~和~\verb|etex|~来嵌入一些~\TeX~内容，比如数学标注。 + +\begin{code} +draw unitsquare xscaled 10u yscaled 4u; +label.top("top", (5u,4u)); +label.bot("bottom", (5u,0)); +label.lft("left", (0,2u)); +label.rt("right", (10u,2u)); +\end{code} +\begin{code} +label.ulft("upper left", (0,4u)); +label.urt("upper right", (10u,4u)); +label.llft("lower left", (0,0)); +label.lrt("lower right", (10u,0)); +label.rt(btex $E=mc^2$ etex, (3u,2u)); +\end{code} + +\begin{out} +\includegraphics{examples/label.mps} +\end{out} + +因为用缺省方法编译生成的~MPS~不嵌入字体，当~\MP~包含文字时，GSview~就不能正常查看。这时我们可以给编译命令加个参数，生成的~MPS~就会包含字体信息。注意这种方法生成的~MPS~虽然~GSview~能查看，\verb|dvipdfmx|~却不能正常处理。 + +\begin{code} +mpost \prologues:=2; input fig.mp +\end{code} + +\subsection{编程功能} + +\subsubsection{数据类型和变量} +\MP~中有10~种基本数据类型：numeric、pair、path、pen、~color~、cmykcolor、transform、string、boolean、picture。我们已经接触过其中几种，比如缩放系数~u~就是一个~numeric，一个点的坐标是一个~pair，几个点用直线或曲线连起来是一个~path，pencircle~是一种~pen，black~是一种~color，scaled、rotated、shifted~都是~transform。 + +numeric~类型变量的精度是~1/65536，它的绝对值不能超过~4096，在计算过程中数值可以达到~32768。这样的规定也应归功于当年的电脑硬件，不过对于科技文档插图而言，4096~一般还是够用的。 + +除了缺省的~numeric，其它变量在使用之前都需要用数据类型来显式声明。相同类型的变量可以在一行语句中声明，但是带下标的变量不能放在同一行（这个规定很蹊跷）。 +\begin{code} +numeric x,y,z; %正确 +numeric x1,x2,x3; %错误 +numeric x[]; %正确 +\end{code} + +\subsubsection{数学运算} +\MP~中可以使用普通的运算符，比如~\verb|+ - * /|；也提供一些特殊的运算符，比如~\verb|a++b|~表示$\sqrt{a^2+b^2}$，\verb|a+-+b|~表示$\sqrt{a^2-b^2}$；另外\Fref{tab:math_function}~列出一些常用数学函数。 + +\begin{table}[htbp] +\caption{数学函数} +\label{tab:math_function} +\centering +\begin{tabular}{llll} + \toprule + abs & 绝对值 & mexp & 指数 \\ + round & 四舍五入 & mlog & 对数 \\ + ceiling & 向上圆整 & sind & 正弦 \\ + floor & 向下圆整 & cosd & 余弦 \\ + mod & 模余 & normaldeviate & 正态分布随机数 \\ + sqrt & 开方 & uniformdeviate & 均匀分布随机数 \\ + \bottomrule +\end{tabular} +\end{table} + +\subsubsection{循环} +当执行重复任务时，循环语句可以让程序变得简洁。注意下例中的循环语句是一条命令，之所以分成三行写是为了看起来清晰点。 + +\begin{fdemo}{\includegraphics{examples/loop.mps}} +draw (0,0) %注意这里没有分号 +for x=1 upto 3: + ..(x*x,x)*u +endfor; +\end{fdemo} + +循环语句缺省步长是~1，我们也可以改用其它步长。\verb|upto|~其实就是~\verb|step 1 until|~的缩写方式。 +\begin{code} +for x=1 step .5 until 3: +\end{code} + +\section{PSTricks} +\label{sec:pstricks} + +PSTricks~是一个基于~PS~的宏包，有了它用户就可以直接在~\LaTeX~文档中插入绘图命令。PSTricks~早期的作者是~Timothy Van Zandt\footnote{法国Insead大学经济系教授。}，初始开发年月不详，他于~1997~年退居二线，之后由~Denis Girou、Sebastian Rahtz\footnote{牛津大学计算机系网管。}、Herbert Voß~等维护。 + +本文只介绍~PSTricks~的基本功能，若想深入了解请参阅~Van Zandt~的《PSTricks User's Guide》\citep{Zandt_2007}。另外\Fref{tab:pst_add}~列出了一些可以和~PsTricks~配合使用的辅助宏包。 + +\begin{table}[htbp] +\caption{PSTricks~辅助宏包} +\label{tab:pst_add} +\centering +\begin{tabular}{llll} + \toprule + multido & 循环语句 & pst-eucl & 几何函数 \\ + pst-plot & 函数绘图 & pst-math & 弧度三角函数 \\ + pst-plot3d & 三维绘图 & pstricks-add & 极坐标 \\ + \bottomrule +\end{tabular} +\end{table} + +\subsection{准备工作} +首先要引入~PSTricks~宏包。PSTricks~中缺省长度单位是~1cm，我们也可以设置自己的单位。 +\psset{unit=10pt} +\begin{code} +\usepackage{pstricks} +\psset{unit=10pt} +\end{code} + +绘图命令一般要放在~\verb|pspicture|~环境里，这样~\LaTeX~就会给图形预留一个矩形区域，注意这个矩形要能容纳所有图形对象。为了节省空间，在本节后面的示例代码中，~\verb|pspicture|~环境将被略去。 + +\begin{code} +\begin{pspicture}(0,0)(4,2) +... +\end{pspicture} +\end{code} + +另外需要注意的是，嵌入~\LaTeX~的~PSTricks~生成的是~PS，\verb|dvips|~可以处理，\verb|dvipdfm|~和pdf\LaTeX~则不能。所以如果使用后两种~driver，需要先行生成~EPS。 + +第一种方法是把~PSTricks~代码放进一个空白的\LaTeX~页面，用它生成一个简单的~DVI。 + +\begin{code} +\documentclass{article} +\usepackage{pstricks} +\pagestyle{empty} %页面样式为空 + +\begin{document} +\psset{unit=10pt} +\colorbox{white}{% + \begin{pspicture}(0,0)(4,2)% + \psdot(0,0)% + \psdots(0,2)(2,2)(4,2)% + \end{pspicture}% +} +\end{document} +\end{code} + +然后用以下命令把~DVI~转为~EPS，\verb|-E|~参数即代表~EPS。上面代码中的~colorbox~使得生成的~EPS~有正确的范围框。 + +\begin{code} +dvips pst_dots(.dvi) -E -o dots.eps +\end{code} + +第二种方法是用~\verb|pst-eps|~宏包，它能够在线处理~PSTricks~代码并生成~EPS，这样用户就可以在同一文件中使用该~EPS。 + +然而~\verb|dvipdfmx|~不能正确处理~\verb|pst-eps|~生成的~EPS。它和~\verb|\rput|、\verb|\uput|~命令，\verb|pst-plot|~宏包中的~\verb|\psaxes|~命令都不兼容。类似的~\verb|ps4pdf|~宏包和~\verb|tabularx|~宏包不兼容。 + +\begin{comment} +\usepackage{pst-eps} +\PSTtoEPS[bbllx=0,bblly=0,bburx=4,bbury=2,makeeps=all] +{dots.eps}{ + \psdot(0,0) + \psdots(0,2)(2,2)(4,2) +} +\includegraphics{dots.eps} +\end{comment} + +\subsection{基本图形对象} +\subsubsection{点} +我们可以用以下命令画一个或多个点。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=4,bbury=2,makeeps=all] +{examples/dot.eps}{ + \psdot(0,0) + \psdots(0,2)(2,2)(4,2) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_dot.eps}} +\psdot(0,0) +\psdots(0,2)(2,2)(4,2) +\end{fdemo} + +\subsubsection{直线、多边形、矩形} +\verb|\psline|~命令把多个点用直线段连接起来，线段之间的连接缺省为尖角，也可以设置圆角。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=2,makeeps=all] +{examples/line.eps}{ + \psline(0,0)(2,2)(4,0) + \psline[linearc=.3](5,0)(7,2)(9,0) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_line.eps}} +\psline(0,0)(2,2)(4,0) +\psline[linearc=.3](5,0)(7,2)(9,0) +\end{fdemo} + +\verb|\pspolygon|~命令和~\verb|\psline|~类似，但是它会形成封闭路径。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=2,makeeps=all] +{examples/polygon.eps}{ + \pspolygon(0,0)(2,2)(4,0) + \pspolygon[linearc=.3](5,0)(7,2)(9,0) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_polygon.eps}} +\pspolygon(0,0)(2,2)(4,0) +\pspolygon[linearc=.3](5,0)(7,2)(9,0) +\end{fdemo} + +矩形用~\verb|\psframe|~命令，其参数就是矩形左下角和右上角的坐标。矩形也可以设置圆角。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=2,makeeps=all] +{examples/frame.eps}{ + \psframe(0,0)(4,2) + \psframe[framearc=.3](5,0)(9,2) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_frame.eps}} +\psframe(0,0)(4,2) +\psframe[framearc=.3](5,0)(9,2) +\end{fdemo} + +\subsubsection{圆、椭圆、圆弧、扇形} +圆形用~\verb|\pscircle|~命令，参数是圆心和半径。椭圆用~\verb|\psellipse|~命令，参数是中心、长径、短径。注意这两个命令的半径参数用不同的括号，可能是作者的笔误。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=7,bbury=2,makeeps=all] +{examples/circle.eps}{ + \pscircle(1,1){1} + \psellipse(5,1)(2,1) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_circle.eps}} +\pscircle(1,1){1} +\psellipse(5,1)(2,1) +\end{fdemo} + +圆弧用~\verb|\psarc|~命令，其参数是圆心、半径、起止角度，逆时针作图。~\verb|\psarcn|~类似，只是顺时针作图。扇形用~\verb|\pswedge|~命令。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=11,bbury=2,makeeps=all] +{examples/arc.eps}{ + \psarc(1,0){2}{0}{120} + \psarcn(5,0){2}{120}{0} + \pswedge(9,0){2}{0}{120} +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_arc.eps}} +\psarc(1,0){2}{0}{120} +\psarcn(5,0){2}{120}{0} +\pswedge(9,0){2}{0}{120} +\end{fdemo} + +\subsubsection{曲线} +\verb|\pscurve|~命令把一系列点用平滑曲线连接起来；它的变形版本~\verb|\psecurve|~命令不显示曲线的两个端点；另一变形命令~\verb|\psccurve|~则把曲线封闭起来。 + +参数~\verb|showpoints=true|~用来显示曲线的构成点，此参数也可用于其它绘图命令。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=15,bbury=2,makeeps=all] +{examples/curve.eps}{ + \pscurve[showpoints=true](0,1)(1,2)(3,0)(4,2)(1,0) + \psecurve[showpoints=true](5,1)(6,2)(8,0)(9,2)(5,0) + \psccurve[showpoints=true](11,1)(12,2)(14,0)(15,2)(12,0) +} +\end{comment} + +\begin{code} +\pscurve[showpoints=true](0,1)(1,2)(3,0)(4,2)(1,0) +\psecurve[showpoints=true](5,1)(6,2)(8,0)(9,2)(5,0) +\psccurve[showpoints=true](11,1)(12,2)(14,0)(15,2)(12,0) +\end{code} +\begin{out} +\includegraphics{examples/pst_curve.eps} +\end{out} + +\verb|\psbezier|~命令输出一条贝塞尔曲线，其参数就是曲线的控制点。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=6,bbury=2,makeeps=all] +{examples/bezier.eps}{ + \psbezier[showpoints=true] + (0,0)(2,2)(4,0)(6,2) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_bezier.eps}} +\psbezier[showpoints=true] + (0,0)(2,2)(4,0)(6,2) +\end{fdemo} + +抛物线用~\verb|\psparabola|~命令，它有两个参数，第一个是抛物线通过的一点，第二个是抛物线的顶点。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=2,bbury=2,makeeps=all] +{examples/parabola.eps}{ + \psparabola[showpoints=true] + (2,2)(1,0) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_parabola.eps}} +\psparabola[showpoints=true] + (2,2)(1,0) +\end{fdemo} + +\subsubsection{网格和坐标} +科技制图通常会用到坐标网格。\verb|\psgrid|~命令输出一个矩形网格，它有三个参数点。网格坐标标注在通过第一个点的两条直线上，第二和第三个点是矩形的两个对角顶点。当第一个参数省略时，坐标标注在通过第一个顶点的两条矩形边上。 +\begin{comment} +\psset{unit=10pt} +\PSTtoEPS[bbllx=-1,bblly=-1,bburx=8.4,bbury=2.4,makeeps=all] +{examples/grid.eps}{ + \psgrid(0,0)(-1,-1)(3,2) + \psgrid(5,0)(8,2) +} +\end{comment} + +\begin{code} +\psgrid(0,0)(-1,-1)(3,2) +\psgrid(5,0)(8,2) +\end{code} +\begin{out} +\includegraphics{examples/pst_grid.eps} +\end{out} + +\verb|pst-plot|~宏包提供的~\verb|\psaxes|~命令输出坐标轴。它的参数和~\verb|\psgrid|~的类似，刻度和标注都可以灵活地设置，也可以把坐标轴改成一个矩形框的形式。 +\begin{code} +\psset{unit=10pt} +\psaxes{<->}(0,0)(-1,-1)(3,2) +\psaxes[tickstyle=top,labels=none]{->}(5,0)(8,2) +\psaxes[axesstyle=frame,tickstyle=top]{->}(10,0)(13,2) +\end{code} +\begin{out} +\includegraphics{examples/pst_axis.eps} +\end{out} + +\subsection{图形控制} +\subsubsection{线型和箭头} +PSTricks~中的缺省线宽是~0.8pt，缺省线型是实线。以下参数可以控制单个绘图命令的线宽和线型。 +\begin{comment} +\psset{unit=10pt} +\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=4,makeeps=all] +{examples/linestyle.eps}{ + \psline[linewidth=1.5pt](0,4)(9,4) + \psline[linestyle=dotted](0,2)(9,2) + \psline[linestyle=dashed](0,0)(9,0) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_linestyle.eps}} +\psline[linewidth=1.5pt](0,4)(9,4) +\psline[linestyle=dotted](0,2)(9,2) +\psline[linestyle=dashed](0,0)(9,0) +\end{fdemo} + +我们也可以用命令~\verb|\psset|~命令来设置全局参数。 +\begin{code} +\psset{linewidth=1pt,linestyle=dashed} +\end{code} + +以下参数可以控制绘图命令的箭头。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=4,makeeps=all] +{examples/arrow.eps}{ + \psline{->}(0,4)(9,4) + \psline{<-}(0,2)(9,2) + \psline{<->}(0,0)(9,0) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_arrow.eps}} +\psline{->}(0,4)(9,4) +\psline{<-}(0,2)(9,2) +\psline{<->}(0,0)(9,0) +\end{fdemo} + +\subsubsection{颜色和填充} +PSTricks~预定义的颜色有~black、darkgray、gray、lightgray、white~等灰度颜色，也有~red、green、blue、cyan、magenta、yellow~等彩色。我们也可以自定义灰度颜色和彩色。 + +\begin{code} +\newgray{mygray}{.3} +\newrgbcolor{mycolor}{.3 .4 .5} +\end{code} + +以下参数可以控制单个绘图命令的颜色，我们也可以用~\verb|\psset|~命令设置全局参数。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=9,bbury=4,makeeps=all] +{examples/color.eps}{ + \psline[linecolor=red](0,4)(9,4) + \psline[linecolor=green](0,2)(9,2) + \psline[linecolor=blue](0,0)(9,0) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_color.eps}} +\psline[linecolor=red](0,4)(9,4) +\psline[linecolor=green](0,2)(9,2) +\psline[linecolor=blue](0,0)(9,0) +\end{fdemo} + +以下参数可以控制单个绘图命令的填充模式和填充颜色，注意只有封闭路径才可以填充。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=11,bbury=2,makeeps=all] +{examples/fill.eps}{ + \pscircle[fillstyle=solid,fillcolor=red](1,1){1} + \pscircle[fillstyle=vlines](4,1){1} + \pscircle[fillstyle=hlines](7,1){1} + \pscircle[fillstyle=crosshatch](10,1){1} +} +\end{comment} + +\begin{code} +\pscircle[fillstyle=solid,fillcolor=red](1,1){1} +\pscircle[fillstyle=vlines](4,1){1} +\pscircle[fillstyle=hlines](7,1){1} +\pscircle[fillstyle=crosshatch](10,1){1} +\end{code} +\begin{out} +\includegraphics{examples/pst_fill.eps} +\end{out} + +\subsection{对象布局} +\subsubsection{平移} +参数~\verb|origin|~可以让一个图形对象平移到指定的坐标点，我们也可以用~\verb|\psset|~命令设置全局平移参数。 +\begin{comment} +\PSTtoEPS[bbllx=0,bblly=0,bburx=7,bbury=2,makeeps=all] +{examples/origin.eps}{ + \psframe(0,0)(3,2) + \psframe[origin={4,0}](0,0)(3,2) +} +\end{comment} + +\begin{fdemo}{\includegraphics{examples/pst_origin.eps}} +\psframe(0,0)(3,2) +\psframe[origin={4,0}](0,0)(3,2) +\end{fdemo} + +\subsubsection{旋转} +\verb|\rput|~命令可以对一个图形对象同时进行旋转和平移操作。它有两个参数，第一个是旋转角度，第二个是平移到的坐标点。 +\begin{fdemo}{\includegraphics{examples/pst_rput.eps}} +\psframe(0,0)(3,2) +\rput{30}(5,0){\psframe(0,0)(3,2)} +\end{fdemo} + +\subsubsection{文字标注} +\verb|\rput|~命令还可以在指定的坐标点标注文字，这时它的第一个参数是坐标点相对于标注的位置。其取值可以是纵向的~t、b（上下），或横向的~l、r（左右），也可以是纵向和横向位置的组合。 +\begin{fdemo}{\includegraphics{examples/pst_label.eps}} +\pspolygon(0,0)(4,0)(2,3) +\rput[r](0,0){A} +\rput[l](4,0){B} +\rput[b](2,3){C} +\end{fdemo} + +\verb|\rput|~生成的标注就在坐标点上，有时会感觉离图形太近。另一个命令~\verb|\uput|~则生成缺省距离指定坐标点~5pt的标注，它的第一个参数是标注相对于坐标点的角度。 +\begin{fdemo}{\includegraphics{examples/pst_uput.eps}} +\pspolygon(0,0)(4,0)(2,3) +\uput[l](0,0){A} +\uput[r](4,0){B} +\uput[u](2,3){C} +\end{fdemo} + +\verb|\uput|~的角度参数可以是任意角度，也可以是字母，参见。注意~\verb|\uput|~的角度参数和~\verb|\rput|~命令的参考点位置参数的定义几乎正好相反，这也许反映了作者洒脱的风格。 + +\begin{table}[htbp] +\caption{uput~命令的角度参数} +\label{tab:uput} +\centering +\begin{tabular}{lrlr} + \toprule + r & 0$^\circ$ & ur & 45$^\circ$ \\ + u & 90$^\circ$ & ul & 135$^\circ$ \\ + l & 180$^\circ$ & dl & 225$^\circ$ \\ + d & 270$^\circ$ & dr & 315$^\circ$ \\ + \bottomrule +\end{tabular} +\end{table} + +\section{PGF} +\label{sec:pgf} +PGF~和~Beamer~的作者都是~Till Tantau\footnote{德国Lübeck大学计算机研究所教授。}。Tantau~当初开发~Beamer~是为了应付~2003~年他的博士学位论文答辩，之后它在~CTAN~上流行开来。2005~年~PGF~从~Beamer~项目中分离出来，成为一个独立的宏包。 + +本文只对~PGF~作简单介绍，若想深入了解请参阅~Tantau~的《TikZ and PGF Manual》\citep{Tantau_2008}。 + +\subsection{准备工作} +一般人们并不直接使用~PGF~命令，而是通过它前端~TikZ~来调用~PGF。在引用~\verb|tikz|~宏包之前，用户需要设置~PGF~系统~driver。 +\begin{code} +\def\pgfsysdriver{pgfsys-dvipdfmx.def} +\usepackage{tikz} +\end{code} + +PGF~的缺省长度单位是~1cm，我们也可以改用其它单位。注意这样预定义的长度单位有时会失效，这可能是~PGF~的~bug。 +\begin{code} +\pgfsetxvec{\pgfpoint{10pt}{0}} +\pgfsetyvec{\pgfpoint{0}{10pt}} +\end{code} + +TikZ~提供一个~\verb|tikz|~命令和一个~\verb|tikzpicture|~环境，具体绘图指令可以放在~\verb|tikz|~后面，也可以放在~\verb|tikzpicture|~中间。两种方法效果相同，用户可以任意选择。为了节省空间，本节的示例将省略部分环境代码。 +\begin{code} +\tikz ... %绘图命令 +\begin{tikzpicture} +... %绘图命令 +\end{tikzpicture} +\end{code} + +\subsection{基本图形对象} +\subsubsection{直线、多边形、矩形} +TikZ~中直线的语法和~\MP~类似，加~\verb|cycle|~参数才能构成真正的封闭路径。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw (0,0)--(4,0)--(2,2)--(0,0); +\draw (5,0)--(9,0)--(7,2)--cycle; +\end{tikzpicture} +} +\draw (0,0)--(4,0)--(2,3)--(0,0); +\draw (5,0)--(9,0)--(7,3)--cycle; +\end{fdemo} + +矩形命令如下，它的两个参数是矩形的两个对角顶点。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw (0,0) rectangle (4,2); +\end{tikzpicture} +} +\draw (0,0) rectangle (4,2); +\end{fdemo} + +\subsubsection{圆、椭圆、弧} +圆和椭圆命令如下，圆的参数是圆心和半径，椭圆的参数是中心、长径、短径。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw (1,1) circle (1); +\draw (5,1) ellipse (2 and 1); +\end{tikzpicture} +} +\draw (1,1) circle (1); +\draw (5,1) ellipse (2 and 1); +\end{fdemo} + +圆弧和椭圆弧命令如下，圆弧的参数是起始点，起始角度、终止角度、半径；椭圆弧则把半径换成了长径和短径。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw (2,1) arc (0:270:1); +\draw (7,1) arc (0:270:2 and 1); +\end{tikzpicture} +} +\draw (2,1) arc (0:270:1); +\draw (7,1) arc (0:270:2 and 1); +\end{fdemo} + +\subsubsection{曲线和抛物线} +曲线命令如下，中间的参数是控制点。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw (0,0) .. controls (2,2) + and (4,2) .. (4,0); +\filldraw (0,0) circle (.1) + (2,2) circle (.1) + (4,2) circle (.1) + (4,0) circle (.1); +\end{tikzpicture} +} +\draw (0,0) .. controls (2,2) + and (4,2) .. (4,0); +\end{fdemo} + +抛物线命令如下，除了起止点还可以指定顶点。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw (-1,1) parabola bend (0,0) (1.414,2); +\filldraw (-1,1) circle (.1) + (0,0) circle (.1) + (1.414,2) circle (.1); +\end{tikzpicture} +} +\draw (-1,1) parabola + bend (0,0) (1.414,2); +\end{fdemo} + +\subsection{图形控制} +\subsubsection{线型和箭头} +绘图命令可以设置线型和箭头参数。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw[line width=2pt] (0,3)--(9,3); +\draw[->] (0,2)--(9,2); +\draw[<-] (0,1)--(9,1); +\draw[<->] (0,0)--(9,0); +\end{tikzpicture} +} +\draw[line width=2pt] (0,0)--(9,0); +\draw[->] (0,1)--(9,1); +\draw[<-] (0,2)--(9,2); +\draw[<->] (0,3)--(9,3); +\end{fdemo} + +\subsubsection{颜色、填充、阴影} +颜色参数的用法如下。PGF~可以使用~\verb|xcolor|~宏包\citep{Kern_2007}中定义的所有颜色。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw[red] (0,4)--(9,4); +\draw[green] (0,2)--(9,2); +\draw[blue] (0,0)--(9,0); +\end{tikzpicture} +} +\draw[red] (0,4)--(9,4); +\draw[green] (0,2)--(9,2); +\draw[blue] (0,0)--(9,0); +\end{fdemo} + +封闭路径可以用颜色填充，\verb|\filldraw|~命令可以分别指定边框色和填充色。 +\begin{fdemo}{ +\begin{tikzpicture} +\fill[red] (1,1) circle (1); +\filldraw[fill=lightgray,draw=black] + (4,1) circle (1); +\end{tikzpicture} +} +\fill[red] (1,1) circle (1); +\filldraw[fill=lightgray,draw=black] + (4,1) circle (1); +\end{fdemo} + +\verb|\shade|~命令可以产生渐变和光影效果，缺省是从上到下，灰色渐变为白色。我们也可以使用其它方向和颜色的渐变。 +\begin{code} +\shade (0,0) rectangle (2,2); +\shade[left color=red,right color=orange] (3,0) rectangle (5,2); +\shade[inner color=red,outer color=orange] (6,0) rectangle (8,2); +\shade[ball color=blue] (10,1) circle (1); +\end{code} + +\begin{out} +\begin{tikzpicture} +\shade (0,0) rectangle (2,2); +\shade[left color=red,right color=orange] (3,0) rectangle (5,2); +\shade[inner color=red,outer color=orange] (6,0) rectangle (8,2); +\shade[ball color=blue] (10,1) circle (1); +\end{tikzpicture} +\end{out} + +\subsubsection{图形变换} +对图形对象可以进行平移和旋转操作，注意如果两种操作同时进行，它们是有顺序的。注意预定义的长度单位在这里对平移参数失效。 +\begin{code} +\draw (0,0) rectangle (2,2); +\draw[xshift=30pt] (0,0) rectangle (2,2); +\draw[xshift=75pt,rotate=45] (0,0) rectangle (2,2); +\end{code} + +\begin{out} +\begin{tikzpicture} +\draw (0,0) rectangle (2,2); +\draw[xshift=30pt] (0,0) rectangle (2,2); +\draw[xshift=75pt,rotate=45] (0,0) rectangle (2,2); +\end{tikzpicture} +\end{out} + +\subsection{样式} +PGF~比~\MP~和~PSTricks~多了一个有趣的概念：样式（style），它的思路和~HTML~的~CSS~相近。我们可以先定义两种样式， +\tikzset{ + myline/.style={line width=2pt}, + myblueline/.style={myline,blue} +} +\begin{code} +\tikzset{ + myline/.style={line width=2pt}, + myblueline/.style={myline,blue} +} +\end{code} + +然后就可以在绘图命令中这样使用样式。 +\begin{fdemo}{ +\begin{tikzpicture} +\draw[myline] (0,2)--(9,2); +\draw[myblueline] (0,0)--(9,0); +\end{tikzpicture} +} +\draw[myline] (0,2)--(9,2); +\draw[myblueline] (0,0)--(9,0); +\end{fdemo} + +除了用~\verb|\tikzset|~命令定义样式，我们也可以在~\verb|tikzpicture|~环境头部声明样式。前者是全局性的，后者则是局部性的。 +\begin{code} +\begin{tikzpicture}[ + thickline/.style=2pt, + bluethickline/.style={thickline,color=blue} +] +... +\end{tikzpicture} +\end{code} + +注意在样式中预定义长度单位有时会失效，所以最好使用绝对单位。 + +\subsection{流程图} +\subsubsection{节点} +PGF~中的节点（node）可以是简单的标签，也可以有各种形状的边框，还可以有各种复杂的属性。比如下例中的节点样式：\verb|box|，它的边框是矩形，有圆角；它有最小宽度、高度、文字和边框的距离，边框和填充颜色等属性。 + +\begin{code} +\tikzset{ + box/.style={rectangle, rounded corners=6pt, + minimum width=50pt, minimum height=20pt, inner sep=6pt, + draw=gray,thick, fill=lightgray} +} +\end{code} + +除了上述类别属性，节点还可以有名字、位置等属性。在下例中，我们先画了三个有名字的文本框；然后用箭头把文本框连接起来，注意连接时要引用文本框的名字；接着在箭头上加了标签。 +\begin{code} +\node[box] (tex) at(0,0) {.tex}; %文本框 +\node[box] (dvi) at(10,0) {.dvi}; %文本框 +\node[box] (pdf) at(20,0) {.pdf}; %文本框 +\draw[->] (tex)--(dvi); %箭头 +\draw[->] (dvi)--(pdf); %箭头 +\node at (5,1) {latex}; %标签 +\node at (15,1) {dvipdfmx}; %标签 +\end{code} + +\begin{out} +\begin{tikzpicture} +\node[box] (tex) at(0,0) {.tex}; +\node[box] (dvi) at(10,0) {.dvi}; +\node[box] (pdf) at(20,0) {.pdf}; +\draw[->] (tex)--(dvi); +\draw[->] (dvi)--(pdf); +\node at (5,1) {latex}; +\node at (15,1) {dvipdfmx}; +\end{tikzpicture} +\end{out} + +在上例中的节点都使用了绝对位置，PGF~中还可以使用更灵活一点的相对位置。比如在下例中，dvi~节点在~tex~节点右边~50pt~处（我们前面定义的基本长度单位是~10pt），而~pdf~节点又在~dvi~节点右边~50pt~处。 + +箭头可以换为专门用来连接节点的~\verb|edge|~；标签也改成相对位置，箭头上方~5pt~处。 +\begin{code} +\node[box] (tex) {.tex}; +\node[box,right=5 of tex] (dvi) {.dvi}; +\node[box,right=6 of dvi] (pdf) {.pdf}; +\path (tex) edge[->] node[above=.5] {latex} (dvi) + (dvi) edge[->] node[above=.5] {dvipdfmx} (pdf); +\end{code} + +\begin{out} +\begin{tikzpicture} +\node[box] (tex) {.tex}; +\node[box,right=5 of tex] (dvi) {.dvi}; +\node[box,right=6 of dvi] (pdf) {.pdf}; +\path (tex) edge[->] node[above=.5] {latex} (dvi) + (dvi) edge[->] node[above=.5] {dvipdfmx} (pdf); +\end{tikzpicture} +\end{out} + +\subsubsection{树} +下面是一棵简单的树。我们可以用一个参数控制相邻节点的距离，预定义长度单位对此参数也会失效。 +\begin{code} +\begin{tikzpicture}[sibling distance=80pt] +\node[box] {TeX} + child {node[box] {Plain\TeX}} + child {node[box] {\LaTeX} + child {node[box] {MiKTeX}} + child {node[box] {TeX Live}} + child {node[box] {MacTeX}} + }; +\end{tikzpicture} +\end{code} + +\begin{out} +\begin{tikzpicture}[sibling distance=80pt] +\node[box] {TeX} + child {node[box] {Plain\TeX}} + child {node[box] {\LaTeX} + child {node[box] {MiKTeX}} + child {node[box] {TeX Live}} + child {node[box] {MacTeX}} + }; +\end{tikzpicture} +\end{out} + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/i18n.tex b/Master/texmf-doc/doc/chinese/lnotes/src/i18n.tex new file mode 100644 index 00000000000..bdc974649f3 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/i18n.tex @@ -0,0 +1,73 @@ +\chapter{中文} + +\section{字符集和编码} +\label{sec:encoding} + +众所周知电脑内部采用二进制编码，因为它易于用电子电路实现。所有字符（包括字母、数字、符号、控制码等）在电脑内部都是用二进制表示的，字符集（Character Set）的二进制编码被称为字符编码（Character Encoding），有时人们也会混用这两个术语。 + +1963~年发布的~American Standard Code for Information Interchange（~ASCII）是最早出现的字符编码，它用~7~位（bit）表示了~$2^7=128$个字符，只能勉强覆盖英文字符。 + +美国人发明了电脑，英语被优先考虑是很自然的事情。随着电脑技术的传播，人们呼吁把字符编码扩充到~8~位也就是一个字节（byte），于是国际标准化组织（International Organization for Standardization，ISO）推出了~ISO 8859。$2^8=256$个字符显然也不能满足需要，所以~8859~被分为十几个部分，从~8859-1（西欧语言）、8859-2（中欧语言），直到~8859-16（东南欧语言），覆盖了大部分使用拉丁字母的语言文字。 + +在~ISO~标准完全定型之前，IBM~就有一系列自己的字符编码，他们称之为代码页（Code Page），其中著名的有~1981~年就被用于~IBM PC~的~437（扩展~ASCII）、850（西欧语言）、852（东欧语言）。IBM~代码页通常被用于控制台（Console）环境，也就是~MS-DOS~或~Unix Shell~那样的命令行环境。 + +微软将~IBM~代码页称为~OEM~代码页，自己定义的称为~ANSI~代码页，后者中著名的有1252（西欧语言）、1250（东欧语言）、936（GBK~简体中文）、950（Big5~繁体中文）、932（SJIS~日文）、949（EUC-KR~韩文）等。 + +1981~年，中国大陆推出了第一个自己的字符集标准~GB2312，它是一个~$94*94$~的表，包括~7445~个字符（含~6763~个汉字）。GB2312~通常采用双字节的EUC-CN编码，所以后者也常常被称为~GB2312~编码；其实~GB2312~还有另一种编码方式~HZ，只是不常用。GB2312~不包含朱镕基的“镕”字，政府、新闻、出版、印刷等行业和部门在使用中感到十分不便，于是它在~1993~年被扩展为~GBK，后者包括~21886~个字符（含~21003~个汉字），没有形成正式标准。2000~年发布的~GB18030~包含~70244~个字符（含~27533~个汉字），采用四字节编码。GB18030~之前还出现过一个~GB13000，没有形成气候。 + +1990~年ISO~推出了通用字符集（Universal Character Set，UCS），即~ISO 10646，意图一统江湖。它有两种编码：双字节的~UCS-2~和四字节的~UCS-4。 + +ISO~之外还有个希望一统江湖的组织：统一码联盟（The Unicode Consortium），它于~1991~年推出了~Unicode 1.0。后来两家组织意识到没必要做重复工作，于是开始合并双方的成果，携手奔小康。从~Unicode 2.0~开始，Unicode~采用了与~ISO 10646-1~相同的编码。 + +Unicode~主要有三种编码：UTF-8、UTF-16、UTF-32。UTF-8~使用一至四个~8~位编码。互联网工程任务组（Internet Engineering Task Force，~IETF）要求所有网络协议都支持~UTF-8，互联网电子邮件联盟（Internet Mail Consortium，IMC）也建议所有电子邮件软件都支持~UTF-8，所以它已成为互联网上的事实标准。UTF-16~用一或两个~16~位编码，基本上是~UCS-2~的超集，和~ASCII~不兼容。UTF-32~用一个~32~位编码，它是~UCS-4~的一个子集。 + +\section{中文解决方案} +\TeX~是基于单字节编码的，因为~Knuth~当初开发~\TeX~时没考虑那么远，也没有现成的标准可以借鉴。 + +\LaTeX~对中文的支持主要有两种方法：张林波\footnote{中科院计算数学所某实验室主任。}开发的~\href{ftp://ftp.cc.ac.cn/pub/cct/}{CCT}~和~Werner Lemberg\footnote{1968~年生于奥地利，从维也纳音乐学院获得作曲、指挥、钢琴、乐团管理、歌手教练等五个专业文凭，后自学中文和数学。曾任职于奥地利和德国多家剧院和乐团，现任德国科布伦茨某剧院指挥。}开发的~CJK~宏包。早期~CCT~比较流行，新的~CCT~也可以和~CJK~配合使用，网上可以找到的最后更新是~2003~年的。CJK~是当前主流，它不仅支持中日韩等东亚文字，还支持几十种其他不同语言的多种编码。 + +支持简体中文的~\LaTeX~发行版有吴凌云\footnote{中科院应用数学所研究员。}的~CTeX~和李树钧\footnote{德国哈根函授大学研究员。}的~ChinaTeX，繁体中文的有吴聪敏\footnote{台湾大学电机系学士，美国罗彻斯特大学经济学博士，现任台湾大学经济系教授。}、吴聪慧兄弟的~cwTeX~和蔡奇伟\footnote{美国犹他大学计算机博士，现任台湾静宜大学资讯工程系教授。}的~PUTeX。后面两个台湾的发行版包老师不熟悉，前面两个大陆的发行版都包含~MikTeX、CCT、CJK、WinEdt~等。 + +\section{CJK的使用} +CJK~的作者写的使用说明比较凌乱和晦涩，读者可以参阅李果正的《我的CJK》\citep{Lee_2004a}。 + +CJK~有两个基本宏包：\verb|CJK|~和~\verb|CJKutf8|，后者面向~UTF-8~编码。CJK~环境的一般使用方法如下： + +\begin{code} +\usepackage{CJK(utf8)} +... +\begin{document} +\begin{CJK}{<encoding>}{<family>} +... +\end{CJK} +\end{document} +\end{code} + +简体中文常用编码是~GBK~和~UTF8~。family~是指宋体、楷体、隶书等，具体引用要看电脑上安装了什么字体。麻烦的是~GBK~和~UTF8~字体不通用，也就是说每种编码需要自己的字体。CJK~自带的~UTF8~简体字体有~gbsn（宋体）和~gkai（楷体）。CTeX~提供的~GBK~字体有~song（宋体）、fs（仿宋）、kai（楷体）、hei（黑体）、li（隶书）、~you（幼圆）等。 + +注意使用~\verb|CJKutf8|~宏包时，\verb|CJK|~环境的编码最好是~UTF8，否则可能遭遇不测。 + +下面是一个简单的~GBK~示例和一个~UTF8~示例，注意用编辑器保存时要选则相应的编码格式，比如前者用~ANSI，后者用~UTF-8。 +\begin{code} +\documentclass{article} +\usepackage{CJK} +\begin{document} +\begin{CJK}{GBK}{song} +这是一个CJK例子，使用了GBK编码和song字体。 +\end{CJK} +\end{document} +\end{code} + +\begin{code} +\documentclass{article} +\usepackage{CJKutf8} +\begin{document} +\begin{CJK}{UTF8}{gbsn} +这是一个CJK例子，使用了UTF-8编码和gbsn字体。 +\end{CJK} +\end{document} +\end{code} + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/introduction.tex b/Master/texmf-doc/doc/chinese/lnotes/src/introduction.tex new file mode 100644 index 00000000000..3a2aa35e00b --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/introduction.tex @@ -0,0 +1,111 @@ +\chapter{简介} + +\begin{quotation} +滚滚长江东逝水，浪花淘尽英雄。是非成败转头空。青山依旧在，几度夕阳红。 + +白发渔樵江渚上，惯看秋月春风。一壶浊酒喜相逢。古今多少事，都付笑谈中。 +\begin{flushright} +---~杨慎《临江仙》 +\end{flushright} +\end{quotation} + +\section{历史回顾} + +\LaTeX~是一种面向数学和其它科技文档的电子排版系统。一般人们提到的~\LaTeX~是一个总称，它包括~\TeX、\LaTeX、\AmS-\LaTeX~等\footnote{一般认为~\TeX~是一种引擎，\LaTeX~是一种格式，而~\AmS-\LaTeX~等是宏集。此处目的是简介，故不展开讨论。}。 + +\TeX~的开发始于~1977~年~5~月，Donald E. Knuth\footnote{斯坦福大学计算机系教授，已退休。}开发它的初衷是用于《The Art of Computer Programming》的排版。1962~年~Knuth~开始写一本关于编译器设计的书，原计划是~12~章的单行本。不久~Knuth~觉得此书涉及的领域应该扩大，于是越写越多，如滔滔江水连绵不绝，又如黄河泛滥一发不可收拾。1965~年完成的初稿居然有~3000~页，全是手写的！据出版商估计，这些手稿印刷出来需要~2000~页，出书的计划只好改为七卷，每卷一或两章。1976~年~Knuth~改写第二卷的第二版时，很郁闷地发现第一卷的铅版不见了，而当时电子排版刚刚兴起，质量还差强人意。于是~Knuth~仰天长啸：“我要扼住命运的咽喉”，决定自己开发一个全新的系统，这就是~\TeX。 + +1978~年~\TeX~第一版发布后好评如潮，Knuth~趁热打铁在~1982~年发布了第二版。人们现在使用的~\TeX~基本就是第二版，中间只有一些小的改进。1990~年~\TeX~ v3.0~发布后，Knuth~宣布除了修正~bug~外停止~\TeX~的开发，因为他要集中精力完成那本巨著的后几卷\footnote{已出版的前三卷是：《Fundamental Algorithms》、《Seminumerical Algorithms》、《Sorting and Searching》；第四卷《Combinatorial Algorithms》和第五卷《Syntactic Algorithms》正在写作中，预计~2015~年出版；第六卷《Theory of Context-free Languages》和第七卷《Compiler Techniques》尚未安排上工作日程。}。此后每发布一个修正版，版本号就增加一位小数，使得它趋近于$\pi$（目前是~3.141592）。Knuth~希望将来他离世时，\TeX~的版本号永远固定下来，从此人们不再改动他的代码。他开发的另一个软件~\MF~也作类似处理，它的版本号趋近于$e$，目前是~2.71828。 + +\TeX~是一种语言也是一个宏处理器，这使得它很好很强大，但是它同时又很繁琐，让人难以接近。因此~Knuth~提供了一个对~\TeX~进行了封装的宏集~Plain \TeX，里面有一些高级命令，有了它最终用户就无须直接面对枯燥无味的~\TeX。 + +然而~Plain \TeX~还是不够高级，所以~Leslie Lamport\footnote{现供职于微软研究院。}在~80~年代初期开发了另一个基于~\TeX~的宏集~\LaTeX。1992~年~\LaTeX~ v2.09~发布后，Lamport~退居二线，之后的开发活动由~Frank Mittelbach~领导的~The LaTeX Team~接管。此小组发布的最后版本是~1994~年的~\LaTeXe，他们同时还在进行~\LaTeX~3~的开发，只是正式版看起来遥遥无期。 + +起初，美国数学学会（American Mathematical Society，AMS）看着\TeX~是好的，就派~Michael Spivak~写了~\AmS-\TeX，这项基于~Plain \TeX~的开发活动进行了两年（1983--1985）。后来与时俱进的~AMS~又看着~\LaTeX~是好的，就想转移阵地，但是他们的字体遇到了麻烦。恰好~Mittelbach~和~Rainer Schöpf（后者也是~LaTeX Team~的成员）刚刚发布了~New Font Selection Scheme for \LaTeX（NFSS），AMS~看着还不错，就拜托他们把~AMSFonts加入~\LaTeX，继而在~1989~年请他们开发~\AmS-\LaTeX。\AmS-\LaTeX~发布于~1990~年，之后它被整合为~\AmS~宏包，像其它宏包一样可以直接运行于~\LaTeX。 + +\section{优点和缺点} +当前的文字处理系统大致可以分为两种：标记语言（Markup Language）式的，比如\LaTeX；所见即所得（WYSIWYG）式的，比如~MS Word\footnote{其实~Word~也有自己的标记语言域代码（field code），只是一般用户不了解。}。 + +一般而言，\LaTeX~相对于所见即所得系统有如下优点： +\begin{itemize} + \item 高质量\ 它制作的版面看起来更专业，数学公式尤其赏心悦目。 + \item 结构化\ 它的文档结构清晰。 + \item 批处理\ 它的源文件是文本文件，便于批处理，虽然解释（parse）源文件可能很费劲。 + \item 跨平台\ 它几乎可以运行于所有电脑硬件和操作系统平台。 + \item 免费\ 多数~\LaTeX~软件都是免费的，虽然也有一些商业软件。 +\end{itemize} + +相应地，\LaTeX~的工作流程、设计原则，资源的缺乏，以及开发人员的历史局限性等种种原因也导致了一些缺陷： +\begin{itemize} + \item 制作过程繁琐，有时需要反复编译，不能直接或实时看到结果。 + \item 宏包鱼龙混杂，水准参差不齐，风格不够统一。 + \item 排版风格比较统一，但因而缺乏灵活性。 + \item 用户支持不够好，文档不完善。 + \item 对国际语言和字体的支持很差。 +\end{itemize} + +抛开~MS Word~不谈，即使跟同为标记语言的~HTML/Web~系统相比，\LaTeX~也有一些不足之处。比如~Web~浏览器对~HTML~内容的渲染（render）比~DVI~浏览器对~\LaTeX~内容的渲染要快上许多，基本上可以算是实时。虽然~HTML~内容可能没有~LaTeX~那么复杂，但是~DVI~毕竟是已经被~\LaTeX~编译过的格式。 + +还有一点令人困惑的是，有一部分~\LaTeX~阵营的人士习惯于称对方为“邪恶的”或“出卖灵魂的”，如果昂贵的微软系统应当为人诟病，那么更贵的苹果系统为何却被人追捧？ + +2000~年有记者在采访~Lamport~时问：“为什么当前没有高质量的所见即所得排版系统？”他回答道：“门槛太高了，一个所见即所得系统要做到~\LaTeX~当前的水平，工作量之大不是单枪匹马所能完成\footnote{\TeX/\LaTeX~也不单单是那几个大腕儿完成的，他们背后还有众多默默无闻的小人物，比如当年~Knuth~手下的大批学生。此所谓一将功成万骨枯。}。微软那样的大公司可以做，但是市场太小了。我偶尔也会想加入“Dark Side”，让微软给我一组人马来开发一个这样的系统。”（包老师注：他果然于次年加入微软。） + +窃以为这两大阵营其实是萝卜青菜的关系，与其抱残守缺、互相攻讦，不如各取所需；甚至可以捐弃前嫌、取长补短，共建和谐社会。 + +\section{软件准备} +\label{sec:latexsoft} + +\LaTeX~是一个软件系统，同时也是一套标准。遵照这些标准，实现了（implement）所要求功能的软件集合被称为发行版（distribution）。与此类似的例子有~Java~和~Linux，比如SUN、IBM、BEA~等公司都有自己的~Java~虚拟机（JVM），它们都被称作~Java~的实现；而Linux~有~Red Hat/~Fedora、Ubuntu、SuSE~等众多的发行版。 + +\begin{table}[htbp] +\caption{\LaTeX~发行版与编辑器} +\label{tab:latexsoft} +\centering +\begin{tabular}{lll} + \toprule + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & \href{http://www.miktex.org/}{MikTeX} & \href{http://www.toolscenter.org/}{TeXnicCenter}、\href{http://www.winedt.com/}{WinEdt} \\ + Unix/Linux & \href{http://www.tug.org/texlive/}{TeX Live} & \href{http://www.gnu.org/software/emacs/emacs.html}{Emacs}、\href{http://vim.sourceforge.net/}{vim}、\href{http://kile.sourceforge.net/}{Kile} \\ + Mac OS & \href{http://www.tug.org/mactex/}{MacTeX} & \href{http://www.uoregon.edu/~koch/texshop/}{TeXShop} \\ + \bottomrule +\end{tabular} +\end{table} + +\LaTeX~发行版只提供了一个~\LaTeX~后台处理机制，用户还需要一个前台编辑器来编辑它的源文件。常用的~\LaTeX~发行版和编辑器见\fref{tab:latexsoft}。在使用~\LaTeX~的过程中可能还需要其它一些软件，将在后面相关章节中分别介绍。 + +\section{学习方法} +\begin{quotation} +在科学上没有平坦的大道，只有那些不畏劳苦沿着陡峭山路攀登的人，才有希望达到光辉的顶点。 +\begin{flushright} +---~卡尔·马克思 +\end{flushright} +\end{quotation} + +\begin{quotation} +无他，唯手熟尔。 +\begin{flushright} +---~卖油翁 +\end{flushright} +\end{quotation} + +\begin{quotation} +用心。 +\begin{flushright} +---~斯蒂芬·周 +\end{flushright} +\end{quotation} + +限于篇幅和水平，本文只能提供一个概览外加一些八卦。比较严谨的入门资料有~Tobias Oetiker~的《A (Not So) Short Introduction to \LaTeXe》\citep{Oetiker_2008}（简称lshort）；若想对~\LaTeX~有更深入全面的了解，可以拜读~Mittelbach~的《The \LaTeX~ Companion》\citep{Mittelbach_2004}。 + +中文资料可参考李果正的《大家来学~\LaTeX》\citep{Lee_2004}，lshort~有吴凌云等人翻译的中文版本\footnote{此译本首发于~CTeX~论坛，但是需要注册才能看见链接，所以请读者自行搜索。}。 + +\href{http://www.ctan.org/}{Comprehensive TeX Archive Network}（CTAN）和~\href{http://www.tug.org/}{TeX Users Group}~（TUG）提供了权威、丰富的资源。 + +\href{http://www.text.ac.uk/}{英国TUG}~和~\href{http://www.ctex.org}{CTeX}~分别提供了常见问题集（FAQ）\citep{UKTUG_FAQ,CTeX_FAQ}，一般问题多会在这里找到答案。 + +中文~\TeX~论坛有\href{http://www.smth.org/bbsdoc.php?board=TeX}{水木清华~BBS TeX~版}、\href{http://bbs.ctex.org/}{CTeX~论坛}。 + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/lnotes.tex b/Master/texmf-doc/doc/chinese/lnotes/src/lnotes.tex new file mode 100644 index 00000000000..9dcf5446669 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/lnotes.tex @@ -0,0 +1,296 @@ +\documentclass[11pt]{book} + +%\usepackage{lnote} + +\usepackage{CJKutf8,CJKnumb} +%\usepackage{CJKpunct} %a homemade package + +\usepackage{fancyhdr} +\usepackage{titlesec} + +\usepackage{indentfirst} +\usepackage{paralist} +\usepackage{verbatim} + +\usepackage[plain]{fancyref} +\usepackage[bookmarksnumbered,dvipdfmx,unicode, pdfborder=1,breaklinks,colorlinks,linkcolor=RoyalBlue3,urlcolor=blue]{hyperref} +\usepackage{makeidx} + +\usepackage{mflogo,texnames} +\usepackage{textcomp} + +\usepackage{amsmath,amsfonts,amsthm} + +\usepackage[x11names]{xcolor} %must before tikz, x11names defines RoyalBlue3 +\usepackage{graphicx} +%\usepackage{ps4pdf} %conflict with tabularx +\usepackage{pstricks,pst-plot,pst-eps} +\usepackage{subfig} +\def\pgfsysdriver{pgfsys-dvipdfmx.def} %put before tikz +\usepackage{tikz} + +\usepackage{booktabs,tabularx,multirow,colortbl,longtable} + +\usepackage{chapterbib} +\usepackage[sectionbib,super,square,sort&compress]{natbib} + + +%中文设置 +\newcommand{\song}{\CJKfamily{usong}} +\newcommand{\fang}{\CJKfamily{ufang}} +\newcommand{\kai}{\CJKfamily{ukai}} +\newcommand{\hei}{\CJKfamily{uhei}} + +%\AtBeginDvi{\special{pdf:tounicode GBK-EUC-UCS2}} %not necessary if use UTF8. + +%行距 +\renewcommand{\baselinestretch}{1.25} + +%页眉页脚 +\pagestyle{fancy} +\fancyhf{} +\fancyhead[LE,RO]{\thepage} +\fancyhead[RE]{\leftmark} +\fancyhead[LO]{\rightmark} +\fancypagestyle{plain}{%设置plain页格式 + \fancyhf{} + \renewcommand{\headrulewidth}{0pt} +} + +%章节 +\renewcommand{\chaptername}{第\CJKnumber{\thechapter}章} +\newcommand{\sectionname}{节} +\renewcommand{\figurename}{图} +\renewcommand{\tablename}{表} +\renewcommand{\bibname}{参考文献} +\renewcommand{\contentsname}{目~录} +\renewcommand{\listfigurename}{图~目~录} +\renewcommand{\listtablename}{表~目~录} +\renewcommand{\indexname}{索~引} +\titleformat{\chapter}[block]{\center\Huge}{\chaptername}{20pt}{} + +\makeindex + +%空白页 +\makeatletter +\def\cleardoublepage{ + \clearpage\if@twoside\ifodd\c@page\else + \hbox{} + \vspace*{\fill} + \begin{center} + 看什么看，没见过空白页？ + \end{center} + \vspace{\fill} + \thispagestyle{empty} + \newpage + \if@twocolumn\hbox{}\newpage\fi\fi\fi +} +\makeatother + +%Code demo +\makeatletter +\newenvironment{mycode}{ + \noindent + \newsavebox{\mybox} + \begin{lrbox}{\mybox} + \begin{minipage}[c]{.945\textwidth} + \begin{verbatim} +}{ + \end{verbatim} + \end{minipage} + \end{lrbox}% + \setlength{\fboxsep}{8pt} + \colorbox{demo@bgcolor}{\usebox{\mybox}} + \setlength{\fboxsep}{\oldfboxsep} +} + +\newenvironment{myoutput}{ + \noindent + \begin{lrbox}{\@tempboxa} + \begin{minipage}[c]{.945\textwidth} +}{ + \end{minipage} + \end{lrbox}% + \setlength{\fboxsep}{8pt} + \fbox{\usebox{\@tempboxa}} + \setlength{\fboxsep}{\oldfboxsep} +} +\makeatother + + +\definecolor{demo@bgcolor}{gray}{.8} +\let\oldfboxsep\fboxsep +\newwrite\file +\newsavebox{\mybox} + +\makeatletter +\def\demo@start{ + \begingroup% Lets Keep the Changes Local + \@bsphack + \immediate\openout \file \jobname.exa + \let\do\@makeother\dospecials + \catcode`\^^M\active + \def\verbatim@processline{ + \immediate\write\file{\the\verbatim@line} + } + \verbatim@start +} + +\def\demo@end{\immediate\closeout\file\@esphack\endgroup} + +\def\demo@code#1#2{% + \setlength{\fboxsep}{8pt}% + \colorbox{#1}{% + \begin{minipage}[c]{#2} + \setlength{\fboxsep}{\oldfboxsep} + \small\verbatiminput{\jobname.exa} + \end{minipage}% + }% +} + +\def\demo@out#1{% + \setlength{\fboxsep}{8pt}% + \fbox{% + \begin{minipage}[c]{#1} + \setlength{\fboxsep}{\oldfboxsep} + \small\input{\jobname.exa} + \end{minipage}% + }% +} + +\newenvironment{code}{ + \demo@start +}{ + \demo@end + \list{}{\itemindent-\leftmargin} + \item + \demo@code{demo@bgcolor}{.95\textwidth} + \endlist +} + +\newenvironment{halfcode}{ + \demo@start +}{ + \demo@end + \list{}{\itemindent-\leftmargin} + \item + \demo@code{demo@bgcolor}{.52\textwidth} + \endlist +} + +\newenvironment{out}{ + \demo@start +}{ + \demo@end + \list{}{\itemindent-\leftmargin} + \item + \demo@out{.95\textwidth} + \endlist +} + +\newenvironment{demo}{ + \demo@start +}{ + \demo@end + \list{}{\itemindent-\leftmargin} + \item + \makebox[\textwidth][c]{% + \demo@code{demo@bgcolor}{.52\textwidth}% + \hspace{10pt}% + \demo@out{.36\textwidth}% + } + \endlist +} + +\newenvironment{fdemo}[1]{ + \begin{lrbox}{\mybox}% + \setlength{\fboxsep}{8pt}% + \fbox{% + \begin{minipage}[c]{.36\textwidth} + \setlength{\fboxsep}{\oldfboxsep} + \small{#1} + \end{minipage}% + }% + \end{lrbox} + \demo@start +}{ + \demo@end + \list{}{\itemindent-\leftmargin} + \item + \makebox[\textwidth][c]{% + \demo@code{demo@bgcolor}{0.52\textwidth}% + \hspace{10pt}% + \usebox{\mybox}% + } + \endlist +} +\makeatother + +\def\reflect#1{{\setbox0=\hbox{#1}\rlap{\kern0.5\wd0 + \special{x:gsave}\special{x:scale -1 1}}\box0 \special{x:grestore}}} +\def\XeTeX{\leavevmode + \setbox0=\hbox{X\lower.5ex\hbox{\kern-.15em\reflect{E}}\kern-.1667em \TeX}% + \dp0=0pt\ht0=0pt\box0 } + +%图形设置 +\DeclareGraphicsExtensions{.eps,.mps,.pdf,.jpg,.png} + +\usetikzlibrary{arrows,decorations,positioning} +\pgfsetxvec{\pgfpoint{10pt}{0}} +\pgfsetyvec{\pgfpoint{0}{10pt}} +\tikzset{ + box/.style={rectangle,rounded corners=6pt, + minimum width=40pt, minimum height=20pt, inner sep=6pt, + draw=gray,thick,fill=lightgray}, + arrow/.style={->, shorten >=1pt, >=stealth', semithick}, + larrow/.style={->, shorten >=1pt, >=stealth', semithick}, + bloop/.style={semithick, to path={-- ++(0,-35pt) -| (\tikztotarget)}}, + rloop/.style={semithick, to path={-- ++(10pt,0) |- (\tikztotarget)}} +} + +\begin{document} +\begin{CJK*}{UTF8}{usong} +\CJKindent %can only be used in the CJK environment +\CJKtilde + +\frontmatter + +\title{\Huge\LaTeX~ Notes v~1.17} +\author{Alpha Huang\footnote{\url{http://www.dralpha.com/}}} +\date{2008年6月2日} +\maketitle + + +%\setcitestyle{numbers,square} + +%前言页眉 +\renewcommand{\chaptermark}[1]{\markboth{#1}{}} + +\include{preface} +\tableofcontents + +\mainmatter +%正文页眉 +\renewcommand{\chaptermark}[1]{\markboth{\chaptername\ #1}{}} +\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}} + +\include{introduction} +\include{basics} +\include{math} +\include{graphics} +\include{tables} +\include{misc} +\include{i18n} +\include{fonts} + +\backmatter +\include{postcript} + +%chapter*{索引} +%\printindex + +\newpage + +\end{CJK*} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/math.tex b/Master/texmf-doc/doc/chinese/lnotes/src/math.tex new file mode 100644 index 00000000000..aa28fede957 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/math.tex @@ -0,0 +1,350 @@ +\chapter{数学} + +\begin{quotation} +今有上禾三秉，中禾二秉，下禾一秉，实三十九斗；上禾二秉，中禾三秉，下禾一秉，实三十四斗；上禾一秉，中禾二秉，下禾三秉，实二十六斗。问上、中、下禾实一秉各几何？ +\begin{gather*} +\begin{split} + 3x+2y+z &= 39 \\ + 2x+3y+z &= 34 \\ + x+2y+3z &= 26 \\ +\end{split} +\end{gather*} +\begin{flushright} +--- 《九章算术》 +\end{flushright} +\end{quotation} + +%\begin{quotation} +%邺下谚曰：博士买驴，书券三纸，未有驴字。 +%\begin{flushright} +%--- 颜之推《颜氏家训·勉学》 +%\end{flushright} +%\end{quotation} + +为了使用~\AmS-\LaTeX~提供的数学功能，我们首先需要在文档的序言部分加载~\verb|amsmath|~宏包，其详细用法可参阅《amsmath User's Guide》\citep{AMS_2002}。更全面的数学内容排版可参阅~George Grätzer\footnote{匈牙利裔，加拿大~Manitoba~大学数学系教授。}的《More Math into \LaTeX, 4th Edition》\citep{Gratzer_2007}。 +%\begin{code} +%\usepackage[options]{amsmath} +%\end{code} + +\section{数学模式} +\LaTeX~中的数学模式有两种形式：inline~和~display。前者是指在正文插入行间数学公式，后者独立排列，可以有或没有编号。 + +行间公式用一对~\verb|$...$|~来输入，独立公式用~\verb|equation|~或~\verb|equation*|~环境来输入，有~\verb|*|~的版本不生成公式编号。 + +前文提到~\verb|\fbox|~命令可以给文本内容加个方框，数学模式下也有类似的命令~\verb|\boxed|。 + +\begin{demo} +爱因斯坦的$E=mc^2$方程 +\begin{equation} + E=mc^2 +\end{equation} +\[ E=mc^2 \] +\[ \boxed{E=mc^2} \] +\end{demo} + +\section{基本原素} +\subsection{字母} + +英文字母在数学模式下可以直接输入，希腊字母则需要用\Fref{tab:greek}~中的命令输入，注意大写希腊字母的命令首字母也是大写。 + +\begin{table}[htbp] +\caption{希腊字母} +\label{tab:greek} +\centering +\begin{tabular}{llllllll} + \toprule + $\alpha$ & \verb|\alpha| & $\theta$ & \verb|\theta| & + $o$ & \verb|o| & $\tau$ & \verb|\tau| \\ + $\beta$ & \verb|\beta| & $\vartheta$ & \verb|\vartheta| & + $\pi$ & \verb|\pi| & $\upsilon$ & \verb|\upsilon| \\ + $\gamma$ & \verb|\gamma| & $\iota$ & \verb|\iota| & + $\varpi$ & \verb|\varpi| & $\phi$ & \verb|\phi| \\ + $\delta$ & \verb|\delta| & $\kappa$ & \verb|\kappa| & + $\rho$ & \verb|\rho| & $\varphi$ & \verb|\varphi| \\ + $\epsilon$ & \verb|\epsilon| & $\lambda$ & \verb|\lambda| & + $\varrho$ & \verb|\varrho| & $\chi$ & \verb|\chi| \\ + $\varepsilon$ & \verb|\varepsilon| & $\mu$ & \verb|\mu| & + $\sigma$ & \verb|\sigma| & $\psi$ & \verb|\psi| \\ + $\zeta$ & \verb|\zeta| & $\nu$ & \verb|\nu| & + $\varsigma$ & \verb|\varsigma| & $\omega$ & \verb|\omega| \\ + $\eta$ & \verb|\eta| & $\xi$ & \verb|\xi| & + & & & \\ + $\Gamma$ & \verb|\Gamma| & $\Lambda$ & \verb|\Lambda| & + $\Sigma$ & \verb|\Sigma| & $\Psi$ & \verb|\Psi| \\ + $\Delta$ & \verb|\Delta| & $\Xi$ & \verb|\Xi| & + $\Upsilon$ & \verb|\Upsilon| & $\Omega$ & \verb|\Omega| \\ + $\Theta$ & \verb|\Theta| & $\Pi$ & \verb|\Pi| & + $\Phi$ & \verb|\Phi| & & \\ + \bottomrule +\end{tabular} +\end{table} + +\subsection{指数、下标、根号} +指数或上标用~\verb|^|~表示，下标用~\verb|_|~表示，根号用~\verb|\sqrt|~表示。上下标如果多于一个字母或符号，需要用一对~\verb|{}|~括起来。 +\begin{demo} +\[x_{ij}^2\quad \sqrt[2]{x}\] +\end{demo} + +\subsection{分数} +分数用~\verb|\frac|~命令表示，它会自动调整字号，比如在行间公式中小一点，在独立公式则大一点。\verb|\dfrac|~命令把分数的字号显式设置为独立公式中的大小，\verb|\tfrac|~命令则把字号设为行间公式中的大小。 +\begin{demo} +$\frac{1}{2} \dfrac{1}{2}$ +\[\frac{1}{2} \tfrac{1}{2}\] +\end{demo} + +\subsection{运算符} +有些小的运算符（operator）例如~\verb|+ - * /|~等可以直接输入，另一些则需要特殊命令。完整的数学符号参见~Scott Pakin~的《The Comprehensive \LaTeX~ Symbol List》\citep{Pakin_2008}。 +\begin{code} +\[\pm \times \div \cdot \cap \cup \geq \leq \neq \approx \equiv\] +\end{code} + +\begin{out} +\[\pm\quad \times\quad \div\quad \cdot\quad \cap\quad \cup\quad \geq\quad \leq\quad \neq\quad \approx\quad \equiv\] +\end{out} + +和、积、极限、积分等大运算符用~\verb|\sum \prod \lim \int|~等表示。它们的上下标在行间公式中被压缩，以适应行高。。 + +\begin{code} +$\sum_{i=1}^n i \prod_{i=1}^n \lim_{x\to0}x^2 \int_a^b x^2 dx\$ +\[\sum_{i=1}^n i \prod_{i=1}^n \lim_{x\to0}x^2 \int_a^b x^2 dx\] +\end{code} + +\begin{out} +$\sum_{i=1}^n i\quad \prod_{i=1}^n\ \lim_{x\to0}x^2\ \int_a^b x^2\mathrm{d}x$ +\[\sum_{i=1}^n i\quad \prod_{i=1}^n\ \lim_{x\to0}x^2\ \int_a^b x^2\mathrm{d}x\] +\end{out} + +多重积分如果用多个~\verb|\int|~来输入的话，积分号间距过宽。正确的方法是用~\verb|\iint \iiint \iiiint \idotsint|~等命令输入。从下例中可以看出两种方法的差异。 + +\begin{out} +\[\iint\quad \iiint\quad \iiiint\quad \idotsint\] +\[\int\int\quad \int\int\int\quad \int\int\int\int\quad \int\dots\int\] +\end{out} + +\subsection{分隔符} +各种括号用~\verb|() [] \{\} \langle\rangle|~等命令表示，注意花括号通常用来输入命令和环境的参数，所以在数学公式中它们前面要加~\verb|\|。因为~\LaTeX~中的~\verb+|和\|+~的应用过于随意，~amsamth~宏包推荐用~\verb|\lvert\rvert|~和~\verb|\lVert\rVert|~取而代之。 + +我们可以在上述分隔符前面加~\verb|\big \Big \bigg \Bigg|~等命令来调整大小。\LaTeX~原有的方法是在分隔符前面加~\verb|\left \right|~来自动调整大小，但是效果不佳，所以~amsmath~不推荐用这种方法。 + +\begin{out} +\[\Bigg(\bigg(\Big(\big((x+y)\big)\Big)\bigg)\Bigg)\quad +\Bigg[\bigg[\Big[\big[[x+y]\big]\Big]\bigg]\Bigg]\quad +\Bigg\{\bigg\{\Big\{\big\{\{x+y\}\big\}\Big\}\bigg\}\Bigg\}\] +\[\Bigg\langle\bigg\langle\Big\langle\big\langle\langle x+y \rangle\big\rangle\Big\rangle\bigg\rangle\Bigg\rangle\quad +\Bigg\lvert\bigg\lvert\Big\lvert\big\lvert\lvert x+y \rvert\big\rvert\Big\rvert\bigg\rvert\Bigg\rvert\quad +\Bigg\lVert\bigg\lVert\Big\lVert\big\lVert\lVert x+y \rVert\big\rVert\Big\rVert\bigg\rVert\Bigg\rVert\] +\end{out} + +\subsection{箭头} +\Fref{tab:arrow}~列出了部分箭头的输入方法。另外还有两个命令生成的箭头可以根据上下标自动调整长度。 + +\begin{table}[htbp] +\caption{箭头} +\label{tab:arrow} +\centering +\begin{tabular}{llll} + \toprule + $\leftarrow$ & \verb|\leftarrow| & $\longleftarrow$ & \verb|\longleftarrow| \\ + $\rightarrow$ & \verb|\rightarrow| & $\longrightarrow$ & \verb|\longrightarrow| \\ + $\leftrightarrow$ & \verb|\leftrightarrow| & $\longleftrightarrow$ & \verb|\longleftrightarrow| \\ + $\Leftarrow$ & \verb|\Leftarrow| & $\Longleftarrow$ & \verb|\Longleftarrow| \\ + $\Rightarrow$ & \verb|\Rightarrow| & $\Longrightarrow$ & \verb|\Longrightarrow| \\ + $\Leftrightarrow$ & \verb|\Leftrightarrow| & $\Longleftrightarrow$ & \verb|\Longleftrightarrow| \\ + \bottomrule +\end{tabular} +\end{table} + +\begin{demo} +\[\xleftarrow{x+y+z}\quad +\xrightarrow[x<y]{a*b*c}\] +\end{demo} + +\subsection{标注} +\Fref{tab:accent}~列出一些短的注音符号（accent），\Fref{tab:notation}~则列出一些长的标注符号。 + +\begin{table}[htbp] +\caption{数学注音符号} +\label{tab:accent} +\centering +\begin{tabular}{llllllll} + \toprule + $\acute{x}$ & \verb|\acute{x}| & $\tilde{x}$ & \verb|\tilde{x}| & $\mathring{x}$ & \verb|\mathring{x}| \\ + $\grave{x}$ & \verb|\grave{x}| & $\breve{x}$ & \verb|\breve{x}| & $\dot{x}$ & \verb|\dot{x}| \\ + $\bar{x}$ & \verb|\bar{x}| & $\check{x}$ & \verb|\check{x}| & $\ddot{x}$ & \verb|\ddot{x}| \\ + $\vec{x}$ & \verb|\vec{x}| & $\hat{x}$ & \verb|\hat{x}| & $\dddot{x}$ & \verb|\dddot{x}| \\ + \bottomrule +\end{tabular} +\end{table} + +\begin{table}[htbp] +\caption{长标注符号} +\label{tab:notation} +\centering +\begin{tabular}{llll} + \toprule + $\overline{xxx}$ & \verb|\overline{xxx}| & $\overleftrightarrow{xxx}$ & \verb|\overleftrightarrow{xxx}| \\ + $\underline{xxx}$ & \verb|\underline{xxx}| & $\underleftrightarrow{xxx}$ & \verb|\underleftrightarrow{xxx}| \\ + $\overleftarrow{xxx}$ & \verb|\overleftarrow{xxx}| & $\overbrace{xxx}$ & \verb|\overbrace{xxx}| \\ + $\underleftarrow{xxx}$ & \verb|\underleftarrow{xxx}| & $\underbrace{xxx}$ & \verb|\underbrace{xxx}| \\ + $\overrightarrow{xxx}$ & \verb|\overrightarrow{xxx}| & $\widetilde{xxx}$ & \verb|\widetilde{xxx}| \\ + $\underrightarrow{xxx}$ & \verb|\underrightarrow{xxx}| & $\widehat{xxx}$ & \verb|\widehat{xxx}| \\ + \bottomrule +\end{tabular} +\end{table} + +\subsection{省略号} +省略号用~\verb|\dots \cdots \vdots \ddots|~等命令表示，注意~\verb|\cdots|~和~\verb|\dots|~的差别。 +\begin{out} +\[\dots\quad \cdots\quad \vdots\quad \ddots\] +\end{out} + +\subsection{空白间距} +在数学模式中，我们可以用\Fref{tab:quad}中的命令生成不同的间距，注意负间距命令~\verb|\!|~可以用来减小间距。 + +\begin{table}[htbp] +\caption{空白间距} +\label{tab:quad} +\centering +\begin{tabular}{llll} + \toprule + \verb|\,| & 3/18 em & \verb|\quad| & 1 em \\ + \verb|\:| & 4/18 em & \verb|\qquad| & 2 em \\ + \verb|\;| & 5/18 em & \verb|\!| & -3/18 em \\ + \bottomrule +\end{tabular} +\end{table} + +\section{矩阵和行列式} +数学模式下可以用~\verb|array|~环境来生成行列表。参数~\verb|{ccc}|~用于设置每列的对齐方式，\verb|l、c、r|~分别表示左中右；\verb|\\|~和~\verb|&|~用来分隔行和列。 + +\begin{demo} +\[\begin{array}{ccc} +x_1 & x_2 & \dots \\ +x_3 & x_4 & \dots \\ +\vdots & \vdots & \ddots \\ +\end{array}\] +\end{demo} + +\verb|amsmath|~有几个类似的环境：\verb|pmatrix、bmatrix、Bmatrix、vmatrix|~和~ +\verb|Vmatrix|，它们和~\verb|array|~的主要区别是会在表两端加上~$()\; []\; \{\}\; ||\; \|\|$~等分隔符，其次这些环境没有列对齐方式参数。 + +行间公式可以用~\verb|smallmatrix|~环境来生成排列紧密的小矩阵。 + +\section{多行公式} +有时一个公式太长一行放不下，或几个公式需要写成一组，这时我们就要用到~\verb|amsmath|~提供的几个适合多行公式的环境。 + +\subsection{长公式} +对于多行不需要对齐的长公式，我们可以用~\verb|multiline|~环境。 +\begin{demo} +\begin{multline} +x=a+b+c+\\ +d+e+f+g +\end{multline} +\end{demo} + +需要对齐的长公式可以用~\verb|split|~环境，它本身不能单独使用，因此也称作次环境，必须包含在~\verb|equation|~或其它数学环境内。\verb|split|~环境用~\verb|\\|~和~\verb|&|~来分行和设置对齐位置。 +\begin{demo} +\[ \begin{split} +x=&a+b+c+\\ + &d+e+f+g +\end{split} \] +\end{demo} + +\subsection{公式组} +不需要对齐的公式组用~\verb|gather|环境，需要对齐的用~\verb|align|。 +\begin{demo} +\begin{gather} +a=b+c+d\\ +x=y+z +\end{gather} +\end{demo} + +\begin{demo} +\begin{align} +a&=b+c+d\\ +x&=y+z +\end{align} +\end{demo} + +\verb|multine、gather、align|~等环境都有带~\verb|*|~的版本，它们不生成公式编号。 + +有多种条件的公式组用~\verb|cases|~次环境。 +\begin{demo} +\[ y=\begin{cases} +-x & x<0\\ +x & x\geq0 +\end{cases} \] +\end{demo} + +\section{定理和证明} +\LaTeX~提供了一个~\verb|\newtheorem|~命令来定义定理之类的环境，其语法如下。 +\begin{code} +\newtheorem{环境名}[编号延续]{显示名}[编号层次] +\end{code} + +在下例中，我们定义了四个环境：定义、定理、引理和推论，它们都在一个~\verb|section|~内编号，而引理和推论会延续定理的编号。 +\begin{code} +\newtheorem{defination}{定义}[section] +\newtheorem{theorem}{定理}[section] +\newtheorem{lemma}[theorem]{引理} +\newtheorem{corollary}[theorem]{推论} +\end{code} + +\newtheorem{defination}{定义}[section] +\newtheorem{theorem}{定理}[section] +\newtheorem{lemma}[theorem]{引理} +\newtheorem{corollary}[theorem]{推论} + +定义了上述环境之后，我们就可以象下面这样使用它们。 +\begin{demo} +\begin{defination} +Java是一种跨平台的编程语言。 +\end{defination} +\end{demo} + +\begin{demo} +\begin{theorem} +咖啡因会使人的大脑兴奋。 +\end{theorem} +\end{demo} + +\begin{demo} +\begin{lemma} +茶和咖啡都会使人兴奋。 +\end{lemma} +\end{demo} + +\begin{demo} +\begin{corollary} +晚上喝咖啡会导致失眠。 +\end{corollary} +\end{demo} + +\verb|proof|环境可以用来输入下面这样的证明，它会在证明结尾输入一个~QED~符号\footnote{拉丁语~quod erat demonstrandum~的缩写。}。 + +\begin{demo} +\begin{proof}[命题``物质无限可分''的证明] +一尺之棰，日取其半，万世不竭。 +\end{proof} +\end{demo} + +\section{数学字体} +和文本模式类似，数学模式下可以用\Fref{tab:math_font}~中的命令选择不同字体，其中有些字体需要加载~\verb|amsfonts|~宏包。 + +\begin{table}[htbp] +\caption{数学字体} +\label{tab:math_font} +\centering +\begin{tabular}{ccccccc} + \toprule + 缺省 & \verb|\mathbf| & \verb|\mathit| & \verb|\mathsf| & + \verb|\mathcal| & \verb|\mathbb| \\ + XNZRC & $\mathbf{XNZRC}$ & $\mathit{XNZRC}$ & $\mathsf{XNZRC}$ & + $\mathcal{XNZRC}$ & $\mathbb{XNZRC}$ \\ + \bottomrule +\end{tabular} +\end{table} + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/misc.tex b/Master/texmf-doc/doc/chinese/lnotes/src/misc.tex new file mode 100644 index 00000000000..eed39c5f1a4 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/misc.tex @@ -0,0 +1,322 @@ +\chapter{杂项} + +\section{超链接} +\label{sec:hyperlink} + +\verb|hyperref|~宏包\citep{Rahtz_2006}提供了一些超链接功能。它给文档内部的交叉引用和参考文献自动加上了超链接，还提供了几个命令。 + +\verb|\hyperref|~命令对已经定义的label进行简单包装，加上文字描述。 + +\begin{code} +\usepackage{hyperref} +... +\label{sec:hyperlink} +... +例如\ref{sec:hyperlink}是编号形式的链接，而\hyperref[sec:hyperlink]{这个链接}是文字形式的链接，都指向本节开始。 +\end{code} + +\begin{out} +例如\ref{sec:hyperlink}是编号形式的超链接，而\hyperref[sec:hyperlink]{这个链接}则是文字形式，都指向本节开始。 +\end{out} + +\verb|\url|~和~\verb|\href|~命令可以用来定义外部链接，后者有文字描述。 + +\begin{code} +\url{http://www.dralpha.com/} +\href{http://www.dralpha.com/}{包老师的主页} +\end{code} + +\begin{out} +\url{http://www.dralpha.com/} + +\href{http://www.dralpha.com/}{包老师的主页} +\end{out} + +%hyperref选项 + +\section{长文档} +当文档很长时，我们可以把它分为多个文件，然后在主控文档的正文中引用它们。注意~\verb|\include|~命令会新起一页，如果不想要新页可以改用~\verb|\input|~命令。 +\begin{code} +%master.tex +\begin{document} +\include{chapter1.tex} +\include{chapter2.tex} +... +\end{document} +\end{code} + +当文档很长时，编译一遍也会很花时间，我们可以用~\verb|syntonly|~宏包。这样编译时就只检查语法，而不生成结果文件。 +\begin{code} +\usepackage{syntonly} +... +\syntaxonly +\end{code} + +\section{参考文献} +在文档中，我们经常要引用参考文献（bibliography）。\LaTeX~提供的~\verb|thebibliography|~环境和~\verb|\bibtem|~命令可以用来定义参考文献条目及其列表显示格式，\verb|cite|~命令用来在正文中引用参考文献条目。这种方法把内容和格式混在一起，用户需要为每个条目设置格式，很繁琐且易出错。 + +\subsection{BibTeX} +1985年，~Oren Patashnik\footnote{Wiki~上说他是~Knuth~的学生，我发现他不在~Knuth~的博士生列表上，而在姚期智的博士生列表上，也许他是~Knuth~的硕士生。}和~Lamport~开发了~\BibTeX\citep{Patashnik_1988}，其详细使用方法请参阅~Nicolas Markey~的《Tame the BeaST: The B to X of BibTeX》\citep{Markey_2005} + +\BibTeX~把参考文献的数据放在一个~\verb|.bib|~文件中，显示格式放在~\verb|.bst|~文件中。普通用户一般不需要改动~\verb|.bst|，只须维护~\verb|.bib|~数据库。 + +一个~\verb|.bib|~文件可以包含多个参考文献条目（entry），每个条目有类型、关键字，以及题目、作者、年份等字段。常用条目类型有~article、~book、conference、manual、misc、techreport~等。每种类型都有一些自己的规定字段和可选字段，字段之间用逗号分开。数据库中每个条目的关键字要保持唯一，因为引用时要用到它们。 + +下例显示了一个条目，它的类型是~\verb|manual|，关键字是~\verb|Markey_2005|。~\verb|.bib|~文件可以用普通文本编辑器来编辑，也可以用专门的文献管理软件来提高效率。包老师推荐~\href{http://jabref.sourceforge.net/}{JabRef}。 + +\begin{code} +@MANUAL{Markey_2005, + title = {Tame the BeaST: The B to X of BibTeX}, + author = {Nicolas Markey}, + year = {2005}, + url = {http://www.ctan.org/tex-archive/info/bibtex/ + tamethebeast/} +} +\end{code} + +有了数据库，我们可以象下面这样引用一个条目。 +\begin{demo} +请参阅\cite{Markey_2005}。 +\end{demo} + +前文中我们提到含有交叉引用的文档需要编译两遍。含有参考文献的文档更麻烦，它需要依次执行~\verb|latex、bibtex、latex、latex|~等四次编译操作。 + +\begin{enumerate} + \item 第一遍~\verb|latex|~只把条目的关键字写到中间文件~\verb|.aux|~中去。 + \item \verb|bibtex|~根据\verb|.aux、.bib、.bst|~生成一个~\verb|.bbl|~文件，即参考文献列表。它的内容就是~\verb|thebibliography|~环境和一些~\verb|\bibtem|~命令。 + \item 第二遍~\verb|latex|~把交叉引用写到~\verb|.aux|~中去。 + \item 第三遍~\verb|latex|~则在正文中正确地显示引用。 +\end{enumerate} + +\begin{figure}[htbp] +\centering +\begin{tikzpicture} + \node[box] (tex) {.tex}; + \node[box, right=4 of tex] (aux) {.aux}; + \node[box, right=6 of aux] (bbl) {.bbl}; + \node[box, above=1.5 of aux] (bib) {.bib}; + \node[box, below=1.5 of aux] (bst) {.bst}; + \path (tex) edge [arrow] node[auto] {latex} (aux) + (aux) edge [arrow] node[auto] {bibtex} (bbl) + (bib.east) edge [rloop] (bst); +\end{tikzpicture} +\caption{\BibTeX~的编译} +\label{fig:bibtex} +\end{figure} + +注意在长文档中使用参考文献时，应该用~\verb|latex|~编译主控文档，而用~\verb|bibtex|~编译子文档。 + +\begin{code} +latex master(.tex) +bibtex chapter1(.tex) +latex master(.tex) +latex master(.tex) +\end{code} + +\subsection{natbib} +参考文献的引用通常有两种样式：作者-年份和数字。\LaTeX~本身只支持数字样式，而~\verb|natbib|~宏包\citep{Daly_2007}则同时支持这两种样式。 + +使用~\verb|natbib|~宏包时，我们首先要引用宏包；其次设置文献列表样式和引用样式，每种列表样式都有自己的缺省引用样式，所以后者可选；然后指定参考文献数据库。 +\begin{code} +\usepackage{natbib} +... +\begin{document} +\bibliographystyle{plainnat} +\setcitestyle{square,aysep={},yysep={;}} +\bibliography{mybib.bib} +... +\end{document} +\end{code} + +\verb|natbib|~提供了三种列表样式：plainnat、abbrvnat、unsrtnat。前两种都是作者-年份样式，文献列表按作者-年份排序，后者会使用一些缩写（比如作者的~first name）；unsrtnat~是数字样式，文献列表按引用顺序排序。 + +\verb|\setcitestyle|~命令可以用来改变引用样式的设置，其选项见~\Fref{tab:citestyle}。 + +\begin{table}[htbp] +\caption{参考文献引用样式选项} +\label{tab:citestyle} +\centering +\begin{tabular}{ll} + \toprule + 引用模式 & authoryear、numbers、super \\ + 括号 & round、square、open={char},close={char} \\ + 引用条目分隔符 & 分号、逗号、citesep={char} \\ + 作者年份分隔符 & aysep={char} \\ + 共同作者年份分隔符 & yysep={char} \\ + 注解分隔符 & notesep={text} \\ + \bottomrule +\end{tabular} +\end{table} + +注意在长文档中，每个含参考文献的子文档都需要分别设置列表样式，并指定数据库。 + +\verb|natbib|~提供了多种引用命令，其中最基本的是~\verb|\citet|~和~\verb|\citep|~，它们在不同引用模式下效果不同。一般不推荐使用~\LaTeX~本身提供的~\verb|\cite|，因为它在作者-年份模式下和~\verb|\citet|~一样，在数字模式下和~\verb|\citep|~一样。 + +作者-年份模式下引用命令的效果如下。 +\setcitestyle{authoryear} +\begin{demo} +参阅\cite{Daly_2007}\\ +参阅\citet{Daly_2007}\\ +参阅\citep{Daly_2007} +\end{demo} + +数字模式下引用命令的效果如下。 +\setcitestyle{numbers} +\begin{demo} +参阅\cite{Daly_2007}\\ +参阅\citet{Daly_2007}\\ +参阅\citep{Daly_2007} +\end{demo} + +上标模式下引用命令的效果如下。 +\setcitestyle{super} +\begin{demo} +参阅\cite{Daly_2007}\\ +参阅\citet{Daly_2007}\\ +参阅\citep{Daly_2007} +\end{demo} + +另外还有一些引用命令，如~\verb|\citetext、\citenum、\citeauthor|、~\verb|\citeyear|~等，此处不赘述。 + +\section{索引} +\verb|makeidx|~宏包提供了索引功能。应用它时，我们首先需要在文档序言部分引用宏包，并使用~\verb|makeindex|~命令；其次在正文中需要索引的地方定义索引，注意索引关键字在全文中须保持唯一；最后在合适的地方（一般是文档末尾）打印索引。 + +\begin{code} +\usepackage{makeidx} +\makeindex +... +\begin{document} +\index{索引关键字} +... +\printindex +\end{document} +\end{code} + +当编译含索引的文档时，用户需要执行~\verb|latex、makeindex、latex|~等三次编译操作。 + +\begin{enumerate} + \item 第一遍~\verb|latex|~把索引条目写到一个~\verb|.idx|~文件中去。 + \item \verb|makeindex|~把~\verb|.idx|~排序后写到一个~\verb|.ind|~文件中去。 + \item 第二遍~\verb|latex|~在~\verb|\printindex|~命令的地方引用~\verb|.ind|~的内容，生成正确的DVI。 +\end{enumerate} + +\begin{figure}[htbp] +\centering +\begin{tikzpicture} + \node[box] (tex) {.tex}; + \node[box, right=4 of tex] (idx) {.idx}; + \node[box, right=7 of idx] (ind) {.ind}; + \node[box, right=6 of ind] (dvi) {.dvi}; + \node[box, above=1.5 of ind] (tex1) {.tex}; + \node[right=1 of ind] (point) {}; + \path (tex) edge [arrow] node[auto] {latex} (idx) + (idx) edge [arrow] node[auto] {makeindex} (ind) + (ind) edge [arrow] node[auto] {latex} (dvi) + (tex1.east) edge [rloop] (point); +\end{tikzpicture} +\caption{索引的编译} +\label{fig:makeidx} +\end{figure} + +\section{页面布局} +在~\LaTeX~中用户可以通过~\verb|\pagestyle|~和~\verb|\pagenumbering|~命令来设置页眉（header）、页脚（footer）的样式和内容。页面样式有以下四种。 + +\begin{table}[htbp] +\caption{\LaTeX~页面样式} +\centering +\begin{tabular}{ll} + \toprule + \texttt{empty} & 页眉、页脚空白 \\ + \texttt{plain} & 页眉空白，页脚含居中页码 \\ + \texttt{headings} & 页脚空白，页眉含章节名和页码 \\ + \texttt{myheadings} & 页脚空白，页眉含页码和用户自定义信息 \\ + \bottomrule +\end{tabular} +\end{table} + +\verb|fancyhdr|\citep{Oostrum_2004}宏包提供了更灵活的控制。我们可以用以下代码定制页眉、页脚的内容，以及页眉下方、页脚上方的横线。 + +\begin{code} +\usepackage{fancyhdr} +... +\pagestyle{fancy} %fancyhdr宏包新增的页面风格 +\lhead{左擎苍} +\chead{三个代表} +\rhead{右牵黄} +\lfoot{左青龙} +\cfoot{八荣八耻} +\rfoot{右白虎} +\renewcommand{\headrulewidth}{0.4pt} +\renewcommand{\footrulewidth}{0.4pt} +\end{code} + +\ \\ +\begin{tikzpicture} +\draw (0,0) rectangle (36,10); +\node at(2,9) {左擎苍}; +\node at(18,9) {三个代表}; +\node at(34,9) {右牵黄}; +\draw (.5,8)--(35.5,8); +\node at(18,5) {和谐社会}; +\draw (.5,2)--(35.5,2); +\node at(2,1) {左青龙}; +\node at(18,1) {八荣八耻}; +\node at(34,1) {右白虎}; +\end{tikzpicture} + +用户可以在页眉、页脚中使用一些~\LaTeX~变量，比如分别代表页码和章节编号的~\verb|\thepage、\thechapter、\thesection|；代表章节起始单词（Chapter、Section等）的~\verb|\chaptername、\sectionname|~等。 + +这些变量组合起来可以构成复合标记~\verb|\leftmark|~和~\verb|\rightmark|~。当文档奇偶页面布局不同时，我们可以使用以下方法为奇偶页分别设置页眉、页脚。\verb|fancyhdr|~宏包会自动把每章起始页的样式设为~\verb|plain|，若想去掉页脚中间的页码，可以重定义~\verb|plain|~样式。 + +\begin{code} +\pagestyle{fancy} +\fancyhf{} %清空页眉页脚 +\fancyhead[LE,RO]{\thepage} %偶数页左，奇数页右 +\fancyhead[RE]{\leftmark} %偶数页右 +\fancyhead[LO]{\rightmark} %奇数页左 +\fancypagestyle{plain}{ %重定义plain页面样式 + \fancyhf{} + \renewcommand{\headrulewidth}{0pt} +} +\end{code} + +\ \\ +\begin{tikzpicture} +\draw (0,0) rectangle (36,10); +\node at(2.5,9) {3.2 节名}; +\node at(35,9) {17}; +\draw (.5,8)--(35.5,8); +\node at(18,5) {奇数页}; +\end{tikzpicture} + +\ \\ +\begin{tikzpicture} +\draw (0,0) rectangle (36,10); +\node at(1,9) {18}; +\node at(32,9) {Chapter 3 章名}; +\draw (.5,8)--(35.5,8); +\node at(18,5) {偶数页}; +\end{tikzpicture} + +Lamport当初设计~\LaTeX~时把页面布局变量的定义方式搞得比较晦涩，用户在重定义~\verb|\leftmark|~和~\verb|\rightmark|~时，不能直接用~\verb|\renewcommand|~的方法，而要用另外两个命令。 + +\begin{code} +\markboth{main-mark}{sub-mark} +\markright{sub-mark} +\end{code} + +\verb|\leftmark|~即~main-mark，是一种高层次标记，在~article~文档类中它包含~section~的信息，在~report~和~book~则包含~chapter~的信息；\verb|rightmark|~则是一种低层次标记，在~article~中包含~subsection~信息，在~report~和~book~中包含~section~信息。 + +比如在~\verb|book|~文档类中，章节标记是通过下面的方法定义的，其中的~\verb|#1|~指的是章节的名字。 + +\begin{code} +\renewcommand\chaptermark[1]{\markboth{\chaptername \thechapter. + #1}{}} +\renewcommand\sectionmark[1]{\markright{\thesection. #1}} +\end{code} + +%\section{演示文档} + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/postcript.tex b/Master/texmf-doc/doc/chinese/lnotes/src/postcript.tex new file mode 100644 index 00000000000..0cbbe6a4727 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/postcript.tex @@ -0,0 +1,9 @@ +\chapter{跋}
+
+首先向一路披荆斩棘看到这里的读者表示祝贺，至少在精神上你已经成为一名合格的~\LaTeX{}er。从此你生是~\LaTeX~的人，死是~\LaTeX~的鬼。Once Black, never back。没有坚持到这里的同学自然已经重新投向“邪恶”的~MS Word，毕竟那里点个按钮就可以插入图形，点个下拉框就可以选择字体。
+
+当然~\LaTeX{}er也有简单的出路，就是只使用缺省设置，尽量少用插图；不必理会点阵、矢量，也不必理会~Type 1、Type 3、TrueType、OpenType。因为内容高于形式，你把文章的版面、字体搞得再漂亮，它也不会因此成为《红楼梦》；而《红楼梦》即使是手抄本，也依然是不朽的名著。
+
+包老师曾经以为~\LaTeX~和~Word~的关系就好像是《笑傲江湖》中华山的气宗和剑宗，头十年剑宗进步快，中间十年打个平手，再往后气宗就遥遥领先。至于令狐冲的无招胜有招，风清扬的神龙见首不见尾又是另一重境界，普通人恐怕只能望其颈背。
+
+费尽九牛二虎之力熬到本文杀青的时候，才发现从前的想法很傻很天真。让我们挥一挥衣袖，不带走一片云，卧薪尝胆忍辱负重，耐心等待~\XeTeX~和~Lua\TeX。
\ No newline at end of file diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/preface.tex b/Master/texmf-doc/doc/chinese/lnotes/src/preface.tex new file mode 100644 index 00000000000..b77fc449369 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/preface.tex @@ -0,0 +1,31 @@ +\chapter{序} + +\begin{quotation} +满纸荒唐言，一把辛酸泪！都云作者痴，谁解其中味？\footnote{当年作博士论文时虽不曾增删五次披阅十载，也被折磨得欲仙欲死，故与室友戏言将此五绝加入序言。多年以后的今天终于实现了此夙愿。} +\begin{flushright} +--- 曹雪芹 +\end{flushright} +\end{quotation} + +最早听说~\LaTeX~大约是~2002~年，一位同事演示了用它排版的一篇文章和几幅图。包老师\footnote{吾有多重人格，比如本色的是阿黄，下围棋的是隐忍灰衣人，道貌岸然的是包老师。}不以为然，因为那些东西用~Microsoft Word~和~Visio~也可以做到，而且可以做得更快。再次听说它是王垠同学在闹退学，传说他玩~Linux~和~\LaTeX~而走火入魔。 + +大约是~2005~年底，看了一下~lshort，用~\LaTeX~记了些数学笔记，开始有点感觉。包老师生性愚钝，所以喜欢相对简单的东西。HTML、Java~都用手写，FrontPage、Dreamweaver、JBuilder~之类笨重的家伙看两眼就扔了，所以喜欢上~\LaTeX~只是时间问题。 + +次年老妻要写博士论文，拿出~Word~底稿让我排版。大家都知道~Word~太简单了，谁都能用，但是不是谁都能用好。人称电脑杀手的老妻制作的~Word~文档自然使出了各种奇门遁甲，加上她实验室、学校和家里电脑里的三个~EndNote~版本互不兼容，实在难以驯服。我只好重起炉灶，拿她的博士论文当小白鼠，试验一下~\LaTeX~的威力。 + +就这样接触了两三年，总算略窥门径，感觉~\LaTeX~实在是博大精深，浩如烟海。而人到中年大脑储存空间和处理能力都有点捉襟见肘，故时常作些笔记。一来对常用资料和问题进行汇编索引，便于查询；二来也记录一些心得。 + +日前老妻吵着要学~\LaTeX，便想这份笔记对初学者或有些许借鉴意义，于是系统地整理了一番，添油加醋包装上市。 + +原本打算分九章，以纪念《九章算术》，实际上第八章完成时已如强弩之末，最后一章还须另择黄道吉日。 + +本文第一章谈谈历史背景；第二章介绍入门基础；第三至五章讲解数学、插图、表格等对象的用法；第六章是一些特殊功能；第七、八章讨论中文和字体的处理；第九章附加定制内容。 + +从难易程度上看前两章较简单，插图、字体两章较难。一般认为~\LaTeX~相对于微软的傻瓜型软件比较难学，所以这里采取循序渐进，温水煮青蛙的方法。 + +初则示弱，麻痹读者；再则巧言令色，请君入瓮；三则舌绽莲花，诱敌深入；彼入得罄中则摧动机关，关门打狗；继而严刑拷打，痛加折磨；待其意乱情迷彷徨无计之时，给予当头棒喝醍醐灌顶，虽戛然而止亦余音绕梁。 + +鄙人才疏学浅功力不逮，面对汗牛充栋罄竹难书\footnote{此处用法循阿扁古例。}的资料，未免考虑不周挂一漏万，或有误导，敬请海涵。若有高手高手高高手略拨闲暇指点一二，在下感激不尽\footnote{\href{mailto:huang.xingang@gmail.com}{huang.xingang@gmail.com}} +。 + +借此感谢一下老妻，如果不是伊天天看韩剧，包老师也不会有时间灌水和整理这份笔记。 diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/reading.bib b/Master/texmf-doc/doc/chinese/lnotes/src/reading.bib new file mode 100644 index 00000000000..9abb90c95b8 --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/reading.bib @@ -0,0 +1,914 @@ +% This file was created with JabRef 2.3.1. +% Encoding: UTF8 + +@MISC{CTeX_FAQ, + author = {中国TeX用户组}, + title = {{CTeX}常见问题集}, + year = {2005}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ctex.org/CTeXFAQ/} +} + +@MANUAL{Lee_2004, + title = {大家来学LaTeX}, + author = {李果正}, + year = {2004}, + owner = {Alpha}, + review = {good}, + timestamp = {2008.04.11}, + url = {http://edt1023.sayya.org/tex/latex123/} +} + +@MANUAL{Lee_2004a, + title = {我的CJK}, + author = {李果正}, + year = {2004}, + owner = {Alpha}, + timestamp = {2008.05.12}, + url = {http://edt1023.sayya.org/tex/mycjk/} +} + +@BOOK{Zhang_1997, + title = {数学的思想、方法和应用}, + publisher = {北京大学}, + year = {1997}, + author = {张顺燕}, + review = {good} +} + +@MANUAL{AMS_2002, + title = {amsmath User's Guide}, + author = {AMS}, + year = {2002}, + owner = {Alpha}, + review = {good}, + timestamp = {2008.04.01}, + url = {http://www.ams.org/tex/amslatex.html} +} + +@MANUAL{AMS_short_2002, + title = {Short Math Guide for LaTeX}, + author = {AMS}, + year = {2002}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ams.org/tex/amslatex.html} +} + +@BOOK{ATT_1989, + title = {Unix System V/386 Release 3.2: User's Guide}, + publisher = {Prentice Hall}, + year = {1989}, + author = {AT\&T}, + review = {common} +} + +@BOOK{Baker_1984, + title = {A Concise Introduction to the Theory of Numbers}, + publisher = {Cambridge University}, + year = {1984}, + author = {Alan Baker}, + owner = {Alpha}, + review = {hard}, + timestamp = {2007.06.05} +} + +@BOOK{Baker_1997, + title = {Practical Stylist with Readings and Handbook, 8th Edition}, + publisher = {Longman}, + year = {1997}, + author = {Sheridan Baker}, + owner = {Alpha}, + timestamp = {2008.05.20}, + url = {http://www.amazon.com/exec/obidos/tg/detail/-/0321011821/} +} + +@BOOK{Benz_2005, + title = {Morningstar Guide to Mutual Funds}, + publisher = {Wiley}, + year = {2005}, + author = {Christine Benz}, + owner = {Alpha}, + review = {common}, + timestamp = {2007.11.29} +} + +@BOOK{Black_2001, + title = {The Complete Photo Guide to Home Improvement}, + publisher = {Black \& Decker}, + year = {2001}, + editor = {Philip Schmidt}, + author = {Black}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.10.30} +} + +@BOOK{Brighton_2003, + title = {Introducing Artificial Intelligence}, + publisher = {Totem}, + year = {2003}, + author = {Brighton, Henry and Selina, Howard}, + review = {Good} +} + +@BOOK{Camerson_1998, + title = {Sets, Logic and Categories}, + publisher = {Springer}, + year = {1998}, + author = {Peter J. Camerson}, + owner = {Alpha}, + review = {common}, + timestamp = {2007.07.27} +} + +@BOOK{Campbell_2006, + title = {Zero to Zillionaire}, + publisher = {Sourcebooks}, + year = {2006}, + author = {Chellie Campbell}, + owner = {Alpha}, + review = {bad}, + timestamp = {2007.05.18} +} + +@MANUAL{Carlisle_2004, + title = {The longtable Package}, + author = {David Carlisle}, + year = {2004}, + owner = {Alpha}, + timestamp = {2008.05.13}, + url = {http://www.ctan.org/pkg/longtable} +} + +@MANUAL{Carlisle_2001, + title = {The colortbl Package}, + author = {David Carlisle}, + year = {2001}, + owner = {Alpha}, + timestamp = {2008.05.13}, + url = {http://tug.ctan.org/tex-archive/macros/latex/contrib/colortbl/} +} + +@BOOK{Castro_2006, + title = {HTML, XHTML, and CSS, 6th Edition}, + publisher = {Peachpit}, + year = {2006}, + author = {Elizabeth Castro}, + owner = {Alpha}, + review = {Good for beginners}, + timestamp = {2008.02.06} +} + +@MANUAL{Daly_2007, + title = {Natural Sciences Citations and References}, + author = {Patrick W. Daly}, + year = {2007}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.mps.mpg.de/software/latex/localtex/localltx.html} +} + +@BOOK{Ducharme_1994, + title = {The Operating Systems Handbook: Unix, Openvms, Os/400, Vm, and MVS}, + publisher = {McGraw-Hill}, + year = {1994}, + author = {Ducharme, Bob}, + review = {good} +} + +@BOOK{Dunphy_1991, + title = {The Unix Industry: Evolution, Concepts, Architecture, Applications, + and Standards}, + publisher = {QED}, + year = {1991}, + author = {Dunphy, Ed}, + review = {poor} +} + +@BOOK{Elmaghraby_1978, + title = {Activity Networks}, + publisher = {John Wiley \& Sons}, + year = {1978}, + author = {Elmaghraby, Salah Eldin}, + review = {good} +} + +@BOOK{Black_2005, + title = {Home Improvement 101}, + publisher = {Black \& Decker}, + year = {2005}, + author = {Jerri Farris and Thomas Lemmer}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.10.30} +} + +@MANUAL{Fear_2005, + title = {Publication Quality Tables in LaTeX}, + author = {Simon Fear}, + year = {2005}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ctan.org/tex-archive/macros/latex/contrib/booktabs/} +} + +@BOOK{Flanagan_2006, + title = {JavaScript: The Definitive Guide, 5th Edition}, + publisher = {O'Reilly}, + year = {2006}, + author = {David Flanagan}, + owner = {Alpha}, + review = {good but complex}, + timestamp = {2008.02.08} +} + +@BOOK{Gamow_1988, + title = {One Two Three... Infinity: Facts and Speculations of Science}, + publisher = {Dover}, + year = {1988}, + author = {Gamow, George}, + review = {good} +} + +@BOOK{Geisst_2000, + title = {100 Years of Wall Street}, + publisher = {McGraw-Hill}, + year = {2000}, + author = {Charles R. Geisst}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.30} +} + +@MISC{UKTUG_FAQ, + author = {UK TeX User Group}, + title = {{UK List of TeX Frequently Asked Questions}}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.tex.ac.uk/faq/} +} + +@BOOK{Gratzer_2007, + title = {More Math into LaTeX}, + publisher = {Springer}, + year = {2007}, + author = {George Grätzer}, + edition = {4th}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.amazon.com/exec/obidos/tg/detail/-/0387322892/} +} + +@BOOK{Mobil_2006, + title = {Mobil Travel Guide: Northern Plains 2007}, + publisher = {Mobil Travel Guide}, + year = {2006}, + author = {Mobil Travel Guide}, + owner = {Alpha}, + review = {common}, + timestamp = {2007.12.09} +} + +@BOOK{Gulbransen_2000, + title = {Complete Idiot's Guide to XML}, + publisher = {Alpha}, + year = {2000}, + author = {Gulbransen, David}, + review = {good} +} + +@BOOK{Hardy_1979, + title = {An Introduction to the Theory of Numbers}, + publisher = {Oxford University}, + year = {1979}, + author = {G.H. Hardy and E.M. Wright}, + owner = {Alpha}, + review = {hard}, + timestamp = {2007.06.05} +} + +@BOOK{Harrison_1997, + title = {A Survival Guide to Critical Path Analysis}, + publisher = {Butterworth-Heinemann}, + year = {1997}, + author = {Harrison, Andrew}, + review = {Simple but good} +} + +@BOOK{Higham_1998, + title = {Handbook of Writing for the Mathematical Sciences}, + publisher = {Society for Industrial and Applied Mathematics}, + year = {1998}, + author = {Nicholas J. Higham}, + owner = {Alpha}, + review = {great}, + timestamp = {2008.05.20}, + url = {http://www.siam.org/books/ot63/} +} + +@MANUAL{Hobby_2007, + title = {MetaPost: A User's Manual}, + author = {John D. Hobby}, + year = {2007}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ctan.org/tex-archive/graphics/metapost/} +} + +@BOOK{Johnson_1998, + title = {Elements of Logic via Numbers and Sets}, + publisher = {Springer}, + year = {1998}, + author = {D.L. Johnson}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.07.27} +} + +@BOOK{Jones_2007, + title = {Elementary Number Theory}, + publisher = {Springer}, + year = {1998}, + author = {Gareth A. Jones and J. Mary Jones}, + owner = {Alpha}, + review = {good, detailed}, + timestamp = {2007.07.17} +} + +@BOOK{Kennedy_2007, + title = {Resumes for Dummies}, + publisher = {Wiley}, + year = {2007}, + author = {Joyce Lain Kennedy}, + owner = {Alpha}, + review = {common}, + timestamp = {2008.02.06} +} + +@MANUAL{Kern_2007, + title = {Extending LaTeX's Color Facilities: The xcolor Package}, + author = {Uwe Kern}, + organization = {CTAN}, + year = {2007}, + owner = {Alpha}, + timestamp = {2008.04.30}, + url = {http://www.ukern.de/tex/xcolor.html} +} + +@BOOK{Kidd_1994, + title = {Agile Manufacturing: Forging New Frontiers}, + publisher = {Pearson Education}, + year = {1994}, + author = {Kidd, Paul T.} +} + +@BOOK{Kline_1990, + title = {Mathematical Thought from Ancient to Modern Times}, + publisher = {Oxford University}, + year = {1990}, + author = {Kline, Morris}, + review = {good but too long. 2004/09/20} +} + +@MANUAL{Markey_2005, + title = {Tame the BeaST: The B to X of BibTeX}, + author = {Nicolas Markey}, + organization = {CTAN}, + year = {2005}, + owner = {Alpha}, + timestamp = {2008.05.07}, + url = {http://www.ctan.org/tex-archive/info/bibtex/tamethebeast/} +} + +@BOOK{Meyer_2001, + title = {Matrix Analysis and Applied Linear Algebra}, + publisher = {Society for Industrial and Applied Mathematics}, + year = {2001}, + author = {Carl D. Meyer}, + owner = {Alpha}, + review = {great}, + timestamp = {2008.05.21}, + url = {http://www.matrixanalysis.com/} +} + +@BOOK{Miller_2005, + title = {Furniture: World Styles From Classical to Contemporary}, + publisher = {DK Adult}, + year = {2005}, + author = {Judith Miller}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.11.29} +} + +@BOOK{Better_2004, + title = {Decks Step-by-Step}, + publisher = {Better Homes \& Gardens}, + year = {2004}, + author = {Martin Miller}, + owner = {Alpha}, + timestamp = {2007.10.30} +} + +@BOOK{Mitchell_2003, + title = {Trees of North America}, + publisher = {Thunder Bay}, + year = {2003}, + author = {Alan Mitchell and David More}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.12.09} +} + +@BOOK{Mittelbach_2004, + title = {The LaTeX Companion (Tools and Techniques for Computer Typesetting)}, + publisher = {Addison-Wesley}, + year = {2004}, + author = {Frank Mittelbach and Michel Goossens and Johannes Braams and David + Carlisle and Chris Rowley}, + edition = {2nd}, + owner = {Alpha}, + review = {good}, + timestamp = {2008.04.01}, + url = {http://www.amazon.com/exec/obidos/tg/detail/-/0201362996/} +} + +@BOOK{Moder_1995, + title = {Project Management with CPM, Pert \& Precedence Diagramming}, + publisher = {Blitz}, + year = {1995}, + author = {Moder, Joseph J. and Phillips, Cecil R. and Davis, Edward W.}, + review = {good} +} + +@BOOK{Morley_1999, + title = {The History of Furniture}, + publisher = {Bulfinch}, + year = {1999}, + author = {John Morley}, + owner = {Alpha}, + review = {common}, + timestamp = {2007.11.29} +} + +@BOOK{Nisenfeld_1989, + title = {Artificial Intelligence Handbook: Applications}, + publisher = {Instrumentation Systems}, + year = {1989}, + author = {Nisenfeld, A. Eli} +} + +@MANUAL{Oetiker_2008, + title = {A (Not So) Short Introduction to LaTeX2e}, + author = {Tobias Oetiker}, + year = {2008}, + owner = {Alpha}, + review = {good}, + timestamp = {2008.04.01}, + url = {http://www.ctan.org/tex-archive/info/lshort/english/} +} + +@MANUAL{Oostrum_2004, + title = {Page Layout in LaTeX}, + author = {Piet van Oostrum}, + year = {2004}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://tug.ctan.org/tex-archive/macros/latex/contrib/fancyhdr/} +} + +@BOOK{Ore_1967, + title = {Invitation to Number Theory}, + publisher = {Mathematical Association of America}, + year = {1967}, + author = {Oystein Ore}, + owner = {Alpha}, + review = {good, fun}, + timestamp = {2007.07.11} +} + +@MANUAL{Pakin_2008, + title = {The Comprehensive LaTeX Symbol List}, + author = {Scott Pakin}, + year = {2008}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ctan.org/tex-archive/info/symbols/comprehensive/} +} + +@MANUAL{Patashnik_1988, + title = {BibTeXing}, + author = {Oren Patashnik}, + year = {1988}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/} +} + +@BOOK{Pogue_1997, + title = {Classical Music for Dummies}, + publisher = {Hungry Minds}, + year = {1997}, + author = {David Pogue and Scott Speck}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.12.09} +} + +@MANUAL{Rahtz_2006, + title = {Hypertext Marks in LaTeX: A Manual for hyperref}, + author = {Sebastian Rahtz and Heiko Oberdiek}, + year = {2006}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.tug.org/applications/hyperref/} +} + +@MANUAL{Reckdahl_2006, + title = {Using Imported Graphics in LaTeX and pdfLaTeX}, + author = {Keith Reckdahl}, + year = {2006}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ctan.org/tex-archive/info/epslatex/english/} +} + +@BOOK{Robbins_2006, + title = {Web Design in a Nutshell, 3rd Edition}, + publisher = {O'Reilly}, + year = {2006}, + author = {Jennifer Niederst Robbins}, + owner = {Alpha}, + review = {great}, + timestamp = {2008.02.19} +} + +@BOOK{Robinson_2003, + title = {An Introduction to Abstract Algebra}, + publisher = {Walter De Gruyter}, + year = {2003}, + author = {Derek J.S. Robinson}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.07.28} +} + +@MANUAL{Rokicki_2005, + title = {Dvips: A DVI-to-PostScript Translator}, + author = {Tomas Rokicki}, + year = {2005}, + owner = {Alpha}, + timestamp = {2008.05.12}, + url = {http://tug.org/texinfohtml/dvips.html} +} + +@BOOK{Ross_2000, + title = {Introduction to Probalility Models}, + publisher = {Harcort}, + year = {2000}, + author = {Ross, Sheldon M.}, + edition = {7th Edition}, + review = {good} +} + +@BOOK{Rowling_2005, + title = {Harry Potter and the Half-Blood Prince}, + publisher = {Bloomsbury}, + year = {2005}, + author = {J. K. Rowling}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Rowling_2003, + title = {Harry Potter and the Order of the Phoenix}, + publisher = {Bloomsbury}, + year = {2003}, + author = {J. K. Rowling}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Rowling_2000, + title = {Harry Potter and the Goblet of Fire}, + publisher = {Bloomsbury}, + year = {2000}, + author = {J. K. Rowling}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Rowling_1999, + title = {Harry Potter and the Prisoner of Azkaban}, + publisher = {Bloomsbury}, + year = {1999}, + author = {J. K. Rowling}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Rowling_1998, + title = {Harry Potter and the Chamber of Secrets}, + publisher = {Bloomsbury}, + year = {1998}, + author = {J. K. Rowling}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Rowling_1997, + title = {Harry Potter and the Philosopher's Stone}, + publisher = {Bloomsbury}, + year = {1997}, + author = {J. K. Rowling}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Sardar_1999, + title = {Introducing Mathematics}, + publisher = {Icon}, + year = {1999}, + author = {Sardar, Ziauddin and Ravetz, Jerry and Loon, Borin Van}, + review = {great} +} + +@BOOK{Schulman_1992, + title = {Introduction to UNIX}, + publisher = {Que}, + year = {1992}, + author = {Schulman, Mark}, + review = {good} +} + +@BOOK{Sheldon_2000, + title = {The Sky is Falling}, + publisher = {HarperCollins}, + year = {2000}, + author = {Sidney Sheldon}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.07.05} +} + +@BOOK{Sidney_1997, + title = {The Best laid Plans}, + publisher = {Warner Books}, + year = {1997}, + author = {Sidney Sheldon}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Sidney_1992, + title = {The Stars Shine Down}, + publisher = {Warner Books}, + year = {1992}, + author = {Sidney Sheldon}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Sheldon_1985, + title = {If Tomorrow Comes}, + publisher = {Morrow}, + year = {1985}, + author = {Sidney Sheldon}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.07.02} +} + +@BOOK{Smith_1998, + title = {Introductory Mathematics: Algebra and Analysis}, + publisher = {Springer}, + year = {1998}, + author = {Geoff Smith}, + owner = {Alpha}, + review = {good, light}, + timestamp = {2007.07.13} +} + +@BOOK{Solow_1990, + title = {How to Read and Do Proofs}, + publisher = {Wiley}, + year = {1990}, + author = {Daniel Solow}, + edition = {2nd}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.07.25} +} + +@BOOK{Strang_2005, + title = {Linear Algebra and Its Applications, 4th Edition}, + publisher = {Brooks Cole}, + year = {2005}, + author = {Giblert Strang}, + owner = {Alpha}, + timestamp = {2008.06.09}, + url = {http://www.amazon.com/exec/obidos/tg/detail/-/0030105676/} +} + +@BOOK{Strang_2003, + title = {Introduction to Linear Algebra, 3rd Edition}, + publisher = {Wellesley Cambridge}, + year = {2003}, + author = {Giblert Strang}, + owner = {Alpha}, + review = {common}, + timestamp = {2008.06.09}, + url = {http://www.amazon.com/exec/obidos/tg/detail/-/0961408898/} +} + +@BOOK{Strunk_2005, + title = {Elements of Style Illustrated}, + publisher = {Penguin}, + year = {2005}, + author = {William Strunk and Elwyn B. White}, + owner = {Alpha}, + timestamp = {2008.06.10}, + url = {http://en.wikipedia.org/wiki/Elements_of_Style} +} + +@MANUAL{Tantau_2008, + title = {TikZ and PGF Manual}, + author = {Till Tantau}, + year = {2008}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://sourceforge.net/projects/pgf/} +} + +@MANUAL{Tantau_2007, + title = {User Guide to Beamer}, + author = {Till Tantau}, + year = {2007}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://latex-beamer.sourceforge.net/} +} + +@BOOK{Tolkien_ROK_1988, + title = {The Return of The King}, + publisher = {Houghton Mifflin}, + year = {1988}, + author = {J.R.R. Tolkien}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Tolkien_TT_1988, + title = {The Two Towers}, + publisher = {Houghton Mifflin}, + year = {1988}, + author = {J.R.R. Tolkien}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Tolkien_Hobbit_1976, + title = {The Hobbit}, + publisher = {Ballantine}, + year = {1976}, + author = {Tolkien, J.R.R.}, + review = {good} +} + +@BOOK{Tolkien_FOR_1988, + title = {The Fellowship of the Ring}, + publisher = {Houghton Mifflin}, + year = {1988}, + author = {J. R. R. Tolkien}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.05.16} +} + +@BOOK{Tuthill_1990, + title = {Knowledge Engineering: Concepts and Practices for Knowledge-Based + Systems}, + publisher = {Tab Professional \& Reference}, + year = {1990}, + author = {Tuthill, G. Steven} +} + +@BOOK{Tyson_2004, + title = {Mutual Funds for Dummies}, + publisher = {Wiley}, + year = {2004}, + author = {Eric Tyson}, + owner = {Alpha}, + review = {common}, + timestamp = {2007.05.17} +} + +@BOOK{Tyson_2001, + title = {Home Buying for Dummies}, + publisher = {Wiley}, + year = {2001}, + author = {Eric Tyson}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.06.03} +} + +@BOOK{Valade_2004, + title = {PHP and MySQL for Dummies}, + publisher = {John Wiley \& Sons}, + year = {2004}, + author = {Valade, Janet}, + edition = {2nd Edtion} +} + +@BOOK{Wallis_2000, + title = {A Beginner's Guide to Graph Theory}, + publisher = {Birkhauser}, + year = {2000}, + author = {Wallis, W.D.}, + edition = {1st Edition} +} + +@BOOK{Wels_2001, + title = {Domain Names for Dummies}, + publisher = {Hungry Minds}, + year = {2001}, + author = {Susan Wels}, + owner = {Alpha}, + review = {good}, + timestamp = {2008.02.06} +} + +@MANUAL{Wicks_1999, + title = {Dvipdfm User's Manual}, + author = {Mark A. Wicks}, + year = {1999}, + owner = {Alpha}, + timestamp = {2008.05.12}, + url = {http://gaspra.kettering.edu/dvipdfm/} +} + +@BOOK{Winston_1984, + title = {Artificial Intelligence}, + publisher = {Addison-Wesley}, + year = {1984}, + author = {Winston, Patrick Henry}, + edition = {2nd Edittion}, + review = {good} +} + +@BOOK{Wolf_2005, + title = {A Tour through Mathematical Logic}, + publisher = {Mathematical Association of America}, + year = {2005}, + author = {Robert S. Wolf}, + owner = {Alpha}, + review = {good}, + timestamp = {2007.07.18} +} + +@BOOK{Yen_1998, + title = {Fuzzy Logic: Intelligence, Control, and Information}, + publisher = {Prentice Hall}, + year = {1998}, + author = {Yen, John and Langari, Reza} +} + +@MANUAL{Zandt_2007, + title = {PSTricks User's Guide}, + author = {Timothy van Zandt}, + year = {2007}, + owner = {Alpha}, + timestamp = {2008.04.01}, + url = {http://www.ctan.org/tex-archive/graphics/pstricks/base/doc/} +} + +@BOOK{Zhang_1999, + title = {State Space Search: Algorithms, Complexity, Extensions, and Applications}, + publisher = {Springer}, + year = {1999}, + author = {Zhang, Weixiong} +} + +@BOOK{Chicago_2003, + title = {Chicago Manual of Style, 15th Edition}, + publisher = {University of Chicago}, + year = {2003}, + editor = {UCP}, + owner = {Alpha}, + timestamp = {2008.06.10}, + url = {http://en.wikipedia.org/wiki/Chicago_Manual_of_Style} +} + diff --git a/Master/texmf-doc/doc/chinese/lnotes/src/tables.tex b/Master/texmf-doc/doc/chinese/lnotes/src/tables.tex new file mode 100644 index 00000000000..84e2a94c52e --- /dev/null +++ b/Master/texmf-doc/doc/chinese/lnotes/src/tables.tex @@ -0,0 +1,345 @@ +\chapter{表格} +\label{sec:tables} + +\section{简单表格} +\verb|tabular|~环境提供了最简单的表格功能。它用~\verb|\hline|~命令代表横线，\verb+|+~代表竖线，用~\verb|&|~来分栏。每个栏位的对齐方式可以用~l、c、r（左中右）来控制。 +\begin{code} +\begin{tabular}{|l|c|r|} + \hline + 操作系统 & 发行版 & 编辑器 \\ + \hline + Windows & MikTeX & TeXnicCenter \\ + \hline + Unix/Linux & TeX Live & Emacs \\ + \hline + Mac OS & MacTeX & TeXShop \\ + \hline +\end{tabular} +\end{code} + +\begin{tabular}{|l|c|r|} + \hline + 操作系统 & 发行版 & 编辑器 \\ + \hline + Windows & MikTeX & TeXnicCenter \\ + \hline + Unix/Linux & TeX Live & Emacs \\ + \hline + Mac OS & MacTeX & TeXShop \\ + \hline +\end{tabular} +\ \\ + +和针对插图的~\verb|figure|~环境类似，\LaTeX~还有另一个针对表格的浮动环境~\verb|table|。我们可以用它给上面的示例穿件马甲，顺便把表格简化为科技文献中常用的三线表。 + +\begin{code} +\begin{table}[htbp] +\caption{浮动环境中的三线表} +\label{tab:threesome} +\centering +\begin{tabular}{lll} + \hline + 操作系统 & 发行版 & 编辑器 \\ + \hline + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \hline +\end{tabular} +\end{table} +\end{code} + +\begin{table}[htbp] +\caption{浮动环境中的三线表} +\label{tab:threesome} +\centering +\begin{tabular}{lll} + \hline + 操作系统 & 发行版 & 编辑器 \\ + \hline + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \hline +\end{tabular} +\end{table} + +完美主义者可能觉得上面示例中的三条线一样粗不够美观，这时可以使用~\verb|booktabs|~宏包\citep{Fear_2005}的几个命令。 + +\begin{code} +\begin{table}[htbp] +\caption{浮动环境中的三线表} +\centering +\begin{tabular}{lll} + \toprule + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ +\end{code} + +\begin{code} + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} +\end{code} + +\begin{table}[htbp] +\caption{\texttt{booktabs}~宏包的效果} +\centering +\begin{tabular}{lll} + \toprule + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} + +\section{表格宽度} +有时我们需要控制某栏位宽度，可以将其对齐方式参数从~\verb|l、c、r|~改为~\verb|p{宽度}|~。 +\begin{code} +\begin{table}[htbp] +\caption{控制栏位宽度} +\centering +\begin{tabular}{p{100pt}p{100pt}p{100pt}} + \toprule + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} +\end{code} + +\begin{table}[htbp] +\caption{控制栏位宽度} +\centering +\begin{tabular}{p{100pt}p{100pt}p{100pt}} + \toprule + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} + +若想控制整个表格的宽度可以使用~\verb|tabularx|~宏包，\verb|X|~参数表示某栏可以折行。 + +\begin{code} +\begin{table}[htbp] +\caption{控制表格宽度} +\centering +\begin{tabularx}{350pt}{lXlX} + \toprule + 李白 & 平林漠漠烟如织，寒山一带伤心碧。暝色入高楼，有人楼上愁。玉梯空伫立，宿鸟归飞急。何处是归程，长亭更短亭。& + 泰戈尔 & 夏天的飞鸟，飞到我的窗前唱歌，又飞去了。秋天的黄叶，它们没有什么可唱，只叹息一声，飞落在那里。\\ + \bottomrule +\end{tabularx} +\end{table} +\end{code} + +\begin{table}[htbp] +\caption{控制表格宽度} +\centering +\begin{tabularx}{350pt}{lXlX} + \toprule + 李白 & 平林漠漠烟如织，寒山一带伤心碧。暝色入高楼，有人楼上愁。玉阶空伫立，宿鸟归飞急。何处是归程，长亭更短亭。& + 泰戈尔 & 夏天的飞鸟，飞到我的窗前唱歌，又飞去了。秋天的黄叶，它们没有什么可唱，只叹息一声，飞落在那里。\\ + \bottomrule +\end{tabularx} +\end{table} + +\section{跨行、跨列表格} +有时某栏需要横跨几列，我们可以使用~\verb|\multicolumn|~命令。它的前两个参数指定横跨列数和对齐方式。\verb|booktabs|~宏包的~\verb|\cmidrule|~命令用于横跨几列的横线。 +\begin{code} +\begin{table}[htbp] +\caption{跨栏表格} +\centering +\begin{tabular}{lll} + \toprule + & \multicolumn{2}{c}{常用工具} \\ + \cmidrule{2-3} + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} +\end{code} + +\begin{table}[htbp] +\caption{跨栏表格} +\centering +\begin{tabular}{lll} + \toprule + & \multicolumn{2}{c}{常用工具} \\ + \cmidrule{2-3} + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} + +跨行表格需要使用~\verb|multirow|~宏包，\verb|\multirow|~命令的前两个参数是竖跨的行数和宽度。 +\begin{code} +\usepackage{multirow} +... +\begin{table}[htbp] +\caption{跨行表格} +\centering +\begin{tabular}{lllc} +\end{code} +\begin{code} + \toprule + 操作系统 & 发行版 & 编辑器 & 用户体验\\ + \midrule + Windows & MikTeX & TeXnicCenter & + \multirow{3}{*}{\centering 爽} \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} +\end{code} + +\begin{table}[htbp] +\caption{跨行表格} +\centering +\begin{tabular}{lllc} + \toprule + 操作系统 & 发行版 & 编辑器 & 用户体验 \\ + \midrule + Windows & MikTeX & TeXnicCenter & + \multirow{3}{*}{\centering 爽} \\ + Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} + +\section{彩色表格} +彩色表格需要使用~\verb|colortbl|~宏包\citep{Carlisle_2001}提供的一些命令：\verb|\columncolor|、~\verb|\rowcolor|、\verb|\cellcolor|~等。 +\begin{code} +\usepackage{colortbl} +... +\begin{table}[htbp] +\caption{彩色表格} +\centering +\begin{tabular}{lll} + \toprule + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ +\end{code} +\begin{code} + \rowcolor[gray]{.8} Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} +\end{code} + +\begin{table}[htbp] +\caption{彩色表格} +\centering +\begin{tabular}{lll} + \toprule + 操作系统 & 发行版 & 编辑器 \\ + \midrule + Windows & MikTeX & TeXnicCenter \\ + \rowcolor[gray]{.8} Unix/Linux & TeX Live & Emacs \\ + Mac OS & MacTeX & TeXShop \\ + \bottomrule +\end{tabular} +\end{table} + +\section{长表格} +有时表格太长要跨页，可以使用~\verb|longtable|~宏包\citep{Carlisle_2004}。\verb|\endfirsthead|、~\verb|\endhead|~命令用来定义首页表头和通用表头，\verb|\endfoot|、\verb|\endlastfoot|~命令用来定义通用表尾和末页表尾。 +\begin{code} +\usepackage{longtable} +... +\begin{longtable}{ll} +\caption{长表格} \\ + \toprule + 作者 & 作品 \\ + \midrule + \endfirsthead + \midrule + 作者 & 作品 \\ + \midrule + \endhead + \midrule + \multicolumn{2}{r}{接下页\dots} \\ +\end{code} +\begin{code} + \endfoot + \bottomrule + \endlastfoot + 白居易 & 汉皇重色思倾国，\\ + & 御宇多年求不得。\\ + & 杨家有女初长成，\\ + & 养在深闺人未识。\\ + & 天生丽质难自弃，\\ + & 一朝选在君王侧。\\ + & 回眸一笑百媚生，\\ + & 六宫粉黛无颜色。\\ + & 春寒赐浴华清池，\\ + & 温泉水滑洗凝脂。\\ + & 侍儿扶起娇无力，\\ + & 始是新承恩泽时。\\ + & 云鬓花颜金步摇，\\ + & 芙蓉帐暖度春宵。\\ + & 春宵苦短日高起，\\ + & 从此君王不早朝。\\ +\end{longtable} +\end{code} + +\begin{longtable}{ll} +\caption{长表格} \\ + \toprule + 作者 & 作品 \\ + \midrule + \endfirsthead + \midrule + 作者 & 作品 \\ + \midrule + \endhead + \midrule + \multicolumn{2}{r}{接下页\dots} \\ + \endfoot + \bottomrule + \endlastfoot + 白居易 & 汉皇重色思倾国，\\ + & 御宇多年求不得。\\ + & 杨家有女初长成，\\ + & 养在深闺人未识。\\ + & 天生丽质难自弃，\\ + & 一朝选在君王侧。\\ + & 回眸一笑百媚生，\\ + & 六宫粉黛无颜色。\\ + & 春寒赐浴华清池，\\ + & 温泉水滑洗凝脂。\\ + & 侍儿扶起娇无力，\\ + & 始是新承恩泽时。\\ + & 云鬓花颜金步摇，\\ + & 芙蓉帐暖度春宵。\\ + & 春宵苦短日高起，\\ + & 从此君王不早朝。\\ +\end{longtable} + +\bibliographystyle{unsrtnat} +\bibliography{reading} +\newpage diff --git a/Master/tlpkg/bin/ctan2tds b/Master/tlpkg/bin/ctan2tds index 0c71c204900..5649366f37f 100755 --- a/Master/tlpkg/bin/ctan2tds +++ b/Master/tlpkg/bin/ctan2tds @@ -736,6 +736,7 @@ $standardfmt='latex'; 'latexmp', 'metapost', 'leawood', 'fonts', 'lfb', 'fonts', + 'lnotes', 'chinese', 'lshort-portuguese', 'portuguese', 'lshort-spanish', 'spanish', 'mathdots', 'generic', diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check index a407d7a0eb8..11640e84e2a 100755 --- a/Master/tlpkg/bin/tlpkg-ctan-check +++ b/Master/tlpkg/bin/tlpkg-ctan-check @@ -114,7 +114,7 @@ my @WorkingTLP = qw( layouts lcd lcg lcyw leading leaflet ledmac leftidx lettrine lewis lfb lgreek lh libertine limap linearA lineno linguex - lipsum listings listliketab lkproof lm + lipsum listings listliketab lkproof lm lnotes logpap lps lsc lshort-bulgarian lshort-chinese lshort-dutch lshort-english lshort-finnish lshort-french lshort-german lshort-italian diff --git a/Master/tlpkg/tlpsrc/collection-documentation-chinese.tlpsrc b/Master/tlpkg/tlpsrc/collection-documentation-chinese.tlpsrc index 9a7d0dee1aa..aa6d76df25e 100644 --- a/Master/tlpkg/tlpsrc/collection-documentation-chinese.tlpsrc +++ b/Master/tlpkg/tlpsrc/collection-documentation-chinese.tlpsrc @@ -2,5 +2,6 @@ name collection-documentation-chinese category Collection shortdesc Chinese documentation depend texlive-zh-cn +depend lnotes depend lshort-chinese depend collection-documentation-base diff --git a/Master/tlpkg/tlpsrc/lnotes.tlpsrc b/Master/tlpkg/tlpsrc/lnotes.tlpsrc new file mode 100644 index 00000000000..fa77b42675d --- /dev/null +++ b/Master/tlpkg/tlpsrc/lnotes.tlpsrc @@ -0,0 +1,2 @@ +name lnotes +category Documentation |
