New design pattern chapter.
Next exercises for point processes.
This commit is contained in:
29
designpattern/lecture/Makefile
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29
designpattern/lecture/Makefile
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BASENAME=designpattern
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PYFILES=$(wildcard *.py)
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PYPDFFILES=$(PYFILES:.py=.pdf)
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all : pdf
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# script:
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pdf : $(BASENAME)-chapter.pdf
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$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex $(PYPDFFILES)
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pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
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$(PYPDFFILES) : %.pdf : %.py
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python $<
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clean :
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rm -f *~
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rm -f $(BASENAME).aux $(BASENAME).log
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rm -f $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out
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rm -f $(PYPDFFILES) $(GPTTEXFILES)
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cleanall : clean
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rm -f $(BASENAME)-chapter.pdf
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watchpdf :
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while true; do ! make -q pdf && make pdf; sleep 0.5; done
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225
designpattern/lecture/designpattern-chapter.tex
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225
designpattern/lecture/designpattern-chapter.tex
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\documentclass[12pt]{report}
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%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\title{\tr{Introduction to Scientific Computing}{Einf\"uhrung in die wissenschaftliche Datenverarbeitung}}
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\author{Jan Grewe \& Jan Benda\\Abteilung Neuroethologie\\[2ex]\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
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\date{WS 15/16}
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%%%% language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \newcommand{\tr}[2]{#1} % en
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% \usepackage[english]{babel}
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\newcommand{\tr}[2]{#2} % de
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\usepackage[german]{babel}
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%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{pslatex} % nice font for pdf file
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\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
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%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[left=25mm,right=25mm,top=20mm,bottom=30mm]{geometry}
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\setcounter{tocdepth}{1}
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%%%%% section style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[sf,bf,it,big,clearempty]{titlesec}
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\setcounter{secnumdepth}{1}
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%%%%% units %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro
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%%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{graphicx}
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\usepackage{xcolor}
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\pagecolor{white}
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\newcommand{\ruler}{\par\noindent\setlength{\unitlength}{1mm}\begin{picture}(0,6)%
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\put(0,4){\line(1,0){170}}%
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\multiput(0,2)(10,0){18}{\line(0,1){4}}%
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\multiput(0,3)(1,0){170}{\line(0,1){2}}%
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\put(0,0){\makebox(0,0){{\tiny 0}}}%
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\put(150,0){\makebox(0,0){{\tiny 15}}}%
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\put(160,0){\makebox(0,0){{\tiny 16}}}%
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\put(170,0){\makebox(0,0){{\tiny 17}}}%
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\end{picture}\par}
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% figures:
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\setlength{\fboxsep}{0pt}
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\newcommand{\texpicture}[1]{{\sffamily\footnotesize\input{#1.tex}}}
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%\newcommand{\texpicture}[1]{\fbox{\sffamily\footnotesize\input{#1.tex}}}
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%\newcommand{\texpicture}[1]{\setlength{\fboxsep}{2mm}\fbox{#1}}
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%\newcommand{\texpicture}[1]{}
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\newcommand{\figlabel}[1]{\textsf{\textbf{\large \uppercase{#1}}}}
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% maximum number of floats:
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\setcounter{topnumber}{2}
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\setcounter{bottomnumber}{0}
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\setcounter{totalnumber}{2}
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% float placement fractions:
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\renewcommand{\textfraction}{0.2}
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\renewcommand{\topfraction}{0.8}
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\renewcommand{\bottomfraction}{0.0}
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\renewcommand{\floatpagefraction}{0.5}
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% spacing for floats:
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\setlength{\floatsep}{12pt plus 2pt minus 2pt}
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\setlength{\textfloatsep}{20pt plus 4pt minus 2pt}
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\setlength{\intextsep}{12pt plus 2pt minus 2pt}
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% spacing for a floating page:
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\makeatletter
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\setlength{\@fptop}{0pt}
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\setlength{\@fpsep}{8pt plus 2.0fil}
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\setlength{\@fpbot}{0pt plus 1.0fil}
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\makeatother
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% rules for floats:
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\newcommand{\topfigrule}{\vspace*{10pt}{\hrule height0.4pt}\vspace*{-10.4pt}}
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\newcommand{\bottomfigrule}{\vspace*{-10.4pt}{\hrule height0.4pt}\vspace*{10pt}}
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% captions:
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\usepackage[format=plain,singlelinecheck=off,labelfont=bf,font={small,sf}]{caption}
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% put caption on separate float:
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\newcommand{\breakfloat}{\end{figure}\begin{figure}[t]}
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% references to panels of a figure within the caption:
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\newcommand{\figitem}[1]{\textsf{\bfseries\uppercase{#1}}}
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% references to figures:
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\newcommand{\panel}[1]{\textsf{\uppercase{#1}}}
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\newcommand{\fref}[1]{\textup{\ref{#1}}}
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\newcommand{\subfref}[2]{\textup{\ref{#1}}\,\panel{#2}}
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% references to figures in normal text:
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\newcommand{\fig}{Fig.}
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\newcommand{\Fig}{Figure}
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\newcommand{\figs}{Figs.}
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\newcommand{\Figs}{Figures}
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\newcommand{\figref}[1]{\fig~\fref{#1}}
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\newcommand{\Figref}[1]{\Fig~\fref{#1}}
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\newcommand{\figsref}[1]{\figs~\fref{#1}}
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\newcommand{\Figsref}[1]{\Figs~\fref{#1}}
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\newcommand{\subfigref}[2]{\fig~\subfref{#1}{#2}}
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\newcommand{\Subfigref}[2]{\Fig~\subfref{#1}{#2}}
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\newcommand{\subfigsref}[2]{\figs~\subfref{#1}{#2}}
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\newcommand{\Subfigsref}[2]{\Figs~\subfref{#1}{#2}}
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% references to figures within bracketed text:
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\newcommand{\figb}{Fig.}
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\newcommand{\figsb}{Figs.}
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\newcommand{\figrefb}[1]{\figb~\fref{#1}}
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\newcommand{\figsrefb}[1]{\figsb~\fref{#1}}
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\newcommand{\subfigrefb}[2]{\figb~\subfref{#1}{#2}}
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\newcommand{\subfigsrefb}[2]{\figsb~\subfref{#1}{#2}}
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% references to tables:
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\newcommand{\tref}[1]{\textup{\ref{#1}}}
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% references to tables in normal text:
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\newcommand{\tab}{Tab.}
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\newcommand{\Tab}{Table}
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\newcommand{\tabs}{Tabs.}
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\newcommand{\Tabs}{Tables}
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\newcommand{\tabref}[1]{\tab~\tref{#1}}
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\newcommand{\Tabref}[1]{\Tab~\tref{#1}}
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\newcommand{\tabsref}[1]{\tabs~\tref{#1}}
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\newcommand{\Tabsref}[1]{\Tabs~\tref{#1}}
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% references to tables within bracketed text:
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\newcommand{\tabb}{Tab.}
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\newcommand{\tabsb}{Tab.}
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\newcommand{\tabrefb}[1]{\tabb~\tref{#1}}
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\newcommand{\tabsrefb}[1]{\tabsb~\tref{#1}}
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%%%%% equation references %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\newcommand{\eqref}[1]{(\ref{#1})}
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\newcommand{\eqn}{\tr{Eq}{Gl}.}
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\newcommand{\Eqn}{\tr{Eq}{Gl}.}
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\newcommand{\eqns}{\tr{Eqs}{Gln}.}
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\newcommand{\Eqns}{\tr{Eqs}{Gln}.}
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\newcommand{\eqnref}[1]{\eqn~\eqref{#1}}
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\newcommand{\Eqnref}[1]{\Eqn~\eqref{#1}}
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\newcommand{\eqnsref}[1]{\eqns~\eqref{#1}}
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\newcommand{\Eqnsref}[1]{\Eqns~\eqref{#1}}
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%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{listings}
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\lstset{
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inputpath=../code,
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basicstyle=\ttfamily\footnotesize,
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numbers=left,
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showstringspaces=false,
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language=Matlab,
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commentstyle=\itshape\color{darkgray},
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keywordstyle=\color{blue},
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stringstyle=\color{green},
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backgroundcolor=\color{blue!10},
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breaklines=true,
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breakautoindent=true,
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columns=flexible,
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frame=single,
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caption={\protect\filename@parse{\lstname}\protect\filename@base},
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captionpos=t,
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xleftmargin=1em,
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xrightmargin=1em,
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aboveskip=10pt
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}
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%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{amsmath}
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\usepackage{bm}
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\usepackage{dsfont}
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\newcommand{\naZ}{\mathds{N}}
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\newcommand{\gaZ}{\mathds{Z}}
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\newcommand{\raZ}{\mathds{Q}}
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\newcommand{\reZ}{\mathds{R}}
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\newcommand{\reZp}{\mathds{R^+}}
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\newcommand{\reZpN}{\mathds{R^+_0}}
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\newcommand{\koZ}{\mathds{C}}
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%%%%% structure: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{ifthen}
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\newcommand{\code}[1]{\texttt{#1}}
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\newcommand{\source}[1]{
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\begin{flushright}
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\color{gray}\scriptsize \url{#1}
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\end{flushright}
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}
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\newenvironment{definition}[1][]{\medskip\noindent\textbf{Definition}\ifthenelse{\equal{#1}{}}{}{ #1}:\newline}%
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{\medskip}
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\newcounter{maxexercise}
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\setcounter{maxexercise}{9} % show listings up to exercise maxexercise
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\newcounter{theexercise}
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\setcounter{theexercise}{1}
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\newenvironment{exercise}[1][]{\medskip\noindent\textbf{\tr{Exercise}{\"Ubung}
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\arabic{theexercise}:}\newline \newcommand{\exercisesource}{#1}}%
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{\ifthenelse{\equal{\exercisesource}{}}{}{\ifthenelse{\value{theexercise}>\value{maxexercise}}{}{\medskip\lstinputlisting{\exercisesource}}}\medskip\stepcounter{theexercise}}
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\graphicspath{{figures/}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\include{designpattern}
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\end{document}
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166
designpattern/lecture/designpattern.tex
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designpattern/lecture/designpattern.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\chapter{Design Pattern}
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Beim Programmieren sind sich viel Codes in ihrer Grundstruktur sehr
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\"ahnlich. Viele Konstrukte kommen in den verschiedensten Kontexten
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immer wieder in \"ahnlicher Weise vor. In diesem Kapitel stellen wir
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einige dieser ``Design pattern'' zusammen.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Plotten einer mathematischen Funktion}
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Eine mathematische Funktion ordnet einem beliebigen $x$-Wert einen
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$y$-Wert zu. Um eine solche Funktion zeichnen zu k\"onnen, m\"ussen
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wir uns eine Wertetabelle aus vielen $x$-Werten und den
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dazugeh\"origen Funktionswerten $y=f(x)$ erstellen.
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Wir erstellen uns dazu einen Vektor mit geeigneten $x$-Werten, die von
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dem kleinsten bis zu dem gr\"o{\ss}ten $x$-Wert laufen, den wir
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plotten wollen. Die Schrittweite f\"ur die $x$-Werte w\"ahlen wir
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klein genug, um eine sch\"one glatte Kurve zu bekommen. F\"ur jeden
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Wert $x_i$ dieses Vektors berechnen wir den entsprechenden
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Funktionswert und erzeugen damit einen Vektor mit den $y$-Werten. Die
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Werte des $y$-Vektors k\"onnen dann gegen die Werte des $x$-Vektors
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geplottet werden.
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Folgende Programme berechnen und plotten die Funktion $f(x)=e^{-x^2}$:
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\begin{lstlisting}
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xmin = -1.0;
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xmax = 2.0;
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dx = 0.01; % Schrittweite
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x = xmin:dx:xmax; % Vektor mit x-Werten
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y = exp(-x.*x); % keine for Schleife! '.*' fuer elementweises multiplizieren
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plot(x, y);
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\end{lstlisting}
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\begin{lstlisting}
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x = -1:0.01:2; % Vektor mit x-Werten
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y = exp(-x.*x); % keine for Schleife! '.*' fuer elementweises multiplizieren
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plot(x, y);
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\end{lstlisting}
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\begin{lstlisting}
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x = -1:0.01:2; % Vektor mit x-Werten
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plot(x, exp(-x.*x));
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\end{lstlisting}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Skalieren und Verschieben nicht nur von Zufallszahlen}
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Zufallsgeneratoren geben oft nur Zufallszahlen mit festen Mittelwerten
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und Standardabweichungen (auch Skalierungen) zur\"uck. Multiplikation
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mit einem Faktor skaliert die Standardabweichung und Addition einer Zahl
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verschiebt den Mittelwert.
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\begin{lstlisting}
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% 100 random numbers draw from a Gaussian distribution with mean 0 and standard deviation 1.
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x = randn(100, 1);
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% 100 random numbers drawn from a Gaussian distribution with mean 4.8 and standard deviation 2.3.
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mu = 4.8;
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sigma = 2.3;
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y = randn(100, 1)*sigma + mu;
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\end{lstlisting}
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Das ist manchmal auch sinnvoll f\"ur \code{zeros} oder \code{ones}:
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\begin{lstlisting}
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x = -1:0.01:2; % Vektor mit x-Werten
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plot(x, exp(-x.*x));
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% Plotte f\"ur die gleichen x-Werte eine Linie mit y=0.8:
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plot(x, zeros(size(x))+0.8);
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% ... Linie mit y=0.5:
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plot(x, ones(size(x))*0.5);
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\end{lstlisting}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{for Schleifen \"uber Vektoren}
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Manchmal m\"ochte man doch mit einer for-Schleife \"uber einen Vektor iterieren:
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\begin{lstlisting}
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x = [2:3:20]; % irgendein Vektor
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for i=1:length(x)
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% Benutze den Wert des Vektors x an der Stelle des Indexes i:
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do_something( x(i) );
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end
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\end{lstlisting}
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Wenn in der Schleife das Ergebnis in einen Vektor gespeichert werden soll,
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sollten wir uns vor der Schleife schon einen Vektor f\"ur die Ergebnisse
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erstellen:
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\begin{lstlisting}
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x = [2:3:20]; % irgendein Vektor
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y = zeros(size(x)); % Platz fuer die Ergebnisse
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for i=1:length(x)
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% Schreibe den Rueckgabewert der Funktion get_something an die i-te
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% Stelle von y:
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y(i) = get_something( x(i) );
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end
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% jetzt koennen wir den Ergebnisvektor weiter bearbeiten:
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mean(y)
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\end{lstlisting}
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Die Berechnungen in der Schleife k\"onnen statt einer Zahl auch einen Vektor
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zur\"uckgeben. Wenn die L\"ange diese Vektors bekannt ist, dann kann vorher
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eine entsprechend gro{\ss}e Matrix angelegt werden:
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\begin{lstlisting}
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x = [2:3:20]; % irgendein Vektor
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y = zeros(length(x),10); % Platz fuer die Ergebnisse
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for i=1:length(x)
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% Schreibe den Rueckgabewert der Funktion get_something - jetzt ein
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% Vektor mit 10 Elementen - in die i-te
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% Zeile von y:
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y(i,:) = get_something( x(i) );
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end
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% jetzt koennen wir die Ergebnismatrix weiter bearbeiten:
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mean(y, 1)
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\end{lstlisting}
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Alternativ k\"onnen die in der Schleife erzeugten Vektoren zu einem
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einzigen, durchgehenden Vektor zusammengestellt werden:
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\begin{lstlisting}
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x = [2:3:20]; % irgendein Vektor
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y = []; % Leerer Vektor fuer die Ergebnisse
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for i=1:length(x)
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% Die Funktion get_something gibt uns einen Vektor zurueck:
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z = get_something( x(i) );
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% dessen Inhalt h\"angen wir an unseren Ergebnissvektor an:
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y = [y z(:)];
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end
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% jetzt koennen wir dem Ergebnisvektor weiter bearbeiten:
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mean(y)
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\end{lstlisting}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Normierung von Histogrammen}
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Meistens sollten Histogramme normiert werden, damit sie vergleichbar
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mit anderen Histogrammen oder mit theoretischen
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Wahrscheinlichkeitsverteilungen werden.
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Die \code{histogram} Funktion macht das mit den entsprechenden Parametern automatisch:
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\begin{lstlisting}
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x = randn(100, 1); % irgendwelche reellwertige Daten
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histogram(x, 'Normalization', 'pdf');
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\end{lstlisting}
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\begin{lstlisting}
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x = randi(6, 100, 1); % irgendwelche integer Daten
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histogram(x, 'Normalization', 'probability');
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\end{lstlisting}
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So geht es aber auch:
|
||||
\begin{lstlisting}
|
||||
x = randn(100, 1); % irgendwelche reellwertige Daten
|
||||
[h, b] = hist(x); % Histogram berechnen
|
||||
h = h/sum(h)/(b(2)-b(1)); % normieren zu einer Wahrscheinlichkeitsdichte
|
||||
bar(b, h); % und plotten.
|
||||
\end{lstlisting}
|
||||
|
||||
\begin{lstlisting}
|
||||
x = randi(6, 100, 1); % irgendwelche integer Daten
|
||||
[h, b] = hist(x); % Histogram berechnen
|
||||
h = h/sum(h); % normieren zu Wahrscheinlichkeiten
|
||||
bar(b, h); % und plotten.
|
||||
\end{lstlisting}
|
||||
Reference in New Issue
Block a user