100 lines
3.7 KiB
TeX
100 lines
3.7 KiB
TeX
\documentclass[12pt,a4paper,pdftex]{exam}
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\usepackage[german]{babel}
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\usepackage{natbib}
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\usepackage{graphicx}
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\usepackage[small]{caption}
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\usepackage{sidecap}
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\usepackage{pslatex}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\setlength{\marginparwidth}{2cm}
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\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
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%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
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\pagestyle{headandfoot} \header{{\bfseries\large Exercise 4
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}}{{\bfseries\large Boolean Expressions and logical indexing}}{{\bfseries\large 23. Oktober, 2018}}
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\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
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jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{}
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\setlength{\baselineskip}{15pt}
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\setlength{\parindent}{0.0cm}
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\setlength{\parskip}{0.3cm}
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\renewcommand{\baselinestretch}{1.15}
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\newcommand{\code}[1]{\texttt{#1}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\vspace*{-6.5ex}
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\begin{center}
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\textbf{\Large Introduction to scientific computing}\\[1ex]
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{\large Jan Grewe, Jan Benda}\\[-3ex]
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Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
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\end{center}
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The exercises are meant for self-monitoring and revision of the
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lecture. You should try to solve them on your own. Your solution
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should be submitted as a single script (m-file) in the Ilias
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system. Each task should be solved in its own ``cell''. Each cell must
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be executable on its own. The file should be named according to the
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following pattern: ``variables\_datatypes\_\{lastname\}.m''
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(e.g. variables\_datentypes\_mueller.m).
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\section{Boolean expressions}
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\begin{questions}
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\question Consider the following vectors \verb+x = [1 5 2 8 9 0 1]+ and
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\verb+y = [5 2 2 6 0 0 2]+. Execute the following commands and explain.
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\begin{parts}
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\part \verb+x > y+
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\part \verb+y < x+
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\part \verb+x == y+
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\part \verb+x ~= y+
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\part \verb+x & ~y+
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\part \verb+x | y+
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\end{parts}
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\question Find out what the functions \verb+bitand+ and \verb+bitor+ do.
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\begin{parts}
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\part Execute and explain: \verb+bitand(10, 8)+
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\part Execute and explain: \verb+bitor(10, 8)+
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\end{parts}
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\item Implement the following Boolean expressions. Test using randomly selected integer values for \verb+x+ and \verb+y+.
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\begin{parts}
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\part The result should be \verb+true+ if \verb+x+ greater than \verb+y+ and the sum of \verb+x+ and \verb+y+ is not less than 100.
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\part The result should be \verb+true+ if \verb+x+ and \verb+y+ are not equal zero or \verb+x+ and \verb+y+ are equal.
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\end{parts}
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\end{questions}
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\newpage
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\section{Logical Indexing}
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Boolean expressions can be used to select elements of vectors or
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matrices that match in certain criteria. This process is called
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\emph{logical indexing}.
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\begin{questions}
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\question Given are the vectors \verb+x = (1:10)+ and
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\verb+y = [3 1 5 6 8 2 9 4 7 0]+. Try to understand the results of
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the following commands and explain.
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\begin{parts}
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\part \verb+x < 5+
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\part \verb+x( x < 5) )+
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\part \verb+x( (y <= 2) )+
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\part \verb+x( (x > 2) | (y < 8) )+
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\part \verb+x( (x == 0) & (y == 0) )+
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\end{parts}
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\question Test the random number generator:
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\begin{parts}
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\part Create a $100 \times 100$ 2-D matrix that is filled with random numbers in the range 0 to 100. Replace the elements according to these rules: \verb+x < 33+ to 0,
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\verb+x >= 33 and x < 66+ to 1 and all \verb+x >= 66+ to 2.
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\part Count the number of elements in each class using Boolean expressions (\verb+sum+ can be used to count the matches).
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\end{parts}
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\end{questions}
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\end{document}
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