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\header{{\bfseries\large Exercise 4}}{{\bfseries\large Control Flow}}{{\bfseries\large 30. October, 2017}}
\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
  jan.grewe@uni-tuebingen.de}
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\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, revision of the lecture
topic. 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'' benannt werden
(e.g. variables\_datentypes\_mueller.m).

\begin{questions}
  \question Implement \code{for} loops in which the  \emph{running variable}:
  \begin{parts}
    \part ... assumes values from 0 to 10. Print the value of the running variable for each iteration step.
    \part ... assumes values from 10 to 0. Print out the value for each iteration.
    \part ... assumes values from 0 to 1 in steps of 0.1. Print out the value for each iteration.
  \end{parts}

  \question Indexing in vectros:
  \begin{parts}
    \part Define a vector \code{x} that contains values from 1:100.
    \part Use a \code{for} loop to print each element of \code{x}. Use the running variable for the indexing.
    \begin{solution}
      \code{for i = 1:length(x); disp(x(i)); end}
    \end{solution}
    \part Do the same without using the running variable for indexing.
    \begin{solution}
      \code{for i : x; disp(i); end;}
    \end{solution}
  \end{parts}

  \question Create a vector \verb+x+ that contains 50 random numbers in the range 0 - 10.
  \begin{parts}
    \part Use a loop to calculate the arithmetic mean. The mean is defined as:
    $\overline{x}=\frac{1}{n}\sum\limits_{i=0}^{n}x_i $.
    \part Use a loop to estimate the stadard deviation:
    $\sigma=\sqrt{\frac{1}{n}\sum\limits_{i=0}^{n}(x_i-\overline{x})^2}$).
    \part Search the MATLAB help for functions that do the calculations for you :-).
  \end{parts}

  \question Implement a\code{while} loop
  \begin{parts}
    \part ... that iterates  100 times. Print out the current iteration number.
    \part ... iterates endlessly. You can interrupt the execution with the command \code{Strg + C}.
  \end{parts}

  \question Use an endless \code{while} loop to individually print out the elements of a vector that contains 10 elements.

  \question Use the endless \verb+while+ loop to draw random numbers
  (\verb+randn+) until you it is larger than 1.33.
  \begin{parts}
    \part Count the number of required iterations.
    \part Use a \code{for} loop to run the previous test 1000 times. Remeber all counts and calculate the mean of it.
    \part Create a plot that schows for each of the 1000 trials, how often you had to draw.
    \part Play around with the threshold. What happens?
  \end{parts}

  \question Create a vector \verb+x+ that contains 10 random numbers in the range 0:10.
  \begin{parts}
    \part Use a \code{for} loop to delete all those elements 
    (\code{x(index) = [];}) that are smaller than 5.
    \part Delete all elements that are smaller than  5 and larger than 2.
    \part Can you do the same without a loop?
  \end{parts}

  \question Test the random number generator! To do so count the
  number of elements that fall in the classes defined by the edges
  [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]. Store the results in a vector. Use a
  loop to draw 1000 random numbers with \verb+rand()+ (see help). What
  would be the expectation? What is the result?

  \question String parsing: It is quite common to use the names of datasets to encode the conditions under which they were recorded. To find out the required information we have to \emph{parse} he name.
  \begin{parts}
    \part Create a variable
    \verb+filename = '2015-10-12_100Hz_1.25V.dat'+. Obviously, the
    underscore was used as a delimiter.
    \part Use a \verb+for+ loop to find the positions of the underscores and store these in a vector.
    \part Use a second loop to iterate over the previously filled `position' vector and use this information to
    cut filename appropriately.
    \part Print out the individual parts.
  \end{parts}

\end{questions}

\end{document}
