prgramming chapter work
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programming/lectures/control_structures.tex
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programming/lectures/control_structures.tex
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\section{Kontrollstrukturen}
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\begin{definition}[Kontrollstrukturen]
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In der Regel wird ein Programm Zeile f\"ur Zeile von oben nach unten
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ausgef\"uhrt. Manchmal muss der Kontrollfluss aber so gesteuert
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werden, dass bestimmte Teile des Programmcodes wiederholt oder nur
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unter bestimmten Bedingungen ausgef\"uhrt werden. Von grosser
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Bedeutung sind hier zwei Strukturen:
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\begin{enumerate}
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\item Schleigen.
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\item Bedingte Anweisungen und Verzweigungen.
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\end{enumerate}
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\end{definition}
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372
programming/lectures/programming-chapter.tex
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372
programming/lectures/programming-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 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{subcaption}
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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(10,0){\makebox(0,0){{\tiny 1}}}%
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\put(20,0){\makebox(0,0){{\tiny 2}}}%
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\put(30,0){\makebox(0,0){{\tiny 3}}}%
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\put(40,0){\makebox(0,0){{\tiny 4}}}%
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\put(50,0){\makebox(0,0){{\tiny 5}}}%
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\put(60,0){\makebox(0,0){{\tiny 6}}}%
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\put(70,0){\makebox(0,0){{\tiny 7}}}%
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\put(80,0){\makebox(0,0){{\tiny 8}}}%
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\put(90,0){\makebox(0,0){{\tiny 9}}}%
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\put(100,0){\makebox(0,0){{\tiny 10}}}%
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\put(110,0){\makebox(0,0){{\tiny 11}}}%
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\put(120,0){\makebox(0,0){{\tiny 12}}}%
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\put(130,0){\makebox(0,0){{\tiny 13}}}%
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\put(140,0){\makebox(0,0){{\tiny 14}}}%
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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{red!60!black},
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keywordstyle=\color{blue!50!black},
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stringstyle=\color{green!50!black},
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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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\chapter{Grundlagen der Programmierung in Matlab}
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\include{variables_datatypes}
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\include{vectors_matrices}
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\include{control_structures}
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\end{document}
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\end{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Statistics}
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What is "a statistic"? % dt. Sch\"atzfunktion
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\begin{definition}[statistic]
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A statistic (singular) is a single measure of some attribute of a
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sample (e.g., its arithmetic mean value). It is calculated by
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applying a function (statistical algorithm) to the values of the
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items of the sample, which are known together as a set of data.
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\source{http://en.wikipedia.org/wiki/Statistic}
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\end{definition}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Data types}
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\subsection{Nominal scale}
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\begin{itemize}
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\item Binary
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\begin{itemize}
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\item ``yes/no'',
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\item ``true/false'',
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\item ``success/failure'', etc.
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\end{itemize}
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\item Categorial
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\begin{itemize}
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\item cell type (``rod/cone/horizontal cell/bipolar cell/ganglion cell''),
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\item blood type (``A/B/AB/0''),
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\item parts of speech (``noun/veerb/preposition/article/...''),
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\item taxonomic groups (``Coleoptera/Lepidoptera/Diptera/Hymenoptera''), etc.
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\end{itemize}
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\item Each observation/measurement/sample is put into one category
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\item There is no reasonable order among the categories.\\
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example: [rods, cones] vs. [cones, rods]
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\item Statistics: mode, i.e. the most common item
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\end{itemize}
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\subsection{Ordinal scale}
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\begin{itemize}
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\item Like nominal scale, but with an order
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\item Examples: ranks, ratings
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\begin{itemize}
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\item ``bad/ok/good'',
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\item ``cold/warm/hot'',
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\item ``young/old'', etc.
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\end{itemize}
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\item {\bf But:} there is no reasonable measure of {\em distance}
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between the classes
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\item Statistics: mode, median
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\end{itemize}
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\subsection{Interval scale}
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\begin{itemize}
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\item Quantitative/metric values
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\item Reasonable measure of distance between values, but no absolute zero
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\item Examples:
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\begin{itemize}
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\item Temperature in $^\circ$C ($20^\circ$C is not twice as hot as $10^\circ$C)
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\item Direction measured in degrees from magnetic or true north
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\end{itemize}
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\item Statistics:
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\begin{itemize}
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\item Central tendency: mode, median, arithmetic mean
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\item Dispersion: range, standard deviation
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\end{itemize}
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\end{itemize}
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\subsection{Absolute/ratio scale}
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\begin{itemize}
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\item Like interval scale, but with absolute origin/zero
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\item Examples:
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\begin{itemize}
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\item Temperature in $^\circ$K
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\item Length, mass, duration, electric charge, ...
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\item Plane angle, etc.
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\item Count (e.g. number of spikes in response to a stimulus)
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\end{itemize}
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\item Statistics:
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\begin{itemize}
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\item Central tendency: mode, median, arithmetic, geometric, harmonic mean
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\item Dispersion: range, standard deviation
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\item Coefficient of variation (ratio standard deviation/mean)
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\item All other statistical measures
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\end{itemize}
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\end{itemize}
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\subsection{Data types}
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\begin{itemize}
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\item Data type selects
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\begin{itemize}
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\item statistics
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\item type of plots (bar graph versus x-y plot)
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\item correct tests
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\end{itemize}
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\item Scales exhibit increasing information content from nominal
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to absolute.\\
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Conversion ,,downwards'' is always possible
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\item For example: size measured in meter (ratio scale) $\rightarrow$
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categories ``small/medium/large'' (ordinal scale)
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\end{itemize}
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\subsection{Examples from neuroscience}
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\begin{itemize}
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\item {\bf absolute:}
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\begin{itemize}
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\item size of neuron/brain
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\item length of axon
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\item ion concentration
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\item membrane potential
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\item firing rate
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\end{itemize}
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\item {\bf interval:}
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\begin{itemize}
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\item edge orientation
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\end{itemize}
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\item {\bf ordinal:}
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\begin{itemize}
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\item stages of a disease
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\item ratings
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\end{itemize}
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\item {\bf nominal:}
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\begin{itemize}
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\item cell type
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\item odor
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\item states of an ion channel
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\end{itemize}
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\end{itemize}
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165
programming/lectures/variables_datatypes.tex
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programming/lectures/variables_datatypes.tex
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\section{Variablen und Datentypen}
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\subsection{Variablen}
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Eine Variable ist ein Zeiger auf eine Stelle im Speicher. Dieser
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Zeiger hat einen Namen, den Variablennamen, und einen Datentyp
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(Abbildung \ref{variablefig}).Im Speicher wird der Wert der Variablen
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bin\"ar gespeichert. Wird auf den Wert der Variable zugegriffen, wird
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dieses Bitmuster je nach Datentyp interpretiert. Das Beispiel in
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Abbildung \ref{variablefig} zeigt, dass das gleiche Bitmuster im einen
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Fall als 8-Bit Integer Datentyp zur Zahl 38 interpretiert wird und im
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anderen Fall als Character zum kaufm\"annischen ``und'' ausgewertet
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wird. In Matlab sind Datentypen nicht von sehr zentraler
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Bedeutung. Wir werden uns dennoch sp\"ater etwas genauer mit ihnen
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befassen.
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\begin{figure}
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\centering
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\begin{subfigure}{.5\textwidth}
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\includegraphics[width=0.8\textwidth]{images/variable}
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\label{variable:a}
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\end{subfigure}%
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\begin{subfigure}{.5\textwidth}
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\includegraphics[width=.8\textwidth]{images/variableB}
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\label{variable:b}
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\end{subfigure}
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\caption{\textbf{Variablen.} Variablen sind Zeiger auf eine Adresse
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im Speicher, die einen Namen und einen Datentypen beinhalten. Im
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Speicher ist der Wert der Variable bin\"ar gespeichert. Abh\"angig
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vom Datentyp wird dieses Bitmuster unterschiedlich
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interpretiert.}\label{variablefig}
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\end{figure}
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\subsection{Erzeugen von Variablen}
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In Matlab kann eine Variable auf der Kommandozeile, in einem Skript
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oder einer Funktion an beliebiger Stelle erzeugen. Das folgende
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Listing zeigt zwei M\"oglichkeiten:
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\footnotesize
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\begin{lstlisting}[label=varListing1, caption=Erzeugen von Variablen]
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>> y = []
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y =
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[]
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>>
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>> x = 38
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x =
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38
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\end{lstlisting}
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\normalsize
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|
||||
Die Zeile 1 kann etwa so gelesen werden:''Erzeuge eine Variable mit
|
||||
dem Namen y und weise ihr einen leeren Wert zu.'' Das
|
||||
Gleichheitszeichen ist der sogenannte
|
||||
\textit{Zuweisungsoperator}. Zeile 5 definiert eine Variable x, der
|
||||
nun der Zahlenwert 38 zugewiesen wird. Da Matlab, wenn nicht anders
|
||||
angegeben immer den ``double'' Datentypen benutzt, haben beide
|
||||
Variablen diesen Datentyp.
|
||||
|
||||
\footnotesize
|
||||
\begin{lstlisting}[label=varListing2, caption={Erfragen des Datentyps einer Variable, Listen aller definierten Variablen.}]
|
||||
>>disp(class(x))
|
||||
double
|
||||
>>
|
||||
>> who % oder whos um mehr Information zu bekommen
|
||||
\end{lstlisting}
|
||||
\normalsize
|
||||
|
||||
Bei der Namensgebung ist zu beachten, dass Matlab auf Gro{\ss}- und
|
||||
Kleinschreibung achtet und ein Variablennane mit einem alphabethischen
|
||||
Zeichen beginnen muss. Des Weiteren sind Umlaute, Sonder- und
|
||||
Leerzeichen in Variablennamen nicht erlaubt.
|
||||
|
||||
|
||||
\subsection{Arbeiten mit Variablen}
|
||||
|
||||
Nat\"urlich kann man mit den Variablen auch arbeiten, bzw
|
||||
rechnen. Matlab kennt alle normalen arithmetischen Operatoren wie
|
||||
\code{+, -, *. /}. Die Potenz wird \"uber das Dach Symbol \verb+^+
|
||||
dargestellt. Das folgende Listing zeigt, wie sie benutzt werden.
|
||||
|
||||
\footnotesize
|
||||
\begin{lstlisting}[label=varListing3, caption={Rechnen mit Variablen.}]
|
||||
>> x = 1;
|
||||
>> x + 10
|
||||
ans =
|
||||
11
|
||||
>>
|
||||
>> x % x wurde nicht veraendert
|
||||
ans =
|
||||
1
|
||||
>>
|
||||
>> y = 2;
|
||||
>>
|
||||
>> x + y
|
||||
ans =
|
||||
3
|
||||
>>
|
||||
>> z = x + y
|
||||
z =
|
||||
3
|
||||
>>
|
||||
>> z = z * 5;
|
||||
>> z
|
||||
z =
|
||||
15
|
||||
>>
|
||||
>> clear z
|
||||
\end{lstlisting}
|
||||
\normalsize
|
||||
|
||||
Beachtenswert ist z.B. in Zeilen 3 und 6, dass wir mit dem Inhalt
|
||||
einer Variablen rechnen k\"onnen, ohne dass dadurch ihr Wert
|
||||
ver\"andert w\"urde. Wenn der Wert einer Variablen ver\"andert werden
|
||||
soll, dann muss dieser der Variable expliyit zugewiesen werden (mit
|
||||
dem \code{=} Zuweisungsoperator, z.B. Zeilen 16, 20). Zeile 25 zeigt
|
||||
wie eine einzelne Variable gel\"oscht wird.
|
||||
|
||||
|
||||
\subsection{Datentypen}
|
||||
|
||||
Der Datentyp bestimmt, wie die im Speicher abgelegten Bitmuster
|
||||
interpretiert werden. Die Wichtigsten Datentpyen sind folgende:
|
||||
|
||||
\begin{itemize}
|
||||
\item \textit{integer} - Ganze Zahlen. Hier gibt es mehrere
|
||||
Unterarten, die wir in Matlab (meist) ignorieren k\"onnen.
|
||||
\item \textit{double} - Flie{\ss}kommazahlen.
|
||||
\item \textit{complex} - Komplexe Zahlen.
|
||||
\item \textit{logical} - Boolesche Werte, die als wahr
|
||||
(\textit{true}) oder falsch (\textit{false}) interpretiert werden.
|
||||
\item \textit{char} - ASCII Zeichen
|
||||
\end{itemize}
|
||||
|
||||
Unter den numerischen Datentypen gibt es verschiedene Arten mit
|
||||
unterschiedlichem Speicherbedarf und Wertebreich.
|
||||
|
||||
\begin{table}[]
|
||||
\centering
|
||||
\caption{Gel\"aufige Datentypen und ihr Wertebereich.}
|
||||
\label{dtypestab}
|
||||
\begin{tabular}{l|l|c|cl}
|
||||
Datentyp & Speicherbedarf & Wertebereich & Beispiel \\ \cline{1-4}
|
||||
double & 64 bit & $-2^{15} bis 2^{15}-1$ & Flie{\ss}kommazahlen.\\ \cline{1-4}
|
||||
int & 64 bit & $-2^{31} bis 2^{31}-1$ & Ganzzahlige Werte \\ \cline{1-4}
|
||||
int16 & 64 bit & $-2^{15} bis 2^{15}-1$ & Digitalisierte Spannungen. \\ \cline{1-4}
|
||||
uint8 & 64 bit & 0 bis 255 & Digitalisierte Imaging Daten. \\ \cline{1-4}
|
||||
& & &
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
|
||||
Matlab arbeitet meist mit dem ``double'' Datentyp wenn numerische
|
||||
Daten gespeichert werden. Dennoch lohnt es sich, sich ein wenig mit
|
||||
den DAtentypen auseinanderzusetzen. Ein Szenario, dass in der
|
||||
Neurobiologie nicht selten ist, ist, dass wir die elektrische
|
||||
Aktivit\"at einer Nervenzelle messen. Die gemessenen Spannungen werden
|
||||
mittels Messkarte digitalisiert und auf dem Rechner
|
||||
gespeichert. Typischerweise k\"onnen mit solchen Messkarten Spannungen
|
||||
im Bereich $\pm 10$\,V gemessen werden. Die Aufl\"osung der Wandler
|
||||
betr\"agt typischerweise 16 bit. Das heisst, dass der gesamte
|
||||
Spannungsbereich in $2^{16}$ Schritte aufgeteilt ist. Um Speicherplatz
|
||||
zu sparen ist es sinnvoll, die gemessenen Daten als ``int16'' Werte im
|
||||
Rechner abzulegen. Die Daten als ``echte'' Spannungen, also als
|
||||
Flie{\ss}kommawerte, abzulegen w\"urde den 4-fachen Speicherplatz
|
||||
ben\"otigen.
|
||||
39
programming/lectures/vectors_matrices.tex
Normal file
39
programming/lectures/vectors_matrices.tex
Normal file
@ -0,0 +1,39 @@
|
||||
\section{Vektoren und Matrizen}
|
||||
|
||||
\begin{definition}[Vektoren und Matrizen]
|
||||
Vektoren und Matrizen sind die wichtigsten Datenstrukturen in
|
||||
Matlab. In andern Programmiersprachen spricht man von ein-
|
||||
bzw. mehrdimensionalen Feldern. Felder sind Datenstrukturen, die
|
||||
mehrere Werte des geleichen Datentyps in einer Variablen
|
||||
vereinen. Da Matalb seinen Ursprung in der Verarbeitung von
|
||||
mathematischen Vektoren und Matrizen hat werden sie hier auch so
|
||||
genannt.\\
|
||||
|
||||
In Wahrheit existiert auch in Matlab kein Unterschied zwischen
|
||||
beiden Datenstrukturen. Im Hintergrund sind auch Vektoren auch
|
||||
2-diemsensionale Matrizen bei denen einen Dimension dir Gr\"o{\ss}e
|
||||
1 hat.
|
||||
\end{definition}
|
||||
|
||||
|
||||
\subsection{Vektoren}
|
||||
|
||||
Im Gegensatz zu den Variablen, die einzelene Werte beinhalten,
|
||||
Skalare, kann ein Vektor mehrere Werte des gleichen Datentyps
|
||||
beinhalten (Abbildung \ref{vectorfig} B).
|
||||
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=0.8\columnwidth]{images/scalarArray}
|
||||
\caption{\textbf{Skalare und Vektoren. A)} Eine skalare Variable kann
|
||||
genau einen Wert tragen. \textbf{B)} Ein Vektor kann mehrer
|
||||
Werte des gleichen Datentyps (z.B. ganzzahlige Integer Werte)
|
||||
beinhalten. Matlab kennt den Zeilen- (row-) und Spaltenvektor
|
||||
(columnvector).}\label{vectorfig}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Unterscheidung Zeilen- und Spaltenvektoren}
|
||||
|
||||
|
||||
\subsection{Matrizen}
|
||||
Reference in New Issue
Block a user