Merge branch 'master' of https://whale.am28.uni-tuebingen.de/git/teaching/scientificComputing

programming/exercises/control_flow.tex

@@ -58,7 +58,7 @@ following pattern: ``variables\_datatypes\_\{lastname\}.m''
   \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 the indexing.
+    \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}
@@ -68,38 +68,161 @@ following pattern: ``variables\_datatypes\_\{lastname\}.m''
     \end{solution}
   \end{parts}
 
-  \question Create a vector \verb+x+ that contains 50 random numbers in the value range 0 - 10.
+  \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:
-    $\sigma=\sqrt{\frac{1}{n}\sum\limits_{i=0}^{n}(x_i-\overline{x})^2}$).
+    $\sigma=\sqrt{\frac{1}{n}\sum\limits_{i=0}^{n}(x_i-\overline{x})^2}$.
-    \part Search the MATLAB help for functions that do the calculations for you :-).
+    \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
+  \question Implement a \code{while} loop that iterates ...
   \begin{parts}
-    \part ... that iterates 100 times. Print out the current iteration number.
+    \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 smaller than 5.
+    (\code{x(index) = [];}) that are less than 5.
-    \part Delete all elements that are smaller than  5 and larger than 2.
+    \begin{solution}
-    \part Can you do the same without a loop?
+      \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
@@ -107,6 +230,22 @@ following pattern: ``variables\_datatypes\_\{lastname\}.m''
   [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}
@@ -114,9 +253,32 @@ following pattern: ``variables\_datatypes\_\{lastname\}.m''
     \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.
+    cut \verb+filename+ appropriately and display the individual parts.
-    \part Print out 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}