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\pagestyle{headandfoot} \header{{\bfseries\large Exercise 4
    }}{{\bfseries\large Boolean Expressions and logical indexing}}{{\bfseries\large 23. Oktober, 2018}}
\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
  jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{}

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\begin{document}

\vspace*{-6.5ex}
\begin{center}
  \textbf{\Large Introduction to scientific computing}\\[1ex]
  {\large Jan Grewe, Jan Benda}\\[-3ex]
  Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
\end{center}

The exercises are meant for self-monitoring and revision of the
lecture. You should try to solve them on your own. Your solution
should be submitted as a single script (m-file) in the Ilias
system. Each task should be solved in its own ``cell''. Each cell must
be executable on its own. The file should be named according to the
following pattern: ``variables\_datatypes\_\{lastname\}.m''
(e.g. variables\_datentypes\_mueller.m).

\section{Boolean expressions}

\begin{questions}
  \question Consider the following vectors \verb+x = [1 5 2 8 9 0 1]+ and
  \verb+y = [5 2 2 6 0 0 2]+. Execute the following commands and explain.
  \begin{parts}
    \part \verb+x > y+
    \part \verb+y < x+
    \part \verb+x == y+
    \part \verb+x ~= y+
    \part \verb+x & ~y+
    \part \verb+x | y+
  \end{parts}

  \question Find out what the functions \verb+bitand+ and \verb+bitor+ do.
  \begin{parts}
    \part Execute and explain: \verb+bitand(10, 8)+
    \part Execute and explain: \verb+bitor(10, 8)+
  \end{parts}
\item Implement the following Boolean expressions. Test using randomly selected integer values for \verb+x+ and \verb+y+.
  \begin{parts}
    \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.
    \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.
  \end{parts}
\end{questions}

\newpage
\section{Logical Indexing}

Boolean expressions can be used to select elements of vectors or
matrices that match in certain criteria. This process is called
\emph{logical indexing}.

\begin{questions}
  \question Given are the vectors \verb+x = (1:10)+ and
  \verb+y = [3 1 5 6 8 2 9 4 7 0]+. Try to understand the results of
  the following commands and explain.
  \begin{parts}
    \part \verb+x < 5+
    \part \verb+x( x < 5) )+
    \part \verb+x( (y <= 2) )+
    \part \verb+x( (x > 2) | (y < 8) )+
    \part \verb+x( (x == 0) & (y == 0) )+
  \end{parts}

  \question Test the random number generator:
  \begin{parts}
    \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,
    \verb+x >= 33 and x < 66+ to 1 and all \verb+x >= 66+ to 2.
    \part Count the number of elements in each class using Boolean expressions (\verb+sum+ can be used to count the matches).
  \end{parts}
\end{questions}

\end{document}
