\documentclass[12pt,a4paper,pdftex]{exam}

\newcommand{\exercisetopic}{Control flow}
\newcommand{\exercisenum}{5}
\newcommand{\exercisedate}{24. November, 2020}

\input{../../exercisesheader}

\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de}

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\begin{document}

\input{../../exercisestitle}

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).

\begin{questions}
  \question Implement \code{for} loops in which the  \emph{running variable}:
  \begin{parts}
    \part ... assumes values from 0 to 10. Print (\code{disp}) the value of the running variable for each iteration step.
    \begin{solution}
      for i = 1:10 disp(i); end;
    \end{solution}
    \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 vectors:
  \begin{parts}
    \part Define a vector \code{x} that contains values ranging from 101 to 200 in steps of 1.
    \part Use a \code{for} loop to print each element of \code{x}. Use the running variable for indexing.
    \begin{solution}
      \code{for i = 1:length(x); disp(x(i)); end}
    \end{solution}
    \part Do the same without using the running variable directly (not 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 value 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 $.
    \begin{solution}
      \begin{verbatim}
      x = rand(50, 1) .* 10;
      total = 0;
      for i = 1:length(x)
          total = total + x(i);
      end
      average = total / length(x);
      disp(average)
      \end{verbatim}
    \end{solution}
    \part Use a loop to estimate the standard deviation:
    $\sigma=\sqrt{\frac{1}{n}\sum\limits_{i=0}^{n}(x_i-\overline{x})^2}$.
    \begin{solution}
      \begin{verbatim}
      x = rand(50, 1) .* 10;
      total = 0;
      for i = 1:length(x)
          total = total + x(i);
      end
      average = total / length(x);
      deviation = 0
      for i = 1:length(x)
          deviation = deviation + (x(i) - average)^2$;
      end
      standarddeviation = sqrt(deviation/length(x));
      \end{verbatim}
    \end{solution}
    \part Search the MATLAB help for functions that do these calculations for you :-).
    \begin{solution}
      \verb+sqrt+ and \verb+mean+ do the job for you.
    \end{solution}
  \end{parts}

  \question Implement a \code{while} loop that iterates ...
  \begin{parts}
    \part ... 100 times and displays the current iteration number.
    \begin{solution}
    \begin{verbatim}
      max_iterations = 100;
      iteration_count = 0;
      while iteration_count < max_iterations
          disp(iteration_count);
          iteration_count = iteration_count + 1;
      end
    \end{verbatim}
    \end{solution}
    \part ... iterates endlessly. You can interrupt the execution with the command \code{Strg + C}.
    \begin{solution}
    \begin{verbatim}
      while true
          disp('i am still running');
      end
    \end{verbatim}
    \end{solution}
  \end{parts}

  \question Use an endless \code{while} loop to individually display the elements of a vector that contains 10 elements. Stop the execution after all elements have been displayed on the command line.
  \begin{solution}
  \begin{verbatim}
    x = rand(10, 1);
    index = 0;
    while true
      disp(x(index);
      if index >= length(x)
        break;
      end
      index = index + 1;
    end
  \end{verbatim}
  \end{solution}

  \question Use the endless \verb+while+ loop to draw random numbers
  (\verb+randn+) until you hit one that is larger than 1.33.
  \begin{parts}
    \part Count the number of required iterations.
    \begin{solution}
      \begin{verbatim}
      count = 1;
      threshold = 1.33;  
      while true
        x = randn(1);
        if x > threshold
          break;
        end
        count = count + 1;
      end
      \end{verbatim}
    \end{solution}
    \part Use a \code{for} loop to run the previous test 1000 times. Store all counts and calculate the mean of it.
    \begin{solution}
      \begin{verbatim}
      trials = 1000;
      threshold = 1.33;
      counts = zeros(trials, 1);
      for i = 1:trials
        while true
          x = randn(1);
          counts(i) = counts(i) + 1;
          if x > threshold
            break
          end
        end
      end
      \end{verbatim}
    \end{solution}
    \part Create a plot that shows for each of the 1000 trials, how often you had to draw.
    \begin{solution}
    \begin{verbatim}
      plot(counts)
      hold on
      plot([0, trials], [mean(counts), mean(counts)])
      xlabel('trials')
      ylabel('number of samples')
    \end{verbatim}
    \end{solution}
    \part Play around with the threshold. What happens?
    \begin{solution}
      When lowering the threshold, the average number of counts is reduced, when increasing it, the counts increase!
    \end{solution}
  \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 less than 5.
    \begin{solution}
      \begin{verbatim}
      x = rand(10, 1) .* 10;
      for i = length(x):-1:1
        if x(i) < 5
          x(i) = [];
        end
      end
      \end{verbatim}
    \end{solution}
    \part Delete all elements that are less than 5 and greater than 2.
     \begin{solution}
      \begin{verbatim}
      x = rand(10, 1) .* 10;
      for i = length(x):-1:1
        if x(i) < 5 & x(i) < 2
          x(i) = [];
        end
      end
      \end{verbatim}
    \end{solution}
     \part Can you do the same without a loop?
     \begin{solution}
       \verb+x((x < 5) & (x > 2))) = [];+
     \end{solution}
  \end{parts}

  \question Test the random number generator! To do so count the
  number of elements that fall into 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?
  \begin{solution}
    We expect each catergory to contain the same amount of data points.
    \begin{verbatim}
    edges = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0];
    counts = zeros(length(edges)-1, 1);
    trials = 1000;
    for i = 1:trials
      x = rand(1);
      for j = 2:length(edges)   % using a nested for loop we can avoid a complicated if elseif construct
        if x > edges(j-1) & x < edges(j)
          counts(j-1) = counts(j-1) + 1;
        end
      end
    end
   \end{verbatim}
  \end{solution}

  \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} the 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.
    \begin{solution}
      \begin{verbatim}
      positions = [];
      for i = 1:length(filename)
        if filename(i) == '_'
          positions(end + 1) = i
        end
      end
      \end{verbatim}
    \end{solution}
    \part Use a second loop to iterate over the previously filled `position' vector and use this information to
    cut \verb+filename+ appropriately and display the individual parts.
    \begin{solution}
      Tricky thing here, we need to catch the corner cases!
    \begin{verbatim}
      for i = 1:length(positions)
        if i == 1
          disp(filename(1:positions(i)))
        elseif i == length(positions)
          disp(filename(positions(i-1):end))
        else
          disp(filename(positions(i-1):positions(i)))
        end
      end
    \end{verbatim}
    \end{solution}
  \end{parts}

\end{questions}

\end{document}